This paper is concerned with tests and con…dence intervals for parameters that are not necessarily identi…ed and are de…ned by moment inequalities. In the literature, di¤erent test statistics, critical value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test stati...

Loss functions play an important role in analyzing insurance portfolios. A fundamental issue in the study of loss functions involves the selection of probability models for claim frequencies. In this article, we propose a semiparametric approach based on the generalized method of moments (GMM) to solve the specification problems concerning claim frequency distributions. The GMM-based testing pr...

This dissertation consists of three chapters. Chapter 1 proposes a new method to solve the many moment problem: in Generalized Method of Moments (GMM), when the number of moment conditions is comparable to or larger than the sample size, the traditional methods lead to biased estimators. We propose a LASSO based selection procedure in order to choose the informative moments and then, using the ...

The GMM (generalized min-max) kernel was recently proposed [5] as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted to the (generalized) consistent weighted sampling (GCWS) to convert the GMM kernel to linear kernel. We call this approach as “GMM-GCWS”. In the machine learning l...

Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator (GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related ...

Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator (GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related ...

We consider nonlinear moment restriction semiparametric models where both the dimension of parameter vector and number restrictions are divergent with sample size an unknown smooth function is involved. propose estimation method based on sieve generalized moments (sieve-GMM). establish consistency asymptotic normality for estimated quantities when parameters increases modestly size. also case p...