Generally, blind separation of sources from their nonlinear mixtures is rather difficult. This nonlinear mapping, constituted by unsupervised linear mixing followed by unknown and invertible nonlinear distortion, is found in many signal processing cases. We propose using a kernel density estimator incorporated within an equivariant gradient algorithm to separate the nonlinear mixed sources. The...

This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.

Often times there is a need to infer the true underlying probability based on the observations, such as in, including but not limited to, data-mining, optimizing the process control parameters etc., Histograms, very rudimentary empirical density estimators, divide the whole data range into either equal or unequal sub intervals (bins) and then obtain the frequency of occurrence of each bin. They...

This paper investigates nonparametric estimation of density on [0,1]. The kernel estimator of density on [0,1] has been found to be sensitive to both bandwidth and kernel. This paper proposes a unified Bayesian framework for choosing both the bandwidth and kernel function. In a simulation study, the Bayesian bandwidth estimator performed better than others, and kernel estimators were sensitive ...

The performance of a kernel HAC estimator depends on the accuracy of the estimation of the normalized curvature, an unknown quantity in the optimal bandwidth represented as the spectral density and its derivative. This paper proposes to estimate it with a general class of kernels. The AMSE of the kernel estimator and the AMSE-optimal bandwidth are derived. It is shown that the optimal bandwidth...

This paper introduces a simple and efficient density estimator that enables fast systematic search. To show its advantage over commonly used kernel density estimator, we apply it to outlying aspects mining. Outlying aspects mining discovers feature subsets (or subspaces) that describe how a query stand out from a given dataset. The task demands a systematic search of subspaces. We identify that...

We apply the stochastic approximation method to construct a large class of recursive kernel estimators of a probability density, including the one introduced by Hall and Patil (1994). We study the properties of these estimators and compare them with Rosenblatt’s nonrecursive estimator. It turns out that, for pointwise estimation, it is preferable to use the nonrecursive Rosenblatt’s kernel esti...

Estimating an unknown probability density function is a common problem arising frequently in many scientific disciplines. Among many density estimation methods, the kernel density estimators are widely used. However, the classical kernel density estimators suffer from an intrinsic problem as they assign positive values outside the support of the target density. This problem is commonly known as...

In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by ...

Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions...