This article develops an efficient method for estimating the discrete mixtures of normal family based on the continuous empirical characteristic function (CECF). An iterated estimation procedure based on the closed form objective distance function is proposed to improve the estimation...

Bandwidth selection in multivariate kernel density estimation has received considerable attention. In addition to classical methods of bandwidth selection, such as plug-in and cross-validation methods, Bayesian approaches have also been previously investigated. Bayesian estimation of adaptive...

It is shown that the integrated squared errors of wavelet projection estimators of a density f satisfy both the central limit theorem and the law of the iterated logarithm under the essentially minimal assumption f∈Lp for some p>2 and very mild conditions on the scaling function.

A central limit theorem for the weighted integrated squared error of kernel type estimators of the first two derivatives of a nonparametric regression function is proved by using results for martingale differences and U-statistics. The results focus on the setting of the Nadaraya-Watson...

We consider a family of proper random variables which converges to an improper random variable. The limit in distribution is found and applied to obtain a closed-form expression for the limiting power of the Cliff-Ord test for autocorrelation. The applications include the theory of...