Related papers: Adaptive testing method for ergodic diffusion proc…

New inference methods for the multivariate coefficient of variation and its reciprocal, the standardized mean, are presented. While there are various testing procedures for both parameters in the univariate case, it is less known how to do…

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…

We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…

A Markov chain is geometrically ergodic if it converges to its in- variant distribution at a geometric rate in total variation norm. We study geo- metric ergodicity of deterministic and random scan versions of the two-variable Gibbs…

We propose a new method of the construction of the asymptotically efficient estimator-processes asymptotically equivalent to the MLE and the same time much more easy to calculate. We suppose that the observed process is ergodic diffusion…

We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models…

We use the Random Matrix Theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed…

The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…

The aim of this paper is to study the behavior of the weighted empirical measures of the decreasing step Euler scheme of a one-dimensional diffusion process having multiple invariant measures. This situation can occur when the drift and the…

For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…

This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…

In this paper, we propose two new tests for testing the equality of the covariance functions of several functional populations, namely a quasi GPF test and a quasi $F_{\max}$ test. The asymptotic random expressions of the two tests under…

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…

Although several nonparametric tests are available for testing population identical distributions or equal means in multiple groups problem, the Van der Waerden test has asymptotically the same efficiency as the classical one-way analysis…

I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find…

We provide necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives of chi-squared test for testing of hypothesis of homogeneity. The number of cells of chi-squared test increases with sample size…

The main purpose of this paper is to propose an ergodic theoretic approach to the study of entire holomorphic curves. Brody curves are one-Lipschitz holomorphic maps from the complex plane to the complex projective space. They naturally…

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates…

Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…

This paper investigates the size performance of Wald tests for CAViaR models (Engle and Manganelli, 2004). We find that the usual estimation strategy on test statistics yields inaccuracies. Indeed, we show that existing density estimation…