统计理论

This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…

The Pickands estimator for the extreme value index is beneficial due to its universal consistency, location, and scale invariance, which sets it apart from other types of estimators. However, similar to many extreme value index estimators,…

This manuscript studies the preventive replacement policy for a series or parallel system consisting of n independent or dependent heterogeneous components. Firstly, for the age replacement policy, Some sufficient conditions for the…

We study the disassortative stochastic block model with three communities, a well-studied model of graph partitioning and Bayesian inference for which detailed predictions based on the cavity method exist [Decelle et al. (2011)]. We provide…

A method of constructing Markov chains on finite state spaces is provided. The chain is specified by three constraints: stationarity, dependence and marginal distributions. The generalized Pythagorean theorem in information geometry plays a…

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…

The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…

Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…

We address the challenge of estimating the hyperuniformity exponent $\alpha$ of a spatial point process, given only one realization of it. Assuming that the structure factor $S$ of the point process follows a vanishing power law at the…

We study the asymptotic error of score-based diffusion model sampling in large-sample scenarios from a non-parametric statistics perspective. We show that a kernel-based score estimator achieves an optimal mean square error of…

In some scientific fields, it is common to have certain variables of interest that are of particular importance and for which there are many studies indicating a relationship with different explanatory variables. In such cases, particularly…

We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…

In this paper, we consider finite mixture models with modified proportional hazard rates. Sufficient conditions for the usual stochastic order and the hazard order are established under chain majorization. We study stochastic comparisons…

We develop $(\epsilon,\delta)$-differentially private projection-depth-based medians using the propose-test-release (PTR) and exponential mechanisms. Under general conditions on the input parameters and the population measure, (e.g. we do…

We study the problem of maximum likelihood (ML) estimation for statistical models defined by reflexive polytopes. Our focus is on the maximum likelihood degree of these models as an algebraic measure of complexity of the corresponding…

In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbounded settings, however, hitherto available results require…

Real networks often have severe degree heterogeneity, with the maximum, average, and minimum node degrees differing significantly. This paper examines the impact of degree heterogeneity on statistical limits of network data analysis.…

Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…

We propose a modified weighted Nadaraya-Watson estimator for the conditional distribution of a time series with heavy tails. We establish the asymptotic normality of the proposed estimator. Simulation study is carried out to assess the…

We noisily observe solutions of an ordinary differential equation $\dot u = f(u)$ at given times, where $u$ lives in a $d$-dimensional state space. The model function $f$ is unknown and belongs to a H\"older-type smoothness class with…