Statistical Computing
Raheleh Zamini
Abstract
In various statistical model, such as density estimation and estimation of regression curves or hazardrates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametricstatistics is to estimate a monotone density function f on a compact interval. A known estimator ...
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In various statistical model, such as density estimation and estimation of regression curves or hazardrates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametricstatistics is to estimate a monotone density function f on a compact interval. A known estimator fordensity function of f under the restriction that f is decreasing, is Grenander estimator, where is the leftderivative of the least concave majorant of the empirical distribution function of the data. Many authorsworked on this estimator and obtained very useful properties from this estimator. Grenander estimatoris a step function and as a consequence it is not smooth. In this paper, we discuss the estimation of adecreasing density function by the kernel smoothing method. Many works have been done due to theimportance and applicability of Berry-Esseen bounds for the density estimator. In this paper, we studya Berry- Esseen type bound for a smoothed version of Grenander estimator.
