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Extensions of semiparametric expectile regression
Extensions of semiparametric expectile regression
Expectile regression can be seen as an extension of available (mean) regression models as it describes more general properties of the response distribution. This thesis introduces to expectile regression and presents new extensions of existing semiparametric regression models. The dissertation consists of four central parts. First, the one-to-one-connection between expectiles, the cumulative distribution function (cdf) and quantiles is used to calculate the cdf and quantiles from a fine grid of expectiles. Quantiles-from-expectiles-estimates are introduced and compared with direct quantile estimates regarding e�ciency. Second, a method to estimate non-crossing expectile curves based on splines is developed. Also, the case of clustered or longitudinal observations is handled by introducing random individual components which leads to an extension of mixed models to mixed expectile models. Third, quantiles-from-expectiles-estimates in the framework of unequal probability sampling are proposed. All methods are implemented and available within the package expectreg via the open source software R. As fourth part, a description of the package expectreg is given at the end of this thesis.
Regression analysis, P-splines, Random effects, Non-crossing, Quantile regression, Unequal probability sampling
Schulze Waltrup, Linda
2015
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Schulze Waltrup, Linda (2015): Extensions of semiparametric expectile regression. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
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Abstract

Expectile regression can be seen as an extension of available (mean) regression models as it describes more general properties of the response distribution. This thesis introduces to expectile regression and presents new extensions of existing semiparametric regression models. The dissertation consists of four central parts. First, the one-to-one-connection between expectiles, the cumulative distribution function (cdf) and quantiles is used to calculate the cdf and quantiles from a fine grid of expectiles. Quantiles-from-expectiles-estimates are introduced and compared with direct quantile estimates regarding e�ciency. Second, a method to estimate non-crossing expectile curves based on splines is developed. Also, the case of clustered or longitudinal observations is handled by introducing random individual components which leads to an extension of mixed models to mixed expectile models. Third, quantiles-from-expectiles-estimates in the framework of unequal probability sampling are proposed. All methods are implemented and available within the package expectreg via the open source software R. As fourth part, a description of the package expectreg is given at the end of this thesis.