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Asymptotics of Some Estimators and Sequential Residual Empiricals in Nonlinear Time Series
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Asymptotics of Some Estimators and Sequential Residual Empiricals in Nonlinear Time Series
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Journal Article
Asymptotics of Some Estimators and Sequential Residual Empiricals in Nonlinear Time Series
1996
Overview
This paper establishes the asymptotic uniform linearity of M- and R-scores in a family of nonlinear time series and regression models. It also gives an asymptotic expansion of the standardized sequential residual empirical process in these models. These results are, in turn, used to obtain the asymptotic normality of certain classes of M-, R- and minimum distance estimators of the underlying parameters. The classes of estimators considered include analogs of Hodges-Lehmann, Huber and LAD (least absolute deviation) estimators. Some applications to the change point and testing of the goodness-of-fit problems in threshold and amplitude-dependent exponential autoregression models are also given. The paper thus offers a unified functional approach to some aspects of robust inference for a large class of nonlinear time series models.
Publisher
Institute of Mathematical Statistics,The Institute of Mathematical Statistics
Subject
/ 62M10
/ Asymptotic uniform linearity
/ asymptotically distribution free
/ Exact sciences and technology
/ Inference from stochastic processes; time series analysis
/ Integers
/ Maximum likelihood estimation
/ Probability theory and stochastic processes
/ Sciences and techniques of general use
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