Interval estimation of the density of an asymptotically non-correlated process. (Russian) Zbl 0577.60040

Tursunov, G. T.

Teor. Veroyatn. Mat. Stat. 29, 114-122 (1983).

In this article a recurrent estimate \(f_ n\) for an unknown density f of a strongly stationary, asymptotically non-correlated process is considered. The sample size is supposed to be random. Let for every \(\epsilon >0\), \(\nu_{\epsilon}\) be a random variable with values in \({\mathbb{N}}\). Under suitable conditions it is shown that \(f_{\nu_{\epsilon}}\) is asymptotically normal. Constructed is a stopping time \(\nu_{\epsilon}\) for every \(\epsilon >0\), such that under some additional conditions the confidence interval of fixed size is asymptotically consistent and \(\nu_{\epsilon}\) asymptotically efficient.

Reviewer: C.Baldauf

MSC:

60G35	Signal detection and filtering (aspects of stochastic processes)
62M09	Non-Markovian processes: estimation
60F99	Limit theorems in probability theory

Keywords:

strongly stationary; asymptotically normal; stopping time; asymptotically consistent; asymptotically efficient