相关论文: Beyond the law of large numbers: Introducing progr…

We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…

The paper aims at reconsidering the famous Le Cam LAN theory. The main features of the approach which make it different from the classical one are as follows: (1) the study is nonasymptotic, that is, the sample size is fixed and does not…

One of the main differences between the central limit theorem and the Poisson law of small numbers is that the former possesses the large sample property (LSP), i.e., the error of normal approximation to the sum of $n$ independent…

Well-spread samples are desirable in many disciplines because they improve estimation when target variables exhibit spatial structure. This paper introduces an integrated methodological framework for spreading samples over the population's…

The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…

We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. Based on these representations,…

This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…

The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a…

The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…

Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…

The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of a graph. Some of the most useful graph metrics, especially those measuring social cohesion, are based on…

Consider a multi-dimensional supercritical branching process with offspring distribution in a parametric family. Here, each vector coordinate corresponds to the number of offspring of a given type. The process is observed under family-size…

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social…

We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…

The law of large numbers extends to random sets by employing Minkowski addition. Above that, a central limit theorem is available for set-valued random variables. The existing results use abstract isometries to describe convergence of the…

We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and…

Sampling-based decoding underlies complex reasoning in large language models (LLMs), where decoding strategies critically shape model behavior. Temperature- and truncation-based methods reshape the next-token distribution through global…