An exact, closed form, and easy to compute expression for the mean integrated squared error (MISE) of a kernel estimator of a normal mixture cumulative distribution function is derived for the class of arbitrary order Gaussian-based kernels. Comparisons are made with MISE of the empirical distribution function, the infeasible minimum MISE of kernel estimators, and the asymptotically optimal second order uniform kernel. The results afford straightforward extensions to other classes of kernel functions and distributions. The analysis also offers a guide on when to use higher order kernels in distribution function estimation.A simple plug-in method of simultaneously selecting the optimal bandwidth and kernel order is proposed based on a non-asymptotic approximation of the unknown distribution by a normal mixture. A simulation study shows that the method works well in finite samples, thus providing a viable alternative to existing bandwidth selection procedures.
This book examines how policies implemented by members of the Organisation for Economic Co-operation and Development (OECD) affect development and poverty in developing and transition economies.'The Global Development Network encourages policy-relevant research from developing countries. This volume assembles some results of this important work, focused here on the influence of policy on foreign trade, migration, and investment and of their influence in turn on growth and poverty in developing countries. Analysis of these influences on particular countries is an essential complement to the large-scale cross-country studies that have become so fashionable. Indeed, this detailed work casts doubt on the generality of some conventional wisdom, although not on the proposition that developing countries can gain significantly from engagement with the world economy. A most useful addition to the policy-relevant literature on developing countries.'
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due to the systematic use of this extra information. The particular interest here is the estimation of densities or distributions of (generalised) residuals in semi-parametric models defined by a finite number of moment restrictions. Such estimates are of great practical interest, being potentially of use for diagnostic purposes, including tests of parametric assumptions on an error distribution, goodness-of-fit tests or tests of overidentifying moment restrictions. The paper gives conditions for the consistency and describes the asymptotic mean squared error properties of the kernel density and distribution estimators proposed in the paper. A simulation study evaluates the small sample performance of these estimators. Supplements provide analytic examples to illustrate situations where kernel weighting provides a reduction in variance together with proofs of the results in the paper.where E[·] denotes expectation taken with respect to the true population probability law of z. The true parameter value β 0 is generally unknown, but can also be fully or partially known in particular applications.Models specified in the form of unconditional moment restrictions (1.1) convey partial information about the distribution F z of z and are ubiquitous in economics; see, e.g., the monographs Hall (2005) and Mátyás (1999). Many other commonly used models lead to estimators that can be reformulated as solutions to a set of moment restrictions. Clearly, models given by conditional moment restrictions imply (1.1). Traditionally, such models are estimated by the generalised method of moments (GMM). However, the performance of GMM estimators and associated test statistics is often poor in finite samples, which has lead to the development of a number of (information-theoretic) alternatives to GMM.This paper focuses on the class of generalised (G) empirical likelihood (EL) estimators, which has attractive large sample properties; see, e.
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