UBC Theses and Dissertations
Relevance weighted smoothing and a new bootstrap method Hu, Feifang
This thesis addresses two quite different topics. First, we consider several relevance weighted smoothing methods for relevant sample information. This topic can be viewed as a generalization of nonparametric smoothing. Second, we propose a new bootstrap method which is based on estimating functions. A statistical problem usually begins with an unknown object of inferential of interest. About this unknown object, we may have three types of information (classified in this thesis): direct information, exact sample information and relevant sample information. Almost all classical statistical theory is about direct information and exact sample in formation. In many cases, relevant sample information is available and useful. But there is no systematic theory about relevant sample information. The problem of this thesis is to extract “the relevant information” contained in the relevant samples. The general methods have been developed under three different lines of approach ( parametric, nonparametric and semiparametric approach). In the parametric approach, we propose the idea of relevance weighted likelihood (REWL). For the nonparametric approach, we develop our theory based on the relevance weighted empirical distribution function (REWED). In the semiparametric approach, the relevance weighted estimating functions are used to extract “relevant information” from relevant samples. From asymptotic results, we find that these proposed methods have many desirable properties. We apply these proposed methods as well as some adjusted methods to generalized smoothing problems. Theoretical results as well as simulation results show our methods to be promising. We also present a new bootstrap method. It has computational and theoretical advan tages over conventional bootstrap methods when the data obtain from non-identically distributed observables. And it differs from conventional methods in that it resamples components of an estimating function rather than the data themselves.
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