The following mixture model-based clustering methods are compared in a simulation study with one-dimensional data, fixed number of clusters and a focus on outliers and uniform “noise”: an ML-estimator (MLE) for Gaussian mixtures, an MLE for a mixture of Gaussians and a uniform distribution (interpreted as “noise component” to catch outliers), an MLE for a mixture of Gaussian distributions where...

Suppose that U = (U(1), … , U(d)) has a Uniform ([0, 1](d)) distribution, that Y = (Y(1), … , Y(d)) has the distribution G on [Formula: see text], and let X = (X(1), … , X(d)) = (U(1)Y(1), … , U(d)Y(d)). The resulting class of distributions of X (as G varies over all distributions on [Formula: see text]) is called the Scale Mixture of Uniforms class of distributions, and the corresponding class...

This paper proposes an efficient numerical integration formula to compute the normalizing constant of Fisher–Bingham distributions. uses a with continuous Euler transform Fourier-type integral representation constant. As this method is fast and accurate, it can be applied calculation high-dimensional More precisely, error decays exponentially increase in points, computation cost increases linea...

Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions and thus is a rich and flexible nonparametric class of distributions. Further, the MLE exists and can be computed with readily available algorithms. Thus, no tuning parameter, such as a bandwidth, i...

We study nonparametric estimation for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler “naive estimator.” Groeneboom, Maathuis and Wellner [Ann. Statist. (2008) 36 1031– 1063] proved that both types of estimators converge globally and locally at rate n1/3. We use these results to...

We study nonparametric estimation for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler 'naive estimator'. Groeneboom, Maathuis and Wellner [8] proved that both types of estimators converge globally and locally at rate n(1/3). We use these results to derive the local limiting dist...

Maximum Entropy Distributions on Graphs by Andre Yohannes Wibisono Master of Arts in Statistics University of California, Berkeley Professor Michael I. Jordan, Chair We study the maximum entropy distribution on weighted graphs with a given expected degree sequence. This distribution on graphs is characterized by independent edge weights parameterized by vertex potentials at each node. Using the...

We discuss some inference problems associated with the fractional Ornstein-Uhlenbeck (fO-U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter H is known and is in [1/2, 1). Under this setting we compute the distributions of the maximum likelihood estimator (MLE) and the minimum co...

A classical characterization result, which can be traced back to Gauss, states that the maximum likelihood estimator (MLE) of the location parameter equals the sample mean for any possible univariate samples of any possible sizes n if and only if the samples are drawn from a Gaussian population. A similar result, in the two-dimensional case, is given in von Mises (1929) for the Fisher-von Mises...