ABSTRACT. A bivariate distribution with continuous margins can be uniquely decomposed via a copula and its marginal distributions. We consider the problem of estimating the copula function and adopt a nonparametric Bayesian approach. On the space of copula functions, we construct a finite dimensional approximation subspace which is parameterized by a doubly stochastic matrix. A major problem he...

Let be the density of a design variable and the regression function. Then , where . The Dirac Æ-function is used to define a generalized empirical function for whose expectation equals . This generalized empirical function exists only in the space of Schwartz distributions, so we introduce a local polynomial of order approximation to which provides estimators of the function and its derivatives...

In the context of ridge regression, the estimation of ridge (shrinkage) parameter plays an important role in analyzing data. Many efforts have been put to develop skills and methods of computing shrinkage estimators for different full-parametric ridge regression approaches, using eigenvalues. However, the estimation of shrinkage parameter is neglected for semiparametric regression models. The m...

X1, . . . , Xn iid ∼ N (θ, σ), with σ known. Our goal is to estimate θ under squared-error loss. For our first guess, pick the natural estimator X. Note that it has constant risk σ 2 n , which suggests minimaxity because we know that Bayes estimators with constant risk are also minimax estimators. However, X is not Bayes for any prior, because under squared-error loss unbiased estimators are Ba...

The author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss. He discusses connections among the weighted likelihood, empirical Bayes and James–Stein estimators. Both simulated and real data sets are used for illu...