A central problem in learning is to select an appropriate model. This is typically done by estimating the unknown generalization errors of a set of models to be selected from and by then choosing the model with minimal generalization error estimate. In this article, we discuss the problem of model selection and generalization error estimation in the context of kernel regression models, e.g., ke...

In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original ...

We study the profile-kernel and backfitting methods in partially linear models for clustered/longitudinal data. For independent data, despite the potential root-n inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix, as shown by Opsomer & Ruppert (1999). In this paper, theoretical comparisons of the two estimators for multi...

The nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias in the boundary region. Here, we propose new estimators based on the gamma kernels for the density...

We present two estimators for discrete non-Gaussian and nonstationary probability density estimation based on a dynamic Bayesian network (DBN). The first estimator is for offline computation and consists of a DBN whose transition distribution is represented in terms of kernel functions. The estimator parameters are the weights and shifts of the kernel functions. The parameters are determined th...

In this paper we present a generalization of kernel density estimation called Convex Adaptive Kernel Density Estimation (CAKE) that replaces single bandwidth selection by a convex aggregation of kernels at all scales, where the convex aggregation is allowed to vary from one training point to another, treating the fundamental problem of heterogeneous smoothness in a novel way. Learning the CAKE ...

We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative. Asymptotic normality and the asymptotic biases are derived. AMS classification: primary 62G05; secondary 62E20, 62G07, 62G20

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.

In regression we can delete outliers based upon a preliminary estimator and reestimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estimator. We provide a stochastic recursion equation for the estimation error in terms of a kernel, the p...

The estimation of conditional probability distribution functions (PDFs) in a kernel nonparametric framework has recently received attention. As emphasized by Hall, Racine & Li (2004), these conditional PDFs are extremely useful for a range of tasks including modelling and predicting consumer choice. The aim of this paper is threefold. First, we implement nonparametric kernel estimation of PDF w...