Bernoulli

Sample splitting with Markov chains

Anton Schick

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Abstract

Sample splitting techniques play an important role in constructing estimates with prescribed influence functions in semi-parametric and nonparametric models when the observations are independent and identically distributed. This paper shows how a contiguity result can be used to modify these techniques to the case when the observations come from a stationary and ergodic Markov chain. As a consequence, sufficient conditions for the construction of efficient estimates in semi-parametric Markov chain models are obtained. The applicability of the resulting theory is demonstrated by constructing an estimate of the innovation variance in a nonparametric autoregression model, by constructing a weighted least-squares estimate with estimated weights in an autoregressive model with martingale innovations, and by constructing an efficient and adaptive estimate of the autoregression parameter in a heteroscedastic autoregressive model with symmetric errors.

Article information

Source
Bernoulli, Volume 7, Number 1 (2001), 33-61.

Dates
First available in Project Euclid: 29 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1080572338

Mathematical Reviews number (MathSciNet)
MR1811743

Zentralblatt MATH identifier
0997.62062

Keywords
contiguity efficient estimation ergodicity heteroscedastic autoregressive model nonparametric autoregressive model semi-parametric models stationary Markov chains V-uniform ergodicity weighted least-squares estimation

Citation

Schick, Anton. Sample splitting with Markov chains. Bernoulli 7 (2001), no. 1, 33--61. https://projecteuclid.org/euclid.bj/1080572338


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