Two coins A and B are tossed N1 and N2 times, respectively. Denote by M1 (M2) the total number of heads (tails) and X the number of heads from coin A. It is well known that conditional on the Mi and Ni, X has a noncentral hypergeometric distribution which depends only on the odds ratio θ between the success probabilities of the two coins. This model is commonly used in the analysis of a single ...

In many applications, the available data come from a sampling scheme that causes loss of information in terms of left truncation. In some cases, in addition to left truncation, the data are weakly dependent. In this paper we are interested in deriving the asymptotic normality as well as a Berry-Esseen type bound for the kernel density estimator of left truncated and weakly dependent data.

In this note we give a completely different proof to a functional inequality established by Ismail and Laforgia for the survival function of the gamma distribution and we show that the inequality in the question is in fact the so-called new-is-better-than-used property, which arises in economic theory. Moreover, we extend this result to arbitrary reliability functions and we present a new simpl...

We derive uniform and non–uniform error bounds in the normal approximation under a general dependence assumption. Our method is tailor made for dynamic time series models employed in the econometric literature but it is also applicable for many other dependent processes. Neither stationarity nor any smoothness conditions of the underlying distributions are required. If the introduced weak depen...

By Louis H.Y. Chen † and Qi-Man Shao ‡ National University of Singapore and University of Oregon §¶ We establish both uniform and non-uniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper than many existing ones in the literature. The proofs cou...

In this paper, the authors investigate the Berry-Esseen bounds of weighted kernel estimator for a nonparametric regression model based on linear process errors under a LNQD random variable sequence. The rate of the normal approximation is shown as [Formula: see text] under some appropriate conditions. The results obtained in the article generalize or improve the corresponding ones for mixing de...

We obtain estimates for the Kolmogorov distance to appropriately chosen gaussians, of linear functions $$\begin{aligned} \sum _{i\in [n]^d} \theta _i X_i \end{aligned}$$ random tensors $$\varvec{X}=\langle X_i:i\in [n]^d\rangle $$ which are symmetric and exchangeable, whose entries have bounded third moment vanish on diagonal indices. These expressed in terms intrinsic (and easily computable) p...