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For random samples of size n obtained from p-variate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the high-dimensional setting. These test statistics have been…
The least squares fit to a straight line, when both variables are affected by all equal uncorrelated errors, leads to very simple results for both the estimated parameters and their standard errors, of widespread applicability. In this…
The Friedman test has been extensively applied as a nonparametric alternative to the conventional F procedure for comparing treatment effects in randomized complete block designs. A chi-square distribution provides a convenient…
We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…
The complexity underlying real-world systems implies that standard statistical hypothesis testing methods may not be adequate for these peculiar applications. Specifically, we show that the likelihood-ratio test's null-distribution needs to…
Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
Background and objective. Circular statistics and Rayleigh tests are important tools for analyzing the occurrence of cyclic events. However, current methods fail in the presence of measurement bias, such as incomplete or otherwise…
There are several assumptions made in a standard $\chi^2$ analysis of data, including the frequent assumption that the likelihood function is well approximated by a multivariate Gaussian distribution. This article briefly reviews the…
Given the vast reservoirs of data stored worldwide, efficient mining of data from a large information store has emerged as a great challenge. Many databases like that of intrusion detection systems, web-click records, player statistics,…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
Least-squares data analysis is based on the assumption that the normal (Gaussian) distribution appropriately characterizes the likelihood, that is, the conditional probability of each measurement d, given a measured quantity y, p(d | y). On…
This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…
We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several…
In subgroup analysis, testing the existence of a subgroup with a differential treatment effect serves as protection against spurious subgroup discovery. Despite its importance, this hypothesis testing possesses a complicated nature:…
Consider $k$ independent random samples from $p$-dimensional multivariate normal distributions. We are interested in the limiting distribution of the log-likelihood ratio test statistics for testing for the equality of $k$ covariance…
In this paper we obtain an adjusted version of the likelihood ratio test for errors-in-variables multivariate linear regression models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical…
The reduced chi-squared statistic is a commonly used goodness-of-fit measure, but it cannot easily detect features near the noise level, even when a large amount of data is available. In this paper, we introduce a new goodness-of-fit…
For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more…
Applying the standard weighted mean formula, [sum_i {n_i sigma^{-2}_i}] / [sum_i {sigma^{-2}_i}], to determine the weighted mean of data, n_i, drawn from a Poisson distribution, will, on average, underestimate the true mean by ~1 for all…