Smooth Estimates of Distribution Functions with Application in Environmental Studies
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Proceedings |
| Conference | Advanced topics on mathematical biology and ecology |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | cumulative distribution function; kernel smoothing; reflection method |
| Description | The most commonly used nonparametric estimate of a cumulative distribution function F is an empirical distribution function F_n. But F_n is a step function even in case that F is continuous. The present paper aims to provide a smooth estimate of F. Kernel methods seem to be adequate for this purpose. There exist several methods how to choose a bandwidth. We propose a method of bandwidth selection based on a suitable estimate of Mean Integrated Square Error. We also focus on an estimate of a cumulative distribution function in case that random variables X_1,...,X_n are nonnegative. The aforementioned methods are not reliable near the point x=0. In order to avoid this problem we propose a~reflection method. A simulation study is conducted to compare the performance of the different methods of bandwidth choice. Theoretical results are applied to the data concerning the content of toxic material in the fish population in Lake Ontario. |
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