We consider a heteroscedastic nonparametric regression model with an autoregressive error process of finite known order p. The heteroscedasticity is incorporated using a scaling function defined at uniformly spaced design points on an interval [0,1]. We provide an innovative nonparametric estimator of the variance function and establish its consistency and asymptotic normality. We also propose ...

We examine homozygosity and G(st) for a subdivided population governed by the finite island model. Assuming an infinite allele model and strong mutation we show that the steady state distributions of G(st) and homozygosity have asymptotic expansions in the mutation rate. We use this observation to derive asymptotic expansions for various moments of homozygosity and to derive rigorous formulas f...

A standard approach to computing expectations with respect to a given target measure is to introduce an overdamped Langevin equation which is reversible with respect to the target distribution, and to approximate the expectation by a time-averaging estimator. As has been noted in recent papers [30, 37, 61, 72], introducing an appropriately chosen nonreversible component to the dynamics is benef...

We consider conditioned Galton–Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe subtrees isomorphic to any given tree, and joint asymptotic normality for several such subtree counts. The offspring distribution defining the random tree is ass...

Newey and Smith (2001) have recently shown that Empirical Likelihood (EL) exhibits desirable higher-order asymptotic properties, namely, that its O ¡ n−1 ¢ bias is particularly small and that biascorrected EL is higher-order efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that the asymptotic variance of EL in the presence of model misspe...

The author introduced previously a large family of one-unit contrast functions to be used in independent component analysis (ICA). In this paper, the family is analyzed mathematically in the case of a nite sample. Two aspects of the estimators obtained using such contrast functions are considered: asymptotic variance, and robustness against outliers. An expression for the contrast function that...

We are interested in modeling a zero mean heteroscedastic time series process with autoregressive error process of finite known order p. The model can be used for testing a martingale difference sequence hypothesis that is often adopted uncritically in financial time series against a fairly general alternative. When the argument is deterministic, we provide an innovative nonparametric estimator...

Econometric applications of kernel estimators are proliferating, suggesting the need for convenient variance estimates and conditions for asymptotic normality. This paper develops a general "delta method" variance estimator for functionals of kernel estimators. Also, regularity conditions for asymptotic normality are given, along with a guide to verifying them for particular estimators. The gen...

We consider probability measure estimation in a nonparametric model using a leastsquares approach under the Prohorov metric framework. We summarize the computational methods and their convergence results that were developed by our group over the past two decades. New results are presented on the bias and the variance due to the approximation and the pointwise asymptotic normality of the approxi...

In this paper, distributed maximum likelihood estimation (MLE) with quantized data is considered under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic parameters. The parameters may include different vector parameters corresponding to marginal pdfs and parameters that describe dependence of observations across sen...