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Let $\{X, X_{n}; n \geq 1\}$ be a sequence of i.i.d. non-degenerate real-valued random variables with $\mathbb{E}X^{2} < \infty$. Let $S_{n} = \sum_{i=1}^{n} X_{i}$, $n \geq 1$. Let $g(\cdot): ~[0, \infty) \rightarrow [0, \infty)$ be a…

Probability · Mathematics 2025-05-02 Deli Li , Yu Miao , Yongcheng Qi

In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the…

Statistics Theory · Mathematics 2012-06-29 Luai Al Labadi , Mahmoud Zarepour

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

Machine Learning · Statistics 2023-10-30 Youngsoo Baek , Samuel I. Berchuck , Sayan Mukherjee

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…

Statistics Theory · Mathematics 2014-12-09 François Bachoc

The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…

Probability · Mathematics 2024-02-14 Guy Louchard , Werner Schachinger , Mark Daniel Ward

This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation that a recent result from the random matrix theory literature…

Probability · Mathematics 2023-05-24 Jiaoyang Huang , Colin McSwiggen

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…

Statistics Theory · Mathematics 2012-02-24 Peter Hall , Tung Pham , M. P. Wand , S. S. J. Wang

Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…

Methodology · Statistics 2017-11-29 Wentao Li , Paul Fearnhead

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…

Statistics Theory · Mathematics 2023-12-25 Chris A. J. Klaassen

Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…

Machine Learning · Computer Science 2012-02-20 Benjamin Marlin , Nando de Freitas

We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of firing rate neurons in which the synaptic weights are Gaussian correlated random variables,…

Probability · Mathematics 2013-06-03 Olivier Faugeras , James MacLaurin

Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often…

Statistical Mechanics · Physics 2021-09-17 Tobias Grafke , Tobias Schäfer , Eric Vanden-Eijnden

Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random vectors in arbitrary dimension, where the order statistics are taken componentwise.

Statistics Theory · Mathematics 2016-07-21 Michael Falk , Florian Wisheckel

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…

Statistics Theory · Mathematics 2022-07-11 Michaël Lalancette , Sebastian Engelke , Stanislav Volgushev

This paper develops an asymptotic distribution theory for an endogenous instrumentation approach in quantile predictive regressions when both generated covariates and persistent predictors are used. The generated covariates are obtained…

Econometrics · Economics 2024-04-23 Christis Katsouris

This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…

Statistics Theory · Mathematics 2025-11-14 Carsten H. Chong , Fabian Mies

In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to…

Numerical Analysis · Mathematics 2025-04-10 Ajay Jasra , Abylay Zhumekenov

In this paper, we consider Bayesian inference on a class of multivariate median and the multivariate quantile functionals of a joint distribution using a Dirichlet process prior. Since, unlike univariate quantiles, the exact posterior…

Statistics Theory · Mathematics 2021-06-03 Indrabati Bhattacharya , Subhashis Ghosal

We prove a moderate deviation principle for subgraph count statistics of Erdos-Renyi random graphs. This is equivalent in showing a moderate deviation principle for the trace of a power of a Bernoulli random matrix. It is done via an…

Probability · Mathematics 2010-03-31 Hanna Döring , Peter Eichelsbacher

We study the statistics of the number of real eigenvalues in the elliptic deformation of the real Ginibre ensemble. As the matrix dimension grows, the law of large numbers and the central limit theorem for the number of real eigenvalues are…

Probability · Mathematics 2025-11-26 Sung-Soo Byun , Jonas Jalowy , Yong-Woo Lee , Grégory Schehr