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Weak Convergence and Empirical Processes: With Applications to Statistics
This chapter discusses Convergence: Weak, Almost Uniform, and in Probability, which focuses on the part of Convergence of the Donsker Property which is concerned with Uniformity and Metrization.
Empirical Processes with Applications to Statistics
Here is the first book to summarize a broad cross-section of the large volume of literature available on one-dimensional empirical processes. Presented is a thorough treatment of the theory of
Information Bounds and Nonparametric Maximum Likelihood Estimation
I. Information Bounds.- 1 Models, scores, and tangent spaces.- 1.1 Introduction.- 1.2 Models P.- 1.3 Scores: Differentiability of the Model.- 1.4 Tangent Sets P0 and Tangent Spaces P.- 1.5 Score
Information and Asymptotic Efficiency in Parametric-Nonparametric Models
Asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems (for regular estimates) and
Two estimators of the mean of a counting process with panel count data
We study two estimators of the mean function of a counting process based on panel count data. The setting for panel count data is one in which n independent subjects, each with a counting process
We consider estimation in a particular semiparametric regression model for the mean of a counting process with \panel count" data. The basic model assumption is that the conditional mean function of
Likelihood Ratio Tests for Monotone Functions
We study the problem of testing for equality at a fixed point in the setting of nonparametric estimation of a monotone function. The likelihood ratio test for this hypothesis is derived in the
Exchangeably Weighted Bootstraps of the General Empirical Process
We consider an exchangeably weighted bootstrap of the general function-indexed empirical process. We find sufficient conditions on the bootstrap weights for the c~ntral limit theorem to hold for the
Estimation of a convex function: characterizations and asymptotic theory.
We study nonparametric estimation of convexregression and density functions by methods of least squares (in the regression and density cases) and maximum likelihood (in the density estimation