Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series A, Pt. 1, pp. 56--67

KERNEL TYPE DENSITY ESTIMATES FOR POITIVE VALUED RANDOM VARIABLES

By

 ISHA BAGAI and B. L. S. PRAKASA RAO, Indian Statistical Institute

SUMMARY.  We propose kernel type estimators for the density function of non negative random variables, where the kernel function is a probability density function on $(0, \infty)$. Properties of these estimators are discussed. A kernel that minimizes the integrated mean square error is obtained. It is shown, however, that any reasonable kernel gives almost the same mean square error. On the basis of simulation studies the use of exponential kernels is recommended.

AMS (1991) subject classification.  Primary 62G05; secondary  62N05.

Key words and phrases. Density estimation, Kernel-type estimators, reliability, standard exponential kernels.

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