Related papers: Coverage Probability of Random Intervals
A new method is proposed for the correction of confidence intervals when the original interval does not have the correct nominal coverage probabilities in the frequentist sense. The proposed method is general and does not require any…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We develop a pseudo-likelihood theory for rank one matrix estimation problems in the high dimensional limit. We prove a variational principle for the limiting pseudo-maximum likelihood which also characterizes the performance of the…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically…
We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…
In this paper we propose a new approach for sequential monitoring of a parameter of a $d$-dimensional time series, which can be estimated by approximately linear functionals of the empirical distribution function. We consider a…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
In the analysis of clustered and longitudinal data, which includes a covariate that varies both between and within clusters (e.g. time-varying covariate in longitudinal data), a Hausman pretest is commonly used to decide whether subsequent…
The idea of maximizing the likelihood of the observed range for a set of jointly realized counts has been employed in a variety of contexts. The applicability of the MLE introduced in [1] has been extended to the general case of a…
We study some properties of binary sequences generated by random substitutions of constant length. Specifically, assuming the alphabet $\{0,1\}$, we consider the following asymmetric substitution rule of length $k$: $0 \to \langle 0, 0,…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory…
We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
A number of writers have supposed that for the full specification of belief, higher order probabilities are required. Some have even supposed that there may be an unending sequence of higher order probabilities of probabilities of…