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  1. M robustified additive nonparametric regression
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    Additive modelling has been widely used in nonparametric regression to circumvent the "curse of dimensionality", by reducing the problem of estimating a multivariate regression function to the estimation of its univariate components. Estimation of... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,69)
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    Additive modelling has been widely used in nonparametric regression to circumvent the "curse of dimensionality", by reducing the problem of estimating a multivariate regression function to the estimation of its univariate components. Estimation of these univariate functions, however, can suffer inaccuracy if the data set is contaminated with extreme observations. As detection and removal of outliers in high dimension is much more difficult than in one dimension, we propose an M type marginal integration estimator that automatically corrects the extreme influence of outliers. We establish the robustness and obtain the asymptotic distribution of the M estimator through the functional approach. As a consequence, our results are valid for ,ß-mixing samples under mild constraints. Monte Carlo study confirm our theoretical results. -- Frechet differential ; kernel estimator ; marginal integration ; M estimator ; outliers ; robustness

     

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    Sprache: Englisch
    Medientyp: Buch (Monographie)
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    hdl: 10419/65354
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,69
    Umfang: Online-Ressource (PDF-Datei: 23, [1] S., 245,47 KB), graph. Darst.
  2. Estimation and testing for varying coefficients in additive models with marginal integration
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,75)
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    We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation. For the test statistic, asymptotic normal theory is established. These theoretical results are derived under the fairly general conditions of absolute regularity (ß-mixing). Application of the test procedure to the West German real GNP data reveals that a partially linear varying coefficient model fits best the data dynamics, a fact that is also confirmed with residual diagnostics. -- Equivalent kernels ; German real GNP ; Local polynomial ; Marginal Integration ; Rate of convergence

     

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    Weitere Identifier:
    hdl: 10419/65358
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,75
    Umfang: Online-Ressource (PDF-Datei: 26 S., 1,14 MB), graph. Darst.
  3. R robustified additive nonparametric regression
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    Additive modelling is known to be useful for multivariate nonparametric regression as it reduces the complexity of problem to the level of univariate regression. This usefulness could be compromised if the data set was contaminated by outliers whose... mehr

    Staats- und Universitätsbibliothek Bremen
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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,78)
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    Additive modelling is known to be useful for multivariate nonparametric regression as it reduces the complexity of problem to the level of univariate regression. This usefulness could be compromised if the data set was contaminated by outliers whose detection and removal are particularly difficult to achieve in high dimension. We propose an estimation procedure for the additive component of the regression function , less sensitive to possible outliers in the sample. Our procedure is based on marginal integration of conditional R-estimators. In addition to univariate rate of convergence and asymptotic distribution, we also obtain robustness results for our estimator. All of our results are valid for a broad class of ß mixing processes. Monte Carlo findings confirm the theoretical results in finite sample. -- R-estimator ; Additive model ; Kernel estimator ; Marginal integration ; Robustness

     

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    Weitere Identifier:
    hdl: 10419/65288
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,78
    Umfang: Online-Ressource (PDF-Datei: 16, [1] S., 211,14 KB), graph. Darst.
  4. Exploring credit data
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    Credit scoring methods aim to assess the default risk of a potential borrower. This involves typically the calculation of a credit score and the estimation of the probability of default. One of the standard approaches is logistic discriminant... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,79)
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    Credit scoring methods aim to assess the default risk of a potential borrower. This involves typically the calculation of a credit score and the estimation of the probability of default. One of the standard approaches is logistic discriminant analysis, also referred to as logit model. This model maps explanatory variables for the default risk to a credit score using a linear function. Nonlinearity can be included by using polynomial terms or piecewise linear functions. This may give however only a limited reflection of a truly nonlinear relationship. Moreover, an additional modeling step may be necessary to determine the optimal polynomial order or the optimal interval classification. This paper presents semiparametric extensions of the logit model which directly allow for nonlinear relationships to be part of the explanatory variables. The technique is based on the theory generalized partial linear models. We illustrate the advantages of this approach using a consumer retail banking data set.

     

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    hdl: 10419/65306
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,79
    Umfang: Online-Ressource (PDF-Datei: 17 S., 515,08 KB), graph. Darst.
  5. Empirical likelihood-based dimension reduction inference for linear error-in-responses models with validation study
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptotic normality, the estimated... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,82)
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    In this paper, linear errors-in-response models are considered in the presence of validation data on the responses. A semiparametric dimension reduction technique is employed to define an estimator of β with asymptotic normality, the estimated empirical loglikelihoods and the adjusted empirical loglikelihoods for the vector of regression coefficients and linear combinations of the regression coefficients, respectively. The estimated empirical log-likelihoods are shown to be asymptotically distributed as weighted sums of independent Χ21 and the adjusted empirical loglikelihoods are proved to be asymptotically distributed as standard chi-squares, respectively. A simulation study is conducted to compare the proposed methods in terms of coverage accuracies and average lengths of the confidence intervals. -- confidence intervals ; error-in-response ; validation data

     

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    Weitere Identifier:
    hdl: 10419/65329
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,82
    Umfang: Online-Ressource (PDF-Datei: 26, [3] S., 206,17 KB)
  6. E-learning
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    Travel arrangements and flight ticket booking via inter-net is widely used nowadays and follow already certain standards. Although increasing activity for multimedia/web education components can be observed, we are far away from standards in this... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,84)
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    Travel arrangements and flight ticket booking via inter-net is widely used nowadays and follow already certain standards. Although increasing activity for multimedia/web education components can be observed, we are far away from standards in this important area. Statistics can possibly profit the most from e-learning since it requires a variety of skills including handling of quantitative data, graphical insights as well as mathematical ability. In this paper we take two positions - the student's view and the teacher's view - and discuss their relative coherence in order to propose standards for e-learning of statistics. The proposed standards are flexible with regard to content, multi-functionality, interactive capability and design. For this reason the main focus may be directed on quality of e-learning tools in order to meet both teacher's and student's requirements. This is especially true for statistics which is taught in various disciplines. We present our thoughts and exemplify them via the e-learning/e-teaching tools MM*Stat and e-stat. The struc-ture and the main characteristics of both multimedia tools will be explained. Then it will be described how such standards may be transferred to other cultures, languages or disciplines via the platform MD*Book.

     

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    Weitere Identifier:
    hdl: 10419/65350
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,84
    Umfang: Online-Ressource (PDF-Datei: [6] S., 1,02 MB), Ill.
  7. Semi-parametric estimation of generalized partially linear single-index models
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    One of the most difficult problems in applications of semiparametric generalized partially linear single-index model (GPLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,56)
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    One of the most difficult problems in applications of semiparametric generalized partially linear single-index model (GPLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-n consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations. In this paper, efficient, constructible and practicable estimators of GPLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. (1997): no root-n pilot estimator for the single index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE). -- Asymptotic distribution ; Generalized partially linear model ; Local linear smoother ; Optimal consistency rate ; Single-index model

     

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    Weitere Identifier:
    hdl: 10419/65301
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,56
    Umfang: Online-Ressource (PDF-Datei: 36 S., 676,41 KB), graph. Darst.
  8. Smoothed L-estimation of regression function
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    The Nadaraya-Watson estimator of regression is known to be highly sensitive to the presence of outliers in the sample. A possible way of robustication consists in using local L-estimates of regression. Whereas the local L-estimation is traditionally... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,88)
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    The Nadaraya-Watson estimator of regression is known to be highly sensitive to the presence of outliers in the sample. A possible way of robustication consists in using local L-estimates of regression. Whereas the local L-estimation is traditionally done using an empirical conditional distribution function, we propose to use instead a smoothed conditional distribution function. We show that this smoothed L-estimation approach provides computational as well as statistical finite sample improvements. The asymptotic distribution of the estimator is derived under mild β-mixing conditions. -- nonparametric regression ; L-estimation ; smoothed cumulative distribution function

     

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    Weitere Identifier:
    hdl: 10419/65287
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,88
    Umfang: Online-Ressource (PDF-Datei: 20 S., 135,04 KB)
  9. How precise are price distributions predicted by implied binomial trees?
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,1)
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    Export in Literaturverwaltung   RIS-Format
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    Sprache: Englisch
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    Weitere Identifier:
    hdl: 10419/65327
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,1
    Umfang: Online-Ressource (PDF-Datei: [26] S., 312,37 KB), graph. Darst.
  10. Semiparametric regression analysis under imputation for missing response data
    Erschienen: 2002
    Verlag:  Humboldt-Universität, Berlin

    We develop inference tools in a semiparametric regression model with missing response data. A semiparametric regression imputation estimator and an empirical likelihood based one for the mean of the response variable are defined. Both the estimators... mehr

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    ZBW - Leibniz-Informationszentrum Wirtschaft, Standort Kiel
    DS 20 (2002,6)
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    We develop inference tools in a semiparametric regression model with missing response data. A semiparametric regression imputation estimator and an empirical likelihood based one for the mean of the response variable are defined. Both the estimators are proved to be asymptotically normal, with asymptotic variances estimated with Jackknife method. The empirical likelihood method is developed. It is shown that when missing responses are imputed using the semiparametric regression method the empirical log-likelihood is asymptotically a scaled chi-square variable or a weighted sum of chi-square variables with unknown weights in the absence of auxiliary information or in the presence of auxiliary information. An adjusted empirical log-likelihood ratio, which is asymptotically standard chi-square, is obtained. Also, a bootstrap empirical log-likelihood ratio is also derived and its distribution is used to approximate that of the imputed empirical log-likelihood ratio. A simulation study is conducted to compare the imputed, adjusted and bootstrap empirical likelihood with the normal approximation based methods in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparison is also made by simulation between the proposed two estimators. The simulation indicates that the empirical likelihood methods developed perform competitively and the use of auxiliary information provides improved inference. -- Asymptotic normality ; Empirical likelihood ; Semiparametric imputation

     

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    Weitere Identifier:
    hdl: 10419/65355
    Schriftenreihe: Discussion papers of interdisciplinary research project 373 ; 2002,6
    Umfang: Online-Ressource (PDF-Datei: 23 S., 172,52 KB)