Assessing local influence in restricted regression models

Abstract In this paper we propose a score distance in order to detect influential observations on the removal of the ordinary least-squares estimate outside the restricted parametric region in inequality constrained linear regression models. We apply the local influence method (Cook, J. Roy. Statist. Soc. Ser. B. 48, 1986) to assess the effect of small perturbations on this displacement. The results are extended to generalized linear models and two illustrative examples are given.

[1]  N. Laubscher,et al.  Normalizing the Noncentral $t$ and $F$ Distributions , 1960 .

[2]  J. Kalbfleisch.  Statistical Inference Under Order Restrictions , 1975 .

[3]  George G. Judge,et al.  Improved methods of inference in econometrics , 1986 .

[4]  Norman E. Breslow,et al.  Multiplicative Models and Cohort Analysis , 1983 .

[5]  H. Nyquist.  Restricted Estimation of Generalized Linear Models , 1991 .

[6]  A. Buse.  The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note , 1982 .

[7]  R. Cook,et al.  Assessing influence on predictions from generalized linear models , 1990 .

[8]  C. K. Liew,et al.  Inequality Constrained Least-Squares Estimation , 1976 .

[9]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[10]  Christopher J. Nachtsheim,et al.  Diagnostics for mixed-model analysis of variance , 1987 .

[11]  Ian Diamond,et al.  On the fitting of generalized linear models with nonnegativity parameter constraints , 1990 .

[12]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[13]  D. Pregibon.  Logistic Regression Diagnostics , 1981 .

[14]  Anthony N. Pettitt,et al.  Case-Weighted Measures of Influence for Proportional Hazards Regression , 1989 .

[15]  Fitting generalized linear models with linear inequality parameter constraints , 1983 .

[16]  L. Fahrmeir,et al.  Correction: Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in Generalized Linear Models , 1985 .

[17]  D. Pierce,et al.  Residuals in Generalized Linear Models , 1986 .

[18]  Clovis de Araujo Peres,et al.  Diagnostics for glms with linear inequality parameter constraints , 1988 .

[19]  C. Panne,et al.  Quadratic Programming as an Extension of Classical Quadratic Maximization , 1960 .

[20]  Anthony J. Lawrance,et al.  Regression Transformation Diagnostics Using Local Influence , 1988 .

[21]  S. Weisberg.  Plots, transformations, and regression , 1985 .

[22]  Norman E. Breslow,et al.  Statistical Methods in Cancer Research, Vol. II: The Design and Analysis of Cohort Studies. , 1990 .

[23]  N. Breslow,et al.  Statistical methods in cancer research. Volume II--The design and analysis of cohort studies. , 1987, IARC scientific publications.