Improved Density Estimation.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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Non-parametric estimation of a continuous probability density function almost always leads to a biased estimator. The purpose of the paper is to attack the problem of bias reduction. The problem is approached by using combinations of estimators of the form studied by Parzen 1962. Combining more than one of these estimators by the jackknife method of Schucany, Gray, and Owen 1971, new estimators are formed which generally have a substantial decrease in bias. The paper studies the properties of these new estimators in detail. Approximations are derived for their variance and bias. General classes of these new estimators are shown to be asymptotically unbiased and mean square consistent. Furthermore, the estimators are shown to be asymptotically better than the original estimators using mean square error as a criterion. Author
- Statistics and Probability