统计理论

The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile…

This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…

We take the testing perspective to understand what the minimal discrimination time between two stimuli is for different types of rate coding neurons. Our main goal is to describe the testing abilities of two different encoding systems:…

The knockoff filter is a recent false discovery rate (FDR) control method for high-dimensional linear models. We point out that knockoff has three key components: ranking algorithm, augmented design, and symmetric statistic, and each…

This paper places conformal testing in a general framework of statistical hypothesis testing. A standard approach to testing a composite null hypothesis $H$ is to test each of its elements and to reject $H$ when each of its elements is…

In this article, we study the critical growth rates of dimension below which Gaussian critical values can be used for hypothesis testing but beyond which they cannot. We are particularly interested in how these growth rates depend on the…

In this study, simultaneous predictive distributions for independent Poisson observables were considered and the performance of predictive distributions was evaluated using the Kullback-Leibler (K-L) loss. This study proposes a class of…

This paper is concerned with noisy matrix completion--the problem of recovering a low-rank matrix from partial and noisy entries. Under uniform sampling and incoherence assumptions, we prove that a tuning-free square-root matrix completion…

The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…

The problem of the mean-square optimal linear estimation of the functional $A\xi=\ \int\limits_{R^s}a(t)\xi(-t)dt,$ which depends on the unknown values of stochastic stationary process $\xi(t)$ from observations of the process…

The problem of optimal linear estimation of functionals depending on the unknown values of a random field $\zeta(t,x)$, which is mean-square continuous periodically correlated with respect to time argument $t\in\mathbb R$ and isotropic on…

The study on the generating function approach to entropy become popular as it generates several well-known entropy measures discussed in the literature. In this work, we define the weighted cumulative residual entropy generating function…

We work out a version of the van Trees inequality in a Hajek--Le Cam spirit, i.e., under minimal assumptions that, in particular, involve no direct pointwise regularity assumptions on densities but rather almost-everywhere differentiability…

We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…

Accelerated life tests (ALTs) play a crucial role in reliability analyses, providing lifetime estimates of highly reliable products. Among ALTs, step-stress design increases the stress level at predefined times, while maintaining a constant…

In this work, we undertake a comprehensive reformulation, modification, and extension of Smith and Spiegelhalter's (1980) and (1982) Bayes Factor work within the evolving subject of Objective Bayes Factors. Our primary focus centers on…

Accelerated life-tests (ALTs) are used for inferring lifetime characteristics of highly reliable products. In particular, step-stress ALTs increase the stress level at which units under test are subject at certain pre-fixed times, thus…

We introduce a random recursive tree model with two communities, called balanced community modulated random recursive tree, or BCMRT in short. In this setting, pairs of nodes of different type appear sequentially. Each node of the pair…

A popular measure of association is the tail dependence coefficient which measures the strength of dependence in either the lower-left or upper-right tail of a bivariate distribution. In this paper, we develop the idea of quantile…

Bayesian networks are widely utilised in various fields, offering elegant representations of factorisations and causal relationships. We use surjective functions to reduce the dimensionality of the Bayesian networks by combining states and…