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Asymptotic normality for deconvolution estimators of multivariate densities of stationary processes. (English) Zbl 0783.62065

The multivariate density deconvolution problem for mixing stationary processes is considered. Let \(\{X_ i\}^ \infty_{i=-\infty}\) be a stationary process having \(p\)-dimensional density function \(f(x;p)\), \(p\geq 1\). The observation process is \(Y_ i= X_ i+ \varepsilon_ i\), where \(\{\varepsilon_ i\}^ \infty_{i=-\infty}\) consists of i.i.d. random variables with known density, independent of \(\{X_ i\}^ \infty_{i=-\infty}\).
The author [IEEE Trans. Inf. Theory 37, No. 4, 1105-1115 (1991; Zbl 0732.60045)] has obtained results on the consistency of kernel-type multivariate density estimators \(\widehat f_ n(x;p)\) based on the observations \(\{Y_ i\}^ n_{i=1}\). In this paper the asymptotic normality for estimators \(\widehat f_ n(x;p)\) is established for \(\rho\)-mixing and strong mixing processes under mild conditions on the mixing coefficients. The cases where the tail of the noise characteristic function decays algebraically and exponentially are treated separately.

MSC:

62M09 Non-Markovian processes: estimation
62E20 Asymptotic distribution theory in statistics
62H12 Estimation in multivariate analysis

Citations:

Zbl 0732.60045
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