相关论文: Student's $t$-test for scale mixture errors

Estimates of finite population cumulativedistribution functions (CDFs) and quantiles are critical forpolicy-making, resource allocation, and public health planning. For instance, federal finance agencies may require accurate estimates of…

A natural (yet unconventional) test for goodness-of-fit measures the discrepancy between the model and empirical distributions via their Euclidean distance (or, equivalently, via its square). The present paper characterizes the statistical…

The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…

We obtain the median, arithmetic mean, and the weighted mean-based central estimates for the distance to M87 using all the measurements collated in De Grijs et al (2020). We then reconstruct the error distribution for the residuals of the…

Gauss--Christoffel quadrature is a fundamental method for numerical integration, and its convergence analysis is closely related to the decay of Chebyshev expansion coefficients. Classical estimates, including those due to Trefethen, are…

We propose the finite mixture of skewed sub-Gaussian stable distributions. The maximum likelihood estimator for the parameters of proposed finite mixture model is computed through the expectation-maximization algorithm. The proposed model…

The error exponent of the typical random code is defined as the asymptotic normalized expectation of the logarithm of the probability of error, as opposed to the traditional definition of the random coding exponent as the normalized…

Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…

Under certain conditions, a symmetric unimodal continuous random variable $\xi$ can be represented as a scale mixture of the standard Normal distribution $Z$, i.e., $\xi = \sqrt{W} Z$, where the mixing distribution $W$ is independent of…

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures…

The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…

The center of gravity is a widespread algorithm for position reconstruction in particle physics. For track fitting, its standard use is always accompanied by an easy guess for the probability distribution of the positioning errors. This is…

We consider the problem of clustering mixtures of mean-separated Gaussians in high dimensions. We are given samples from a mixture of $k$ identity covariance Gaussians, so that the minimum pairwise distance between any two pairs of means is…

A decision must often be made between heavy-tailed and Gaussian errors for a regression or a time series model, and the t-distribution is frequently used when it is assumed that the errors are heavy-tailed distributed. The performance of…

This letter studies the synchrophasor measurement error of electric power distribution systems with on-line and off-line measurements using graphical and numerical tests. It demonstrates that the synchrophasor measurement error follows a…

Given $n$ independent random marked $d$-vectors $X_i$ with a common density, define the measure $\nu_n = \sum_i \xi_i $, where $\xi_i$ is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near…

Confidence limits are common place in physics analysis. Great care must be taken in their calculation and use, especially in cases of limited statistics when often one-sided limits are quoted. In order to estimate the stability of the…

The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…

Cross-validation (CV) is one of the most widely used techniques in statistical learning for estimating the test error of a model, but its behavior is not yet fully understood. It has been shown that standard confidence intervals for test…

Cochran's $Q$ statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value is also used for estimation of between-study variance $\tau^2$. Cochran's $Q$, or $Q_{IV}$, uses estimated inverse-variance weights…