A Comparative Study of Higher Order Kernel Estimation and Kernel Density Derivative Estimation of the Gaussian Kernel Estimator with Data Application

IF 1.1 Q3 STATISTICS & PROBABILITY
Siloko Israel Uzuazor, Ojobor Sunday Amaju
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引用次数: 1

Abstract

Higher-order kernel estimation and kernel density derivative estimation are techniques for reducing the asymptotic mean integrated squared error in nonparametric kernel density estimation. A reduction in the error criterion is an indication of better performance. The estimation of kernel function relies greatly on bandwidth and the identified reduction methods in the literature are bandwidths reliant for their implementation. This study examines the performance of higher order kernel estimation and kernel density derivatives estimation techniques with reference to the Gaussian kernel estimator owing to its wide applicability in real-life-settings. The explicit expressions for the bandwidth selectors of the two techniques in relation to the Gaussian kernel and the bandwidths were accurately obtained. Empirical results using two data sets obviously revealed that kernel density derivative estimation outperformed the higher order kernel estimation excellently well with the asymptotic mean integrated squared error as the criterion function.
高斯核估计的高阶核估计与核密度导数估计的比较研究及数据应用
高阶核估计和核密度导数估计是减少非参数核密度估计中渐近均积分平方误差的技术。误差标准的降低是更好的性能的指示。核函数的估计在很大程度上依赖于带宽,并且文献中确定的归约方法的实现依赖于带宽。由于高阶核估计和核密度导数估计技术在现实生活中具有广泛的适用性,本研究参考高斯核估计来检验其性能。精确地得到了这两种技术的带宽选择器与高斯核和带宽之间的显式表达式。使用两个数据集的经验结果明显表明,以渐近均方误差为准则函数的核密度导数估计优于高阶核估计。
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来源期刊
CiteScore
3.30
自引率
26.70%
发文量
53
期刊介绍: Pakistan Journal of Statistics and Operation Research. PJSOR is a peer-reviewed journal, published four times a year. PJSOR publishes refereed research articles and studies that describe the latest research and developments in the area of statistics, operation research and actuarial statistics.
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