Introduction. The density of the ratio of two random variables with joint bivariate Gaussian density has been derived by several authors and it is important in many applications (see e.g. [8, 13, 14, 15]). In the sequel it is proved that, when the two variables have the same variance, this density satisfies a parabolic partial differential equation whose coefficients depend on both the independ...

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the ...

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of ke...

* To whom correspondence should be addressed. E-mail: [email protected], Tel: +886-2-33664888 ext. 431, Fax: +886-2-23688675. Abstract Though prediction of protein secondary structures has been an active research issue in bioinformatics for quite a few years and many approaches have been proposed, a new challenge emerges as the sizes of contemporary protein structure databases such as the...

We consider kernel-type methods for estimation of a density on [0, 1] which eschew explicit boundary correction. Our starting point is the successful implementation of beta kernel density estimators of Chen (1999). We propose and investigate two alternatives. For the first, we reverse the roles of estimation point x and datapoint Xi in each summand of the estimator. For the second, we provide k...

The authors present a new convolution-type kernel estimator of the marginal density of an MA(1) process with general error distribution. They prove the √ n-consistency of the nonparametric estimator and give asymptotic expressions for the mean square and the integrated mean square error of some unobservable version of the estimator. An extension to MA(q) processes is presented in the case of th...

Context. Galaxies are strongly influenced by their environment. Quantifying the galaxy density is a difficult but critical step in studying the properties of galaxies. Aims. We aim to determine differences in density estimation methods and their applicability in astronomical problems. We study the performance of four density estimation techniques: k-nearest neighbors (kNN), adaptive Gaussian ke...

We consider kernel-type methods for estimation of a density on [0, 1] which eschew explicit boundary correction. Our starting point is the successful implementation of beta kernel density estimators of Chen (1999). We propose and investigate two alternatives. For the first, we reverse the roles of estimation point x and datapoint Xi in each summand of the estimator. For the second, we provide k...

We give an explicit error bound between the invariant density of an elliptic reflected diffusion in a smooth compact domain and the kernel estimator built on the symmetric Euler scheme introduced in Bossy, Gobet and Talay (2004).