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Displaying results 1 to 25 of 26.

  1. A note on maximin and Bayesian D-optimal designs in weighted polynomial regression
    Author: Biedermann, Stefanie; Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,3
    Subjects: Regressionsanalyse; Schätztheorie; Theorie
    Scope: 14 S
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  2. Testing for symmetric error distribution in nonparametric regression models
    Author: Neumeyer, Natalie; Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,11
    Subjects: Regressionsanalyse; Nichtparametrisches Verfahren; Statistischer Test; Theorie
    Scope: 19 S
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  3. Maximin and Bayesian optimal designs for regression models
    Author: Dette, Holger; Haines, Linda M.; Imhof, Lorens A.
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,10
    Subjects: Regressionsanalyse; Schätztheorie; Theorie
    Scope: 15 S
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  4. Locally E-optimal designs for exponential regression models
    Author: Dette, Holger; Melas, Vjačeslav Borisovič; Pepelyshev, Andrey
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,37
    Subjects: Regressionsanalyse; Modellierung; Theorie
    Scope: 19 S
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  5. Finite sample performance of sequential designs for model identification
    Author: Dette, Holger; Kwiecien, Robert
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,32
    Subjects: Regressionsanalyse; Modellierung; Stichprobenerhebung; Theorie
    Scope: 21 S, graph. Darst
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  6. Bayesian and maximin optimal designs for heteroscedastic regression models
    Author: Dette, Holger; Haines, Linda M.; Imhof, Lorens A.
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,36
    Subjects: Regressionsanalyse; Modellierung; Theorie; Heteroskedastizität
    Scope: 23 S
    Notes:
  7. A power comparison between nonparametric regression tests
    Author: Zhang, Chunming; Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,22
    Subjects: Statistischer Test; Nichtparametrisches Verfahren; Regressionsanalyse; Theorie
    Scope: 13 S, graph. Darst
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  8. A note on testing symmetry of the error distribution in linear regression models
    Author: Neumeyer, Natalie; Dette, Holger; Nagel, Eva-Renate
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,25
    Subjects: Regressionsanalyse; Statistischer Test; Theorie
    Scope: 20 S
    Notes:
  9. A simple nonparametric estimator of a monotone regression function
    Author: Dette, Holger; Neumeyer, Natalie; Pilz, Kay F.
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

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    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,26
    Subjects: Regressionsanalyse; Nichtparametrisches Verfahren; Schätztheorie
    Scope: 25 S, graph. Darst
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  10. A note on nonparametric estimation of the effective dose in quantal bioassay
    Author: Dette, Holger; Neumeyer, Natalie; Pilz, Kay Frederik
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    For the common binary response model we propose a direct method for the nonparametric estimation of the effective dose level ED? (0 < ? < 1). The estimator is obtained by the composition of a nonparametric estimate of the quantile response curve and... more

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    For the common binary response model we propose a direct method for the nonparametric estimation of the effective dose level ED? (0 < ? < 1). The estimator is obtained by the composition of a nonparametric estimate of the quantile response curve and a classical density estimate. The new method yields a simple and reliable monotone estimate of the effective dose level curve ? ? ED? and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators or smoothing splines. Moreover it is computationally very efficient, because it does not require a numerical inversion of a monotonized estimate of the quantile dose response curve. We prove asymptotic normality of the new estimate and compare it with an available alternative estimate (based on a monotonized nonparametric estimate of the dose response curve and the calculation of the inverse function) by means of a simulation study.

     
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    hdl: 10419/49357
    Series: [Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2004,01]
    Scope: Online-Ressource (17 S.), graph. Darst.
  11. A note on testing the covariance matrix for large dimension
    Author: Birke, Melanie; Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    We consider the problem of testing hypotheses regarding the covariance matrix of multivariate normal data, if the sample size s and dimension n satisfy lim [n,s→∞] n/s = y. Recently, several tests have been proposed in the case, where the sample size... more

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    We consider the problem of testing hypotheses regarding the covariance matrix of multivariate normal data, if the sample size s and dimension n satisfy lim [n,s→∞] n/s = y. Recently, several tests have been proposed in the case, where the sample size and dimension are of the same order, that is y ∈ (0,∞). In this paper we consider the cases y = 0 and y = ∞. It is demonstrated that standard techniques are not applicable to deal with these cases. A new technique is introduced, which is of its own interest, and is used to derive the asymptotic distribution of the test statistics in the extreme cases y = 0 and y = ∞.

     
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    hdl: 10419/49373
    Series: [Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2004,02]
    Scope: Online-Ressource (9 S.)
  12. Finite sample performance of sequential designs for model identification
    Author: Dette, Holger; Kwiecien, Robert
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    Classical regression analysis is usually performed in two steps. In a first step an appropriate model is identified to describe the data generating process and in a second step statistical inference is performed in the identified model. An... more

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    Classical regression analysis is usually performed in two steps. In a first step an appropriate model is identified to describe the data generating process and in a second step statistical inference is performed in the identified model. An intuitively appealing approach to the design of experiment for these different purposes are sequential strategies, which use parts of the sample for model identification and adapt the design according to the outcome of the identification steps. In this paper we investigate the finite sample properties of two sequential design strategies, which were recently proposed in the literature. A detailed comparison of sequential designs for model discrimination in several regression models is given by means of a simulation study. Some non-sequential designs are also included in the study.

     
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    hdl: 10419/49366
    Series: [Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,32]
    Scope: Online-Ressource (21 S.), graph. Darst.
  13. Maximin optimal designs for the compartmental model
    Author: Biedermann, Stefanie; Dette, Holger; Pepelyshev, Andrey
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    For the compartmental model we determine optimal designs, which are robust against misspecifications of the unknown model parameters. We propose a maximin approach based on D-efficiencies and provide designs that are optimal with respect to the... more

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    For the compartmental model we determine optimal designs, which are robust against misspecifications of the unknown model parameters. We propose a maximin approach based on D-efficiencies and provide designs that are optimal with respect to the particular choice of various parameter regions.

     
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    hdl: 10419/49341
    Series: [Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,35]
    Scope: Online-Ressource (8 S.)
  14. Bayesian and maximin optimal designs for heteroscedastic regression models
    Author: Dette, Holger; Haines, Linda M.; Imhof, Lorens
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by... more

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    The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by Dette, Haines and Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian Φq-optimal designs. The approach is illustrated for two specific weighted polynomial models and also for a particular growth model.

     
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    Other identifier:
    hdl: 10419/49353
    Series: [Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,36]
    Scope: Online-Ressource (23 S.)
  15. Locally E-optimal designs for exponential regression models
    Author: Dette, Holger; Melas, Vjačeslav Borisovič; Pepelyshev, Andrey
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    In this paper we investigate locally E- and c-optimal designs for exponential regression models of the form _k i=1 ai exp(??ix). We establish a numerical method for the construction of efficient and locally optimal designs, which is based on two... more

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    In this paper we investigate locally E- and c-optimal designs for exponential regression models of the form _k i=1 ai exp(??ix). We establish a numerical method for the construction of efficient and locally optimal designs, which is based on two results. First we consider the limit ?i ? ? and show that the optimal designs converge weakly to the optimal designs in a heteroscedastic polynomial regression model. It is then demonstrated that in this model the optimal designs can be easily determined by standard numerical software. Secondly, it is proved that the support points and weights of the locally optimal designs in the exponential regression model are analytic functions of the nonlinear parameters ?1, . . . , ?k. This result is used for the numerical calculation of the locally E-optimal designs by means of a Taylor expansion for any vector (?1, . . . , ?k). It is also demonstrated that in the models under consideration E-optimal designs are usually more efficient for estimating individual parameters than D-optimal designs.

     
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    hdl: 10419/49363
    Series: [Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,37]
    Scope: Online-Ressource (19 S.)
  16. A power comparison between nonparametric regression tests
    Author: Zhang, Chunming; Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    In this paper, we consider three major types of nonparametric regression tests that are based on kernel and local polynomial smoothing techniques. Their asymptotic power comparisons are established systematically under the fixed and contiguous... more

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    In this paper, we consider three major types of nonparametric regression tests that are based on kernel and local polynomial smoothing techniques. Their asymptotic power comparisons are established systematically under the fixed and contiguous alternatives, and are also illustrated through non-asymptotic investigations and finite-sample simulation studies.

     
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    hdl: 10419/49367
    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,22
    Scope: Online-Ressource (13 S.), graph. Darst.
  17. A simple nonparametric estimator of a monotone regression function
    Author: Dette, Holger; Neumeyer, Natalie; Pilz, Kay Frederik
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    In this paper a new method for monotone estimation of a regression function is proposed. The estimator is obtained by the combination of a density and a regression estimate and is appealing to users of conventional smoothing methods as kernel... more

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    In this paper a new method for monotone estimation of a regression function is proposed. The estimator is obtained by the combination of a density and a regression estimate and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators or smoothing splines. The main idea of the new approach is to construct a density estimate from the estimated values ˆm(i/N) (i = 1, . . . ,N) of the regression function to use these “data” for the calculation of an estimate of the inverse of the regression function. The final estimate is then obtained by a numerical inversion. Compared to the conventially used techniques for monotone estimation the new method is computationally more efficient, because it does not require constrained optimization techniques for the calculation of the estimate. We prove asymptotic normality of the new estimate and compare the asymptotic properties with the unconstrained estimate. In particular it is shown that for kernel estimates or local polynomials the monotone estimate is first order asymptotically equivalent to the unconstrained estimate. We also illustrate the performance of the new procedure by means of a simulation study.

     
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    hdl: 10419/49358
    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,26
    Scope: Online-Ressource (25 S.), graph. Darst.
  18. Numerical construction of maximin optimal designs for binary response models
    Author: Biedermann, Stefanie; Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    For the binary response model, we determine optimal designs which are robust wit respect to the misspecifications of the unknown parameters. We propose a maximin approach and provide a numerical method to identify the best two point designs for the... more

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    For the binary response model, we determine optimal designs which are robust wit respect to the misspecifications of the unknown parameters. We propose a maximin approach and provide a numerical method to identify the best two point designs for the commonly applied link functions. This method is broadly applicable and can be extended to designs with a given number (>= 2) of support points and further link functions. The results are illustrated for the logistic and probit model, for which the maximin optimal designs are found explicitly.

     
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    hdl: 10419/49355
    Series: Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen ; 2003,29
    Scope: Online-Ressource (17 S.)
  19. A note on testing symmetry of the error distribution in linear regression models
    Author: Neumeyer, Natalie; Dette, Holger; Nagel, Eva-Renate
    Published: 2003
    Publisher:  [Univ., SFB 475], [Dortmund]

    In the classical linear regression model the problem of testing for symmetry of the error distribution is considered. The test statistic is a functional of the difference between the two empirical distribution functions of the estimated residuals and... more

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    In the classical linear regression model the problem of testing for symmetry of the error distribution is considered. The test statistic is a functional of the difference between the two empirical distribution functions of the estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is established. The covariance structure of this process depends heavily on the density of the error distribution, and for this reason the performance of a symmetric wild bootstrap procedure is discussed in asymptotic theory and by means of a simulation study.

     
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    hdl: 10419/49365
    Series: [Technical Report / Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund ; 2003,25]
    Scope: Online-Ressource ([20] S.)
  20. Design of experiments for microbiological models
    Author: Dette, Holger; Melas, Vjačeslav Borisovič; Strigul, Nikolay
    Published: 2003
    Publisher:  [Univ., SFB 475], [Dortmund]

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    hdl: 10419/49316
    Series: [Technical Report / Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund ; 2003,41]
    Scope: Online-Ressource (48 S.), graph. Darst.
  21. On robust and efficient designs for risk estimation in epidemiologic studies
    Author: Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    We consider the design problem for the estimation of several scalar measures suggested in the epidemiological literature for comparing the success rate in two samples. The designs considered so far in the literature are local in the sense that they... more

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    We consider the design problem for the estimation of several scalar measures suggested in the epidemiological literature for comparing the success rate in two samples. The designs considered so far in the literature are local in the sense that they depend on the unknown probabilities of success in the two groups and are not necessarily robust with respect to their misspecification. A maximin approach is proposed to obtain efficient and robust designs for the estimation of the relative risk, attributable risk and odds ratio, whenever a range for the success rates can be specified by the experimenter. It is demonstrated that the designs obtained by this method are usually more efficient than the uniform design, which allocates equal sample sizes to the two groups.

     
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    hdl: 10419/49368
    Series: [Technical Report / Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund ; 2003,08]
    Scope: Online-Ressource (13 S.), graph. Darst.
  22. A note on the maximization of matrix valued Hankel determinants with applications
    Author: Dette, Holger; Studden, W. J.
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    In this note we consider the problem of maximizing the determinant of moment matrices of matrix measures. The maximizing matrix measure can be characterized explicitly by having equal (matrix valued) weights at the zeros of classical (one... more

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    In this note we consider the problem of maximizing the determinant of moment matrices of matrix measures. The maximizing matrix measure can be characterized explicitly by having equal (matrix valued) weights at the zeros of classical (one dimensional) orthogonal polynomials. The results generalize classical work of Schoenberg (1959) to the case of matrix measures. As a statistical application we consider several optimal design problems in linear models, which generalize the classical weighing design problems.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/49340
    Series: [Technical Report / Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund ; 2003,09]
    Scope: Online-Ressource (13 S.)
  23. A note on maximin and Bayesian D-optimal designs in weighted polynomial regression
    Author: Biedermann, Stefanie; Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    We consider the problem of finding D-optimal designs for estimating the coefficients in a weighted polynominal regression model with a certain efficiency function depending on two unknown parameters, which models he heteroscedastic error structure.... more

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    We consider the problem of finding D-optimal designs for estimating the coefficients in a weighted polynominal regression model with a certain efficiency function depending on two unknown parameters, which models he heteroscedastic error structure. This problem is tackled by adopting a Bayesian and a maximin approach, and optimal designs supported on a minimal number of support points are determined explicitly.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/49349
    Series: [Technical Report / Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund ; 2003,03]
    Scope: Online-Ressource (14 S.)
  24. Maximin and Bayesian optimal designs for regression models
    Author: Dette, Holger; Haines, Linda M.; Imhof, Lorens
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    For many problems of statistical inference in regression modelling, the Fisher information matrix depends on certain nuisance parameters which are unknown and which enter the model nonlinearly. A common strategy to deal with this problem within the... more

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    For many problems of statistical inference in regression modelling, the Fisher information matrix depends on certain nuisance parameters which are unknown and which enter the model nonlinearly. A common strategy to deal with this problem within the context of design is to construct maximin optimal designs as those designs which maximize the minimum value of a real valued (standardized) function of the Fisher information matrix, where the minimum is taken over a specified range of the unknown parameters. The maximin criterion is not differentiable and the construction of the associated optimal designs is therefore difficult to achieve in practice. In the present paper the relationship between maximin optimal designs and a class of Bayesian optimal designs for which the associated criteria are differentiable is explored. In particular, a general methodology for determining maximin optimal designs is introduced based on the fact that in many cases these designs can be obtained as weak limits of appropriate Bayesian optimal designs.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/49339
    Series: [Technical Report / Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund ; 2003,10]
    Scope: Online-Ressource (15 S.)
  25. Testing for symmetric error distribution in nonparametric regression models
    Author: Neumeyer, Natalie; Dette, Holger
    Published: 2003
    Publisher:  Univ., SFB 475, Dortmund

    For the problem of testing symmetry of the error distribution in a nonparametric regression model we propose as a test statistic the difference between the two empirical distribution functions of estimated residuals and their counterparts with... more

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    For the problem of testing symmetry of the error distribution in a nonparametric regression model we propose as a test statistic the difference between the two empirical distribution functions of estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is shown. The covariance structure of this process depends heavily on the density of the error distribution, and for this reason the performance of a symmetric wild bootstrap procedure is discussed in asymptotic theory and by means of a simulation study. In contrast to the available procedures the new test is also applicable under heteroscedasticity.

     
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    Source: Union catalogues
    Language: English
    Media type: Book
    Format: Online
    Other identifier:
    hdl: 10419/49343
    Series: [Technical Report / Sonderforschungsbereich 475, Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund ; 2003,11]
    Scope: Online-Ressource ([19] S.)