Related papers: Cram\'er-type moderate deviation for double index …
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…
Cram\'er type moderate deviation theorems quantify the accuracy of the relative error of the normal approximation and provide theoretical justifications for many commonly used methods in statistics. In this paper, we develop a new…
We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…
We derive Cram\'{e}r type moderate deviations for stationary sequences of bounded random variables. Our results imply the moderate deviation principles and a Berry-Esseen bound. Applications to quantile coupling inequalities, functions of…
Two-sample $U$-statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Cram\'{e}r-type moderate deviation theorems for Studentized…
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 $…
We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…
Cram\'er's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimator used in statistics. In this paper, we establish self-normalized…
We establish Cram\'er type moderate deviation (MD}) results for heavy trimmed L-statistics; we obtain our results under a very mild smoothness condition on the inversion $F^{-1}$ ($F$ is the underlying distribution of i.i.d. observations)…
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 paper, we establish normalized and self-normalized Cram\'er-type moderate deviations for Euler-Maruyama scheme for SDE. As a consequence of our results, Berry-Esseen's bounds and moderate deviation principles are also obtained. Our…
In this article we establish Cram\'er type moderate deviation results for (intermediate) trimmed means $T_n=n^{-1} \sum_{i=k_n+1}^{n-m_n}X_{i:n}$, where $X_{i:n}$ -- the order statistics corresponding to the first $n$ observations of…
In this paper, we study the self-normalized Cram\a'{e}r-type moderate deviations for centered independent random variables $X_1, X_2,...$ with $0<E |X_i|^3 <\infty$. The main results refine Theorems 1.1 and 1.2 of Wang (2011), the…
We establish a Cram\'er-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation…
Let $X_1,X_2,...$ be independent random variables with zero means and finite variances, and let $S_n=\sum_{i=1}^nX_i$ and $V^2_n=\sum_{i=1}^nX^2_i$. A Cram\'{e}r type moderate deviation for the maximum of the self-normalized sums…
Let $(\xi_i,\mathcal{F}_i)_{i\geq1}$ be a sequence of martingale differences. Set $S_n=\sum_{i=1}^n\xi_i $ and $[ S]_n=\sum_{i=1}^n \xi_i^2.$ We prove a Cram\'er type moderate deviation expansion for $\mathbf{P}(S_n/\sqrt{[ S]_n} \geq x)$…
We study the Cram\'er type moderate deviation for partial sums of random fields by applying the conjugate method. The results are applicable to the partial sums of linear random fields with short or long memory and to nonparametric…
Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of…
We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when…
By using the conjugate distribution technique of Cram\'er, we obtain some expansions of large deviation probabilities for martingales with differences satisfying the conditional Bernstein's condition. The expansions are of the same order as…