Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models

• Published in: Journal of the American Statistical Association Vol. 100; no. 470; pp. 628 - 641
• Main Authors: Mancini, Loriano, Ronchetti, Elvezio, Trojani, Fabio
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2005; American Statistical Association; Taylor & Francis Ltd
• Subjects: Approximation; Estimators; Exact sciences and technology; Inference; Inference from stochastic processes; time series analysis; Influence function; M-estimator; Mathematics; Maximum likelihood estimation; Modeling; Monte Carlo simulation; Nonparametric inference; Normal distribution; Parametric inference; Parametric models; Probability and statistics; Robust estimation and testing; Scale modeling; Sciences and techniques of general use; Simulations; Statistical inference; Statistics; Theory and Methods; Time series; Time series model; Time series models; Unbiased estimators; Robust estimation and resting; Conditional distribution; Estimator robustness; M-estimator; Robust estimation; Optimal estimation; Numerical approximation; Scale parameter; Consistent estimator; Pseudolikelihood; Dynamic model; Stationary series; Laplace approximation; Monte Carlo method; Test robustness; Time series; Location parameter; Statistical estimation; Time series model; Heteroscedasticity; Statistical method; Influence function; Unbiased estimation; Non linear model; Maximum likelihood; M estimation; Parametric test; Autoregressive processes
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214504000001402

This article studies the local robustness of estimators and tests for the conditional location and scale parameters in a strictly stationary time series model. We first derive optimal bounded-influence estimators for such settings under a conditionally Gaussian reference model. Based on these results, we obtain optimal bounded-influence versions of the classical likelihood-based tests for parametric hypotheses. We propose a feasible and efficient algorithm for the computation of our robust estimators, which uses analytical Laplace approximations to estimate the auxiliary recentering vectors, ensuring Fisher consistency in robust estimation. This strongly reduces the computation time by avoiding the simulation of multidimensional integrals, a task that typically must be addressed in the robust estimation of nonlinear models for time series. In some Monte Carlo simulations of an AR(1)-ARCH(1) process, we show that our robust procedures maintain a very high efficiency under ideal model conditions and at the same time perform very satisfactorily under several forms of departure from conditional normality. In contrast, classical pseudo-maximum likelihood inference procedures are found to be highly inefficient under such local model misspecifications. These patterns are confirmed by an application to robust testing for autoregressive conditional heteroscedasticity.