Related papers: New Edgeworth-type expansions with finite sample g…
We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…
We provide an asymptotic expansion of the maximal mean squared error (MSE) of the sample median to be attained on shrinking gross error neighborhoods about an ideal central distribution. More specifically, this expansion comes in powers of…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
Approximately unbiased tests based on bootstrap probabilities are considered for the exponential family of distributions with unknown expectation parameter vector, where the null hypothesis is represented as an arbitrary-shaped region with…
The maximum score estimator of Manski (1975) provides an elegant approach to estimate slope coefficient in binary choice models without requiring parametric assumptions on the error distribution. However, under i.i.d. sampling, it admits a…
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…
Testing the equality in distributions of multiple samples is a common task in many fields. However, this problem for high-dimensional or non-Euclidean data has not been well explored. In this paper, we propose new nonparametric tests based…
We study bootstrap inference for the $k$th largest coordinate of a normalized sum of independent high-dimensional random vectors. Existing second-order theory for maxima does not directly extend to order statistics, because the event…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
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…
Dimension is an inherent bottleneck to some modern learning tasks, where optimization methods suffer from the size of the data. In this paper, we study non-isotropic distributions of data and develop tools that aim at reducing these…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
In this paper, we consider the sphericity test for a one-sample problem under high-dimensional two-step monotone incomplete data. Existing asymptotic expansions for the null distributions of the likelihood ratio test (LRT) statistic and…
Recent years have witnessed much progress on Gaussian and bootstrap approximations to the distribution of sums of independent random vectors with dimension $d$ large relative to the sample size $n$. However, for any number of moments $m>2$…
In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work \cite{Yoshida2013}, which establishes Edgeworth…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
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 prove that certain asymptotic moments exist for some random distance expanding dynamical systems and Markov chains in random dynamical environment, and compute them in terms of the derivatives at the $0$ of an appropriate pressure…
An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.
U-statistics are a fundamental class of estimators that generalize the sample mean and underpin much of nonparametric statistics. Although extensively studied in both statistics and probability, key challenges remain: their high…