On A strongly consistent nonparametric density estimator for the deconvolution problem
Taylor, R. L.; Zhang, H. M.; Taylor, R. L.; Department of Statistics, University of Georgia; Zhang, H. M.; Department of Statistics, University of Georgia
Журнал:
Communications in Statistics - Theory and Methods
Дата:
1990
Аннотация:
The problem of nonparametric estimation of a probability density function is studied when the sample observations are contaminated with random noise. Previous authors have proposed estimators which use kernel density and deconvolution techniques. The appearance and properties of the previously proposed estimators are affected by constants M<sub>n</sub> and h<sub>n</sub> which the user may choose. However, the optimal choices of these constants depend on the sample size n, the noise distribution and the unknown distribution which is being estimated. Hence, in practice, M<sub>n</sub> and h<sub>n</sub> are optimally selected as functions of the data. In this paper it is shown that a class of the proposed estimators are uniformly, strongly consistent when M<sub>n</sub> and h<sub>n</sub> are allowed to be random variables. Even when M<sub>n</sub> and h<sub>n</sub> are constants, these results are new findings.
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