Search

In this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models (GPLMs) for longitudinal data or clustered data in general. We approximate the nonparametric function in the GPLM by a regression spline, and use bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers. We show that the regression spline approach avoids some of the intricacies associated with the profile-kernel method, and that robust estimation and inference can be carried out operationally as if a generalized linear model were used.

Some new diagnostic measures in discriminant analysis are proposed. They can be expressed in terms of the two fundamental influence statistics in discriminant analysis: d i 2 and ψ i . A theorem on the asymptotic distributions of the fundamental statistics is derived. Based on the theorem, the proposed measures can be shown to be asymptotically distributed as functions of independent chi-squared and standard normal random variables. Critical values and expected quantiles of the measures can then be constructed. Hence influential observations are detected using Q-Q plots and significance tests. Two measures have analogous forms in regression. The theorem is also useful for getting the asymptotic distributions of existing measures that are functions of d i 2 and ψ i . A comparison of the diagnostics in linear discriminant analysis, linear regression, and linear logistic regression (discriminant) analysis is made. Although discriminant coefficients can be determined under a regression model, regress...