相关论文: A technical note on divergence of the Wald statist…
We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of…
Robust estimators and Wald-type tests are developed for the multinomial logistic regression based on $\phi$-divergence measures. The robustness of the proposed estimators and tests is proved through the study of their influence functions…
We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…
The Wald test remains ubiquitous in statistical practice despite shortcomings such as its inaccuracy in small samples and lack of invariance under reparameterization. This paper develops on another but lesser-known shortcoming called the…
Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…
A sum of a large-dimensional random matrix polynomial and a fixed low-rank matrix polynomial is considered. The main assumption is that the resolvent of the random polynomial converges to some deterministic limit. A formula for the limit of…
With advancement of medicine, alternative exposures or interventions are emerging with respect to a common outcome, and there are needs to formally test the difference in the associations of multiple exposures. We propose a duplication…
In this note, convergence of random variables will be revisited. We will give the answers to 5 questions among the 6 open questions introduced in (Convergence rates in the law of large numbers and new kinds of convergence of random…
In this paper, a new and convenient $\chi^2$ wald test based on MCMC outputs is proposed for hypothesis testing. The new statistic can be explained as MCMC version of Wald test and has several important advantages that make it very…
In this short note a differential version of the classical Weil descent is established in all characteristics. This yields a ready-to-deploy tool of differential restriction of scalars for differential varieties over finite differential…
In the first part of these notes, we review some of the recent developments in the study of the spectral properties of Wigner matrices. In the second part, we present a new proof of a Wegner estimate for the eigenvalues of a large class of…
In this note, a Wegner estimate for random divergence-type operators that are monotone in the randomness is proven. The proof is based on a recently shown unique continuation estimate for the gradient and the ensuing eigenvalue liftings.…
Intraclass correlation in bilateral data has been investigated in recent decades with various statistical methods. In practice, stratifying bilateral data by some control variables will provide more sophisticated statistical results to…
A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…
Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate…
In this note, we study the relationship between the variational gap and the variance of the (log) likelihood ratio. We show that the gap can be upper bounded by some form of dispersion measure of the likelihood ratio, which suggests the…
We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…