In the present paper, we consider the Pearson chi-square statistic defined on a finite alphabet which is assumed to dynamically vary as the sample size increases, and establish its moderate deviation principle.
A sufficient condition is established under which det ( A B A − 1 B − 1 ) = 1 \det (ABA^{-1}B^{-1})=1 for a pair of bounded, invertible operators A , B A,B on a Hilbert space.
We wholeheartedly congratulate Drs. Rohe and Zeng for their insightful paper \cite{rohe2020vintage} on vintage factor analysis with Varimax rotation. This note discusses the conditions to guarantee Varimax consistently recovers the subspace rotation.
We provide confidence bands for isotonic quantile curves in nonparametric univariate regression with guaranteed given coverage probability. The method is an adaptation of the confidence bands of Duembgen and Johns (2004) for isotonic median curves.
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 growth. Nonparametric sets of alternatives can be defined both in terms of densities and distribution functions.
Under a general structural equation framework for causal inference, we provide a definition of the causal effect of a variable X on another variable Y, and propose an approach to estimate this causal effect via the use of instrumental variables.
This paper discusses a design-dependent nature of variance in nonparametric link regression aiming at predicting a mean outcome at a link, i.e., a pair of nodes, based on currently observed data comprising covariates at nodes and outcomes at links.
We are interested in the behavior of particular functionals, in a framework where the only source of randomness is a sampling without replacement. More precisely the aim of this short note is to prove an exponential concentration inequality for special U-statistics of order 2, that can be seen as chaos.
Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we prove a new result on the size of the error in first- and higher-order Laplace approximations, and apply this result to investigate the quality of Laplace approximations to the likelihood in some generalized linear mixed models.
In this paper, we study a functional SAR model in which explanatory variables are sampling points of a continuous-time process. We propose a procedure for the maximum likelihood estimation for the spatial parameter dependence and the parameter function. Both convergence in probability and almost sure convergence of this estimator are stated.
We show that if the exposure and the outcome affect the selection indicator in the same direction and have non-positive interaction on the risk difference, risk ratio or odds ratio scale, the exposure-outcome odds ratio in the selected population is a lower bound for true odds ratio.
We determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon's or Tsallis' entropies in the concomitant variational problem. It is shown that the two variations lead to equivalent solutions that take different appearances but contain the same information. These solutions are linked by our transformation.
Discussion of "Latent variable graphical model selection via convex optimization" by Venkat Chandrasekaran, Pablo A. Parrilo and Alan S. Willsky [arXiv:1008.1290].
Xavier Brossat, Georges Oppenheim, Marie-Claude Viano
This paper presents a backfitting-type method for estimating and forecasting a periodically correlated partially linear model with exogeneous variables and heteroskedastic input noise. A rate of convergence of the estimator is given. The results are valid even if the period is unknown.
Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is considered.
Brownian motion with known positive drift is sampled in stages until it crosses a positive boundary $a$. A family of multistage samplers that control the expected overshoot over the boundary by varying the stage size at each stage is shown to be optimal for large $a$, minimizing a linear combination of overshoot and number of stages. Applications to hypothesis testing are discussed.
Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered there and we prove that MLEs for those plans are also stochastic ordered. We also give some applications to the estimation of reliability.
In this paper, we develop interval estimation methods for means of bounded random variables based on a sequential procedure such that the sampling is continued until the sample sum is no less than a prescribed threshold.
This paper discusses the family of distributions on the Grassmannian of the linear span of r central gaussian vectors parametrized by the covariance matrix. Our main result is an existence and uniqueness criterion for the maximum likelihood estimate of a sample.