Xizhi Wu

Assessing local influence in linear regression models with first-order autoregressive or heteroscedastic error structure

The local influence approach to the linear regression model with first-order autoregressive errors is developed and discussed. An advantage of this approach is that it avoids the inappropriate case-deletion diagnostic in the autoregressive model and it also allows simultaneous perturbations on all responses. Analogously, we obtain the local influence diagnostic on the weighted regression parameter estimate when the heteroscedastic error structure is considered.

Transformation-model diagnostics

We apply the local-influence method of Lawrance to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox regression model. We show that this method is the same as the local-influence method proposed by Cook. Furthermore, the difference in local-influence diagnostics between the case-weights perturbation and the constant-variances perturbation is examined and the relationship between the localinfluence diagnostic and the deletion diagnostic is studied. An example is presented to illustrate local-influence diagnostics.

Residual sum of squares and multiple potential, diagnostics by a second order local approach

Inspired by Cooks (1986) assessment of local influence by studying the curvature of a surface associated with the overall discrepancy measure, this paper assesses the local influence through the curvature of the perturbation-formed surface of residual sum of squares (RSS) and multiple potential respectively. Two examples demonstrate the effectiveness of this method on identification of influential points.

A perturbation scheme for nonlinear models

In nonlinear regression, we measure the interaction between observations in a random perturbation model for assessing the local influence. Our perturbation model perturbs all cases separately, and our measures combine all sides together. Approximations are given for these measures. An example of a nonlinear model shows the effectiveness of these measures when masking exists. This perturbation scheme has proved useful in applications beyond the scope of this paper.

A direct approach to a Bayesian sequential test for a normal mean

A simple, direct approach is presented to approximate the optimal stopping rules associated with the Bayesian sequential test for a normal mean.

Assessing local influence in PLS regression by the second order approach

Partial least squares (PLS) regression has received increasing attention in recent years. However, like other regression methods, PLS fitting could be substantially altered by one or a few influential points. This paper assesses the local influence by examining the second order derivatives on certain perturbed parameter surfaces related to statistics of interest such as criterion and the estimated coefficients . We also illustrate our idea via a numerical example, where the masking phenomenon is present.