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In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…

Machine Learning · Statistics 2024-12-10 Behrad Moniri , Hamed Hassani

In [8], asymptotic expansion of the martingale with mixed normal limit was provided. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard…

Probability · Mathematics 2012-12-27 Nakahiro Yoshida

For two nonstandard renewal risk models, we investigate the precise large deviations of the finite-time ruin probability and a random sum of the net-loss process, and the asymptotics of the random-time ruin probability. Notably, in one of…

Probability · Mathematics 2024-10-11 Yang Chen , Zhaolei Cui , Yuebao Wang

In this work, we attempt to refine the classic asymptotic formulae to describe the probability distribution of likelihood-ratio statistical tests. The idea is to split the probability distribution function into two parts. One part is…

Data Analysis, Statistics and Probability · Physics 2025-07-29 Li-Gang Xia , Yan Zhang

Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…

Statistics Theory · Mathematics 2017-08-10 Ryan J. Tibshirani , Alessandro Rinaldo , Robert Tibshirani , Larry Wasserman

The Hartman-Watson distribution with density $f_r(t)$ is a probability distribution defined on $t \geq 0$ which appears in several problems of applied probability. The density of this distribution is expressed in terms of an integral…

Probability · Mathematics 2024-12-20 Dan Pirjol

In this paper we consider the product of a singular Wishart random matrix and a singular normal random vector. A very useful stochastic representation is derived for this product, using which the characteristic function of the product and…

Statistics Theory · Mathematics 2016-11-10 Taras Bodnar , Stepan Mazur , Stanislas Muhinyuza , Nestor Parolya

We consider the process $\{x-N(t):t\geq 0\}$, where $x\in\mathbb{R}_+$ and $\{N(t):t\geq 0\}$ is a renewal process with light-tailed distributed holding times. We are interested in the joint distribution of $(\tau(x),A(x))$ where $\tau(x)$…

Probability · Mathematics 2022-02-23 Claudio Macci , Barbara Pacchiarotti

For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases quasipolynomial/quasirational representations, for all major factorization length…

Combinatorics · Mathematics 2021-02-05 Stephan Ramon Garcia , Mohamed Omar , Christopher O'Neill , Samuel Yih

Let \{X_1, X_2, ...\} be a sequence of positive independent and identically distributed random variables of Pareto-type with index \alpha>0 and let \{N(t); t\geq 0\} be a mixed Poisson process independent of the X_i's. For t\geq 0, define…

Probability · Mathematics 2007-06-13 S. A. Ladoucette

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which is possibly correlated with the returns of the diffusion…

Statistics Theory · Mathematics 2013-05-07 Yuta Koike

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Statistics Theory · Mathematics 2007-12-18 Jiming Jiang , Yihui Luan , You-Gan Wang

We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples, crude schemes fail to capture the correct limiting…

Numerical Analysis · Mathematics 2020-11-05 Charles-Edouard Bréhier , Shmuel Rakotonirina-Ricquebourg

In this paper we study the asymptotic normality in high-dimensional linear regression. We focus on the case where the covariance matrix of the regression variables has a KMS structure, in asymptotic settings where the number of predictors,…

Statistics Theory · Mathematics 2022-05-17 Saulius Jokubaitis , Remigijus Leipus

We propose a new definition of a multivariate subexponential distribution. We compare this definition with the two existing notions of multivariate subexponentiality, and compute the asymptotic behaviour of the ruin probability in the…

Probability · Mathematics 2015-09-18 Gennady Samorodnitsky , Julian Sun

For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also…

Statistics Theory · Mathematics 2012-06-22 Yindeng Jiang , Michael D. Perlman

Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…

Statistics Theory · Mathematics 2015-07-29 Jinzhu Li , Qihe Tang

Based on the negative binomial model for the duration of wet periods measured in days, an asymptotic approximation is proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the…

Probability · Mathematics 2018-10-16 V. Yu. Korolev , A. K. Gorshenin

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

Statistics Theory · Mathematics 2007-05-23 Teo Sharia

Consider $n$ i.i.d. random elements on $C[0,1]$. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing…

Statistics Theory · Mathematics 2007-06-13 John H. J. Einmahl , Tao Lin