相关论文: Testing the order of a model

Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on…

Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…

Many statistical experiments involve comparing multiple population groups. For example, a public opinion poll may ask which of several political candidates commands the most support; a social scientific survey may report the most common of…

Nonstationarity is ubiquitous in practical classification settings, leading deployed models to perform poorly even when they generalize well to holdout sets available at training time. We address this by reframing nonstationary…

In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…

Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…

Many models such as Long Short Term Memory (LSTMs), Gated Recurrent Units (GRUs) and transformers have been developed to classify time series data with the assumption that events in a sequence are ordered. On the other hand, fewer models…

Estimation of the ordered scale parameter of a two scale mixture of the exponential distribution is considered under Stein loss and symmetric loss. Under certain conditions, we prove that the inadmissibility equivariant estimator exhibits…

This paper considers both the least squares and quasi-maximum likelihood estimation for the recently proposed scalable ARMA model, a parametric infinite-order vector AR model, and their asymptotic normality is also established. It makes…

Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…

We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…

Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

In the framework of matrix valued observables with low rank means, Stein's unbiased risk estimate (SURE) can be useful for risk estimation and for tuning the amount of shrinkage towards low rank matrices. This was demonstrated by Cand\`es…

Order Dependencies (ODs) have many applications, such as query optimization, data integration, and data cleaning. Although many works addressed the problem of discovering OD (and its variants), they do not consider datasets with missing…

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…

This paper explores generalised probabilistic modelling and uncertainty estimation in comparative LLM-as-a-judge frameworks. We show that existing Product-of-Experts methods are specific cases of a broader framework, enabling diverse…

Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…

This paper develops an empirical likelihood approach to testing for the presence of stochastic ordering among univariate distributions based on independent random samples from each distribution. The proposed test statistic is formed by…

The determination of the number of mixture components (the order) of a finite mixture model has been an enduring problem in statistical inference. We prove that the closed testing principle leads to a sequential testing procedure (STP) that…