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October 2016 Estimation in nonlinear regression with Harris recurrent Markov chains
Degui Li, Dag Tjøstheim, Jiti Gao
Ann. Statist. 44(5): 1957-1987 (October 2016). DOI: 10.1214/15-AOS1379

Abstract

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory for the proposed estimators. Our results show that the convergence rates for the estimators rely not only on the properties of the nonlinear regression function, but also on the number of regenerations for the Harris recurrent Markov chain. Furthermore, we discuss the estimation of the parameter vector in a conditional volatility function, and apply our results to the nonlinear regression with $I(1)$ processes and derive an asymptotic distribution theory which is comparable to that obtained by Park and Phillips [Econometrica 69 (2001) 117–161]. Some numerical studies including simulation and empirical application are provided to examine the finite sample performance of the proposed approaches and results.

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Degui Li. Dag Tjøstheim. Jiti Gao. "Estimation in nonlinear regression with Harris recurrent Markov chains." Ann. Statist. 44 (5) 1957 - 1987, October 2016. https://doi.org/10.1214/15-AOS1379

Information

Received: 1 January 2014; Revised: 1 August 2015; Published: October 2016
First available in Project Euclid: 12 September 2016

zbMATH: 1349.62380
MathSciNet: MR3546440
Digital Object Identifier: 10.1214/15-AOS1379

Subjects:
Primary: 62F12
Secondary: 62M05

Keywords: $\beta$-null recurrent Markov chain , asymptotic distribution , asymptotically homogeneous function , Harris recurrence , integrable function , Least squares estimation , Nonlinear regression

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 5 • October 2016
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