Abstract: The selections of the bandwidth and kernel function of a kernel estimator are of great importance in practice. This is not different in the context of spot volatility kernel estimators. In this work, a feasible method of bandwidth and kernel selection is proposed, under some mild conditions on the volatility process, which not only cover classical Brownian motion driven dynamics but a...

Kernel methods use kernel functions to provide nonlinear versions of different methods in machine learning and data mining, such as Principal Component Analysis and Support Vector Machines. These kernel functions require the calculation of some or all of the entries of a matrix of the form XX . The formation of this type of matrix is known to result in potential numerical instability in the cas...

We propose one type of TOP (Tangent vector Of the Posterior log-odds) kernel and apply it to text categorization. In a number of categorization tasks including text categorization, negative examples are usually more common than positive examples and there may be several different types of negative examples. Therefore, we construct a TOP kernel, regarding the probabilistic model of negative exam...

This paper discusses modiications of the convolution type kernel regression estimator. One modiication uses kernel quantile estimators and is analyzed more detailed. This regression estimator combines advantages of local polynomial and kernel regression estimators and can be applied for small to large sample size. Its properties are illustrated by simulation results and asymptotic theory. Espec...