Related papers: Cram\'{e}r moderate deviations for a supercritical…
This paper proposes a novel numerical method for computing the density of the limit random variable associated with a supercritical Galton-Watson process. This random variable captures the effect of early demographic fluctuations and…
We establish a Cram\'er-type moderate deviation theorem for double-index permutation statistics (DIPS). To the best of our knowledge, previous results only provided Berry-Esseen type bounds for DIPS, which cannot yield moderate deviation…
We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive Levy process. As applications of this result, we obtain…
This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of…
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…
Branching processes model the evolution of populations of agents that randomly generate offsprings. These processes, more patently Galton-Watson processes, are widely used to model biological, social, cognitive, and technological phenomena,…
Let $(\eta_i)_{i\geq1}$ be a sequence of $\psi$-mixing random variables. Let $m=\lfloor n^\alpha \rfloor, 0< \alpha < 1, k=\lfloor n/(2m) \rfloor,$ and $Y_j = \sum_{i=1}^m \eta_{m(j-1)+i}, 1\leq j \leq k.$ Set $ S_k^o=\sum_{j=1}^{k } Y_j $…
This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration…
This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…
In the present work, we consider a stable one-dimensional gaussian autoregressive model in continous time. Using the limit theorems with logarithmic averaging obtained for continous local martingales, we construct then an estimator of the…
Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…
In the paper we consider a stochastic model which called Markov Q-processes that forms a continuous-time Markov population system. Markov Q-processes are defined as stochastic Markov branching processes with trajectories continuing in the…
The batch means estimator of the MCMC variance is a simple and effective measure of accuracy for MCMC based ergodic averages. Under various regularity conditions, the estimator has been shown to be consistent for the true variance. However,…
In this paper, a critical Galton-Watson branching process with immigration $Z_{n}$ is studied. We first obtain the convergence rate of the harmonic moment of $Z_{n}$. Then the large deviation of $S_{Z_n}:=\sum_{i=1}^{Z_n} X_i$ is obtained,…
We study moderate deviations of suprema of parametrized sequences of sample bounded Gaussian processes $\{X _x(t), t\in T _x\}$, and first present recent sharp bounds in simple cases. In the almost periodic case, we prove an approximation…
We study a linear-fractional Bienaym\'e-Galton-Watson process with a general type space. The corresponding tree contour process is described by an alternating random walk with the downward jumps having a geometric distribution. This leads…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…
In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cram\'er-type moderate deviation theorem of normal approximation for unbounded…