Local influence analysis for Poisson autoregression with an application to stock transaction data

In statistical diagnostics and sensitivity analysis, the local influence method plays an important role and has certain advantages over other methods in several situations. In this paper, we use this method to study time series of count data when employing a Poisson autoregressive model. We consider case‐weights, scale, data, and additive perturbation schemes to obtain their corresponding vectors and matrices of derivatives for the measures of slope and normal curvatures. Based on the curvature diagnostics, we take a stepwise local influence approach to deal with data with possible masking effects. Finally, our established results are illustrated to be effective by analyzing a stock transactions data set.     

Efficiency comparisons between two estimators based on matrix determinant Kantorovich-type inequalities

We first establish two matrix determinant Kantorovich-type inequalities. Then, based on these two and other inequalities, we introduce new efficiency criteria and present their upper bounds to make efficiency comparisons between the ordinary least squares estimator and the best linear unbiased estimator in the general linear model. We provide numerical examples to examine the upper bounds of some new and old efficiency criteria. Received: June 1999     

A Stein-type shrinkage estimator of the covariance matrix for portfolio selections

The covariance matrix plays a crucial role in portfolio optimization problems as the risk and correlation measure of asset returns. An improved estimation of the covariance matrix can enhance the performance of the portfolio. In this paper, based on the Cholesky decomposition of the covariance matrix, a Stein-type shrinkage strategy for portfolio weights is constructed under the mean-variance framework. Furthermore, according to the agent’s maximum expected utility value, a portfolio selection strategy is proposed. Finally, simulation experiments and an empirical study are used to test the feasibility of the proposed strategy. The numerical results show our portfolio strategy performs satisfactorily.