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BACKGROUND: Of late, high-throughput microarray and sequencing data have been extensively used to monitor biomarkers and biological processes related to many diseases. Under this circumstance, the support vector machine (SVM) has been popularly used and been successful for gene selection in many applications. Despite surpassing benefits of the SVMs, single data analysis using small- and mid-size of data inevitably runs into the problem of low reproducibility and statistical power. To address thi

Abstract This article deals with regression function estimation when the regression function is smooth at all but a finite number of points. An important question is: How can one produce discontinuous output without knowledge of the location of discontinuity points? Unlike most commonly used smoothers that tend to blur discontinuity in the data, we need to find a smoother that can detect such discontinuity. In this article, linear splines are used to estimate discontinuous regression functions.

A method for analyzing electrostatic discharge (ESD) generators and coupling to equipment under test in the frequency domain is proposed. In ESD generators, the pulses are excited by the voltage collapse across relay contacts. The voltage collapse is replaced by one port of a vector network analyer (VNA). All the discrete and structural elements that form the ESD current pulse and the transient fields are excited by the VNA as if they were excited by the voltage collapse. In such a way, the meth

Consider an unknown regression function $f$ of the response $Y$ on a $d$-dimensional measurement variable $X$. It is assumed that $f$ belongs to a class of functions having a smoothness measure $p$. Let $T$ denote a known linear operator of order $q$ which maps $f$ to another function $T(f)$ in a space $G$. Let $\hat{T}_n$ denote an estimator of $T(f)$ based on a random sample of size $n$ from the distribution of $(X, Y)$, and let $\|\hat{T}_n - T(f)\|_G$ be a norm of $\hat{T}_n - T(f)$. Under a

We estimate a probability density function p which is related by a linear operator K to a density function q in sequences of regular exponential families based on a random sample from q. In this paper deconvolution and positron emission tomography are considered. The logarithm of the density function is approximated by basis functions consisting of singular functions of K. While direct maximum likelihood (or minimum Kullback-Leibler) density estimation in exponential families selects the paramet

ABSTRACT. In this paper we consider logspline density estimation for random variables which are contaminated with random noise. In the logspline density estimation for data without noise, the logarithm of an unknown density function is estimated by a polynomial spline, the unknown parameters of which are given by maximum likelihood. When noise is present, B‐splines and the Fourier inversion formula are used to construct the logspline density estimator of the unknown density function. Rates of co

MOTIVATION: The problem of class prediction has received a tremendous amount of attention in the literature recently. In the context of DNA microarrays, where the task is to classify and predict the diagnostic category of a sample on the basis of its gene expression profile, a problem of particular importance is the diagnosis of cancer type based on microarray data. One method of classification which has been very successful in cancer diagnosis is the support vector machine (SVM). The latter has

This paper examines stochastic deconvolution over noncommutative compact Lie groups. This involves Fourier analysis on compact Lie groups as well as convolution products over such groups. An observation process consisting of a known impulse response function convolved with an unknown signal with additive white noise is assumed. Data collected through the observation process then allow us to construct an estimator of the signal. Signal recovery is then assessed through integrated mean squared err

B-splines are considered for the decon volution problem of estimating a probability density function when the sample observations are contaminated with random noise. In the logspline method of density estimation, the logarithm of the unknown density function is approximated by a polynomial spline, the unknown parameters of which are estimated by maximum likelihood. Based on the logspline method, a fully automated procedure involving the EM algorithm, stepwise knot deletion and BIC has been devel