Asymptotic properties of non-parametric regression with Beta kernels

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Show simple item record Natarajan, Balasubramaniam 2017-12-15T22:08:10Z 2017-12-15T22:08:10Z 2018-05-01 en_US
dc.description.abstract Kernel based non-parametric regression is a popular statistical tool to identify the relationship between response and predictor variables when standard parametric regression models are not appropriate. The efficacy of kernel based methods depend both on the kernel choice and the smoothing parameter. With insufficient smoothing, the resulting regression estimate is too rough and with excessive smoothing, important features of the underlying relationship is lost. While the choice of the kernel has been shown to have less of an effect on the quality of regression estimate, it is important to choose kernels to best match the support set of the underlying predictor variables. In the past few decades, there have been multiple efforts to quantify the properties of asymmetric kernel density and regression estimators. Unlike classic symmetric kernel based estimators, asymmetric kernels do not suffer from boundary problems. For example, Beta kernel estimates are especially suitable for investigating the distribution structure of predictor variables with compact support. In this dissertation, two types of Beta kernel based non parametric regression estimators are proposed and analyzed. First, a Nadaraya-Watson type Beta kernel estimator is introduced within the regression setup followed by a local linear regression estimator based on Beta kernels. For both these regression estimators, a comprehensive analysis of its large sample properties is presented. Specifically, for the first time, the asymptotic normality and the uniform almost sure convergence results for the new estimators are established. Additionally, general guidelines for bandwidth selection is provided. The finite sample performance of the proposed estimator is evaluated via both a simulation study and a real data application. The results presented and validated in this dissertation help advance the understanding and use of Beta kernel based methods in other non-parametric regression applications. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Non-parametric regression en_US
dc.subject Beta kernel regression en_US
dc.subject Large sample properties
dc.subject Local linear regression with Beta kernels
dc.title Asymptotic properties of non-parametric regression with Beta kernels en_US
dc.type Dissertation en_US Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Statistics en_US
dc.description.advisor Weixing Song en_US 2018 en_US May en_US

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