A note on the asymptotic behaviour of empirical likelihood statistics

Abstract

This paper develops some theoretical results about the asymptotic behaviour of the empirical likelihood and the empirical profile likelihood statistics, which originate from fairly general estimating functions. The results accommodate, within a unified framework, various situations potentially occurring in a wide range of applications. For this reason, they are potentially useful in several contexts, such as, for example, in inference for dependent data. We provide examples showing that known findings in literature about the asymptotic behaviour of some empirical likelihood statistics in time series models can be derived as particular cases of our results.

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Correspondence to Gianfranco Adimari.

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Adimari, G., Guolo, A. A note on the asymptotic behaviour of empirical likelihood statistics. Stat Methods Appl 19, 463–476 (2010). https://doi.org/10.1007/s10260-010-0137-9

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Keywords

  • Autoregressive model
  • Estimating function
  • GARCH model
  • Pseudo-likelihood
  • Stationary process
  • Whittle’s estimator