Related papers: Moderate deviation principle for the chi-square st…
We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…
The median absolute deviation is a widely used robust measure of statistical dispersion. Using a scale constant, we can use it as an asymptotically consistent estimator for the standard deviation under normality. For finite samples, the…
In this paper, we consider moderate deviations for Good's coverage estimator. The moderate deviation principle and the self-normalized moderate deviation principle for Good's coverage estimator are established. The results are also applied…
I investigate the use of Pearson's chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between…
In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stochastic control arguments, that cover both the averaging and…
In this paper, we expand and generalize the findings presented in our previous work on the law of large numbers and the large deviation principle for Poisson processes with uniform catastrophes. We study three distinct scalings: sublinear…
The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…
Functionals in geometric probability are often expressed as sums of bounded functions exhibiting exponential stabilization. Methods based on cumulant techniques and exponential modifications of measures show that such functionals satisfy…
A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…
In this article, we discuss the sharp moderate and large deviations between the quantiles of population and the quantiles of samples. Cram\'{e}r type moderate deviations and Bahadur-Rao type large deviations are established with some mild…
In this paper, we derive an explicit sample size formula based a mixed criterion of absolute and relative errors for estimating means of Poisson random variables.
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…
In the present paper, we consider the linear autoregressive model in $\rr$, $$ X_{k,n}=\theta_n X_{k,n-1}+\xi_k, k=0,1,...,n, n\ge 1$$ where $\theta_n\in [0,1)$ is unknown, $(\xi_k)_{k\in\zz}$ is a sequence of centered i.i.d. r.v. valued in…
We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide…
We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
We prove that moderate deviations for empirical measures for countable nonhomogeneous Markov chains hold under the assumption of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chains in Ces\`aro…
Small sample sizes in clinical studies arises from factors such as reduced costs, limited subject availability, and the rarity of studied conditions. This creates challenges for accurately calculating confidence intervals (CIs) using the…
The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation…
The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a…