Let f,, be the kernel density estimate with arbitrary smoothing factor h and arbitrary (absolutely integrable) kernel K, based upon an i.i.d. sample of size n drawn from a density f. It is shown that

This paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms. Based on the …xed-bandwidth asymptotic variance and the pre-asymptotic variance, we propose a heteroskedasticity and autocorrelation robust (HAR) variance estimator that achieves double robustness — it is asymptotically valid regardless of whether the temporal ...

Many applied studies collect one or more ordered categorical predictors, which do not fit neatly within classic regression frameworks. In most cases, ordinal predictors are treated as either nominal (unordered) variables or metric (continuous) variables in regression models, which is theoretically and/or computationally undesirable. In this paper, we discuss the benefit of taking a smoothing sp...

The proposed method is to recognize objects based on application of Local Steering Kernels (LSK) as Descriptors to the image patches. In order to represent the local properties of the images, patch is to be extracted where the variations occur in an image. To find the interest point, Wavelet based Salient Point detector is used. Local Steering Kernel is then applied to the resultant pixels, in ...

Abstract The procedures of estimating prediction intervals for ARMA processes can be divided into model based methods and empirical methods. Model based methods require knowledge of the model and the underlying innovation distribution. Empirical methods are based on the sample forecast errors. In this paper we apply nonparametric quantile regression to the empirical forecast errors using lead t...

Introduction: Many DTI studies are starting to use voxel based analysis (VBA) to evaluate differences in the diffusion properties between healthy diseased subjects. Despite the intuitively appealing approach of analyzing diffusion measures at each voxel, VBA results should be interpreted cautiously, since they depend on the applied parameter settings. Since, for example, in the VBA literature o...

Copulas are full measures of dependence among components of random vectors. Unlike the marginal and the joint distributions, which are directly observable, a copula is a hidden dependence structure that couples a joint distribution with its marginals. This makes the task of proposing a parametric copula model non-trivial and is where a nonparametric estimator can play a significant role. In thi...

In computational neuroanatomy, there is need for analyzing data collected on the cortical surface of the human brain. Gaussian kernel smoothing has been widely used in this area in conjunction with random field theory for analyzing data residing in Euclidean spaces. The Gaussian kernel is isotropic in Euclidian space so it assigns the same weights to observations equal distance apart. However, ...

We focus on solving the problem of learning an optimal smoothing kernel for the unsupervised learning problem of kernel density estimation(KDE) by using hyperkernels. The optimal kernel is the one which minimizes the regularized negative leave-one-out-log likelihood score of the train set. We demonstrate that ”fixed bandwidth” and ”variable bandwidth” KDE are special cases of our algorithm.

Abstract. We study an estimator for smoothing irregularly sampled data into a smooth map. The estimator has been widely used in astronomy, owing to its low level of noise; it involves a weight function – or smoothing kernel – w(θ). We show that this estimator is not unbiased, in the sense that the expectation value of the smoothed map is not the underlying process convolved with w, but a convol...