Related papers: A normal distribution for the disturbance term in …
In this paper we prove the central limit theorem for Hotelling's $T^2$ statistic when the dimension of the random vectors is proportional to the sample size.
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
The empirical Orlicz norm based on a random sample is defined as a natural estimator of the Orlicz norm of a univariate probability distribution. A law of large numbers is derived under minimal assumptions. The latter extends readily to a…
We construct an autoregressive model with random coefficients that has a stationary distribution after proper normalization. This limit distribution is found to be stable.
Let ${X}_{k}=(x_{k1}, \cdots, x_{kp})', k=1,\cdots,n$, be a random sample of size $n$ coming from a $p$-dimensional population. For a fixed integer $m\geq 2$, consider a hypercubic random tensor $\mathbf{{T}}$ of $m$-th order and rank $n$…
We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
The transmissivity of a one-dimensional random system that is periodic on average is studied. It is shown that the transmission coefficient for frequencies corresponding to a gap in the band structure of the average periodic system…
We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting…
In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common…
Motivated by sensor networks and other distributed settings, several models for distributed learning are presented. The models differ from classical works in statistical pattern recognition by allocating observations of an independent and…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The…
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…
We investigate large-sample properties of treatment effect estimators under unknown interference in randomized experiments. The inferential target is a generalization of the average treatment effect estimand that marginalizes over potential…
A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…
An initially planar shock wave propagating into a medium of non-uniform density will be perturbed, leading to the generation of post-shock velocity perturbations. Using numerical simulations we study this phenomenon in the case of…
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable…
We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply to the probabilistic model regarding the jam emergence as the formation of a large car cluster on highway. In these terms the breakdown occurs…
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…