Fuqi Chen

On extension of some identities for the bias and risk functions in elliptically contoured distributions

In this paper, we are interested in an estimation problem concerning the mean parameter of a random matrix whose distribution is elliptically contoured. We derive two general formulas for the bias and risk functions of a class of multidimensional shrinkage-type estimators. As a by product, we generalize some recent identities established in Gaussian sample cases for which the shrinking random part is a single Kronecker-product. Here, the variance-covariance matrix of the shrinking random part is the sum of two Kronecker-products.

Inference for a mean-reverting stochastic process with multiple change points

The use of an Ornstein-Uhlenbeck (OU) process is ubiquitous in business, economics and finance to capture various price processes and evolution of economic indicators exhibiting mean-reverting properties. When structural changes happen, economic dynamics drastically change and the times at which these occur are of particular interest to policy makers, investors and financial product providers. This paper addresses the change-point problem under a generalised OU model and investigates the associated statistical inference. We propose two estimation methods to locate multiple change points and show the asymptotic properties of the estimators. An informational approach is employed in detecting the change points, and the consistency of our methods is also theoretically demonstrated. Estimation is considered under the setting where both the number and location of change points are unknown. Three computing algorithms are further developed for implementation. The practical applicability of our methods is illustrated using simulated and observed financial market data.

On Estimation of the Change-points in Multivariate Regression Models with Structural Changes

ABSTRACT In this article, we consider the estimation of possibly multiple change points in multivariate regression models with structural changes. A salient feature of the methods is that the dependence structure of the error terms and the regressors can be as weak as that of -Mixingale arrays of size − 1/2. Further, we also provide some numerical simulations and a real data application to illustrate the efficiency of the proposed methods.

Equivariance and Generalized Inference in Two-Sample Location-Scale Families

We are interested in-typical Behrens-Fisher problem in general location-scale families. We present a method of constructing generalized pivotal quantity (GPQ) and generalized P value (GPV) for the difference between two location parameters. The suggested method is based on the minimum risk equivariant estimators (MREs), and thus, it is an extension of the methods based on maximum likelihood estimators and conditional inference, which have been, so far, applied to some specific distributions. The efficiency of the procedure is illustrated by Monte Carlo simulation studies. Finally, we apply the proposed method to two real datasets.