The nature of the kernel density estimator (KDE) is to find underlying probability function (p.d.f) for a given dataset. key training KDE determine optimal bandwidth or Parzen window. All data points share fixed (scalar univariate and vector multivariate KDE) in (FKDE). In this paper, we propose an improved variable (IVKDE) which determines each point dataset based on integrated squared error (...

The kernel density estimator (KDE) based on a radial positive-semidefinite kernel may be viewed as a sample mean in a reproducing kernel Hilbert space. This mean can be viewed as the solution of a least squares problem in that space. Replacing the squared loss with a robust loss yields a robust kernel density estimator (RKDE). Previous work has shown that RKDEs are weighted kernel density estim...

Using the classical Parzen window (PW) estimate as the target function, the sparse kernel density estimator is constructed in a forward constrained regression manner. The leave-one-out (LOO) test score is used for kernel selection. The jackknife parameter estimator subject to positivity constraint check is used for the parameter estimation of a single parameter at each forward step. As such the...

A nonparametric kernel density estimator for directional–linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions for bias, variance and mean integrated square error (MISE) are derived, jointly with an asymptotic normality result for the proposed estimator. For some part...

Poston, W.L., et al., A qualitative analysis of the resistive grid kernel estimator, Pattern Recognition Letters 15 (1993) 219-225. The ability to estimate a probability density function from random data has applications in discriminant analysis and pattern recognition problems. A resistive grid kernel estimator (RGKE) is described which is suitable for hardware implementation. The one-dimensio...

Suppose we want to estimate a density at a point where we know the values of its first or higher order derivatives. In this case a given kernel estimator of the density can be modified by adding appropriately weighted kernel estimators of these derivatives. We give conditions under which the modified estimators are asymptotically normal. We also determine the optimal weights. When the highest d...

The deconvolution kernel density estimator is a popular technique for solving the deconvolution problem, where the goal is to estimate a density from a sample of contaminated observations. Although this estimator is optimal, it suffers from two major drawbacks: it converges at very slow rates (inherent to the deconvolution problem) and can only be calculated when the density of the errors is co...

This paper analyzes the large sample of a varying kernel density estimator of the marginal density of a nonnegative stationary and ergodic time series that is also strongly mixing. In particular we obtain an approximation for bias, mean square error and establish asymptotic normality of this density estimator.

Error density estimation in a nonparametric functional regression model with functional predictor and scalar response is considered. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance as a constant parameter. This proposed mixture error density has a form of a kernel density estimator of residuals, where the regre...