In this paper we study the estimation of a quantile function based on left truncated and right censored data by the kernel smoothing method. Asymptotic normality and a Berry-Esseen type bound for the kernel quantile estimator are derived. Monte Carlo studies are conducted to compare the proposed estimator with the PL-quantile estimator.

Sharp smoothing estimates are proven for magnetic Schrr odinger semigroups in two dimensions under the assumption that the magnetic eld is bounded below by some positive constant B 0. As a consequence the L 1 norm of the associated integral kernel is bounded by the L 1 norm of the Mehler kernel of the Schrr odinger semigroup with the constant magnetic eld B 0 .

Abs t rac t . To estimate the quantile density function (the derivative of the quantile function) by kernel means, there are two alternative approaches. One is the derivative of the kernel quantile estimator, the other is essentially the reciprocal of the kernel density estimator. We give ways in which the former method has certain advantages over the latter. Various closely related smoothing i...

We present a new unified kernel regression framework on manifolds. Starting with a symmetric positive definite kernel, we formulate a new bivariate kernel regression framework that is related to heat diffusion, kernel smoothing and recently popular diffusion wavelets. Various properties and performance of the proposed kernel regression framework are demonstrated. The method is subsequently appl...

One popular application of kernel density estimation is in kernel discriminant analysis, where kernel estimates of population densities are plugged in the Bayes rule to develop a nonparametric classifier. Performance of these kernel density estimates and that of the corresponding classifier depend on the values of associated smoothing parameters commonly known as the bandwidths. Bandwidths that...

J. E. Lee, M. K. Chung, T. R. Oakes, A. L. Alexander Medical Physics, University of Wisconsin, Madison, WI, United States, The Waisman Laboratory for Functional Brain Imaging and Behavior, University of Wisconsin, Madison, WI, United States, Statistics, University of Wisconsin, Madison, WI, United States Introduction DTI measures, such as FA, trace and the eigenvector orientations, are very sen...

In this paper, we study a kernel smoothing approach for denoising a tensor field. Particularly, both simulation studies and theoretical analysis are conducted to understand the effects of the noise structure and the structure of the tensor field on the performance of different smoothers arising from using different metrics, viz., Euclidean, log-Euclidean and affine invariant metrics. We also st...

In this paper we propose a simple multistep regression smoother which is constructed in an iterative manner, by learning the Nadaraya-Watson estimator with L2boosting. We find, in both theoretical analysis and simulation experiments, that the bias converges exponentially fast, and the variance diverges exponentially slow. The first boosting step is analyzed in more detail, giving asymptotic exp...

We present an algorithm for learning the intrinsic value of a batted ball in baseball. This work addresses the fundamental problem of separating the value of a batted ball at contact from factors such as the defense, weather, and ballpark that can affect its observed outcome. The algorithm uses a Bayesian model to construct a continuous mapping from a vector of batted ball parameters to an intr...

We propose a non-parametric method of smoothing supernova data over redshift using a Gaussian kernel which allows us to reconstruct important cosmological quantities including H(z) and w(z) in a model independent manner. This method is shown to be successful in discriminating between different models of dark energy when the quality of data is commensurate with that expected from the future Supe...