Related papers: Edgeworth expansion for Bernoulli weighted mean

Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given…

We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while only imposing minimal moment conditions. Within this result, we address the case…

We consider the self-normalized sums $T_{n}=\sum_{i=1}^{n}X_{i}Y_{i}/\sum_{i=1}^{n}Y_{i}$, where ${Y_{i} : i\geq 1}$ are non-negative i.i.d. random variables, and ${X_{i} : i\geq 1} $ are i.i.d. random variables, independent of ${Y_{i} : i…

We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…

This paper studies the asymptotic properties of weighted sums of the form $Z_n=\sum_{i=1}^n a_i X_i$, in which $X_1, X_2, \ldots, X_n$ are i.i.d.~random variables and $a_1, a_2, \ldots, a_n$ correspond to either eigenvalues or singular…

This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…

Edgeworth expansions of first and second order are established for general linear rank statistics under the null hypothesis with asymptotically ''sufficiently'' small remainder terms. The methods used are the Stein method combined with an…

In this paper, we derive valid Edgeworth expansions for studentized versions of a large class of statistics when the data are generated by a strongly mixing process. Under dependence, the asymptotic variance of such a statistic is given by…

Non-linear gravitational collapse introduces non-Gaussian statistics into the matter fields of the late Universe. As the large-scale structure is the target of current and future observational campaigns, one would ideally like to have the…

Edgeworth expansion provides higher-order corrections to the normal approximation for a probability distribution. The classical proof of Edgeworth expansion is via characteristic functions. As a powerful method for distributional…

Probability distributions defined on the unit interval are widely used in fields ranging from econometrics to reliability studies. Traditional models such as the beta and Kumaraswamy distributions are well-established due to their…

Let {(X_i,Y_i)}_{i=1}^n be a sequence of independent bivariate random vectors. In this paper, we establish a refined Cram\'er type moderate deviation theorem for the general self-normalized sum \sum_{i=1}^n X_i/(\sum_{i=1}^n Y_i^2)^{1/2},…

In this article, we study a class of lattice random variables in the domain of attraction of an $\alpha$-stable random variable with index $\alpha \in (0,2)$ which satisfy a truncated fractional Edgeworth expansion. Our results include…

Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order $s \geq 2$,…

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…

We consider sums of independent identically distributed random variables whose distributions have $d+1$ atoms. Such distributions never admit an Edgeworth expansion of order $d$ but we show that for almost all parameters the Edgeworth…

Theorem 5.1 in the monograph by Hall (1992) provides rigorous in-probability justification of Edgeworth expansions of bootstrap distributions. Proving this result was rather challenging because bootstrap distributions do not satisfy the…

Consider the matrix products $G_n: = g_n \ldots g_1$, where $(g_{n})_{n\geq 1}$ is a sequence of independent and identically distributed positive random $d\times d$ matrices. Under the optimal third moment condition, we first establish a…

The paper presents a novel asymptotic distribution for a mle when the log--likelihood is strictly concave in the parameter for all data points; for example, the exponential family. The new asymptotic distribution can be seen as a refinement…

In this paper, we provide novel mean value estimates for exponential sums related to the extended main conjecture of Vinogradov's mean value theorem, by developing the Hardy-Littlewood circle method together with a refined shifting…