Related papers: Moderate deviations for a nonparametric estimator …
Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We…
We propose nonparametric estimation of divergence measures between continuous distributions. Our approach is based on a plug-in kernel- type estimators of density functions. We give the uniform in bandwidth consistency for the proposal…
We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which is possibly correlated with the returns of the diffusion…
Doubly protected estimators are widely used for estimating the population mean of an outcome Y from a sample where the response is missing in some individuals. To compensate for the missing responses, a vector X of covariates is observed at…
We study the problem of estimating the mean of a random vector in $\mathbb{R}^d$ based on an i.i.d.\ sample, when the accuracy of the estimator is measured by a general norm on $\mathbb{R}^d$. We construct an estimator (that depends on the…
We propose and study three confidence intervals (CIs) centered at an estimator that is intentionally biased to reduce mean squared error. The first CI simply uses an unbiased estimator's standard error; compared to centering at the unbiased…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
In the present paper, we consider the Pearson chi-square statistic defined on a finite alphabet which is assumed to dynamically vary as the sample size increases, and establish its moderate deviation principle.
Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…
Constructing distribution-free confidence intervals for the median, a classic problem in statistics, has seen numerous solutions in the literature. While coverage validity has received ample attention, less has been explored about interval…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
The Moderate Deviations Principle (MDP) is well-understood for sums of independent random variables, worse understood for stationary random sequences, and scantily understood for random fields. An upper bound for a new class of random…
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…
This note provides a tool to infer moderate deviations principles for specific random variables from deviations principles for their Hubbard-Stratonovich transforms.
The present manuscript is concerned with component-wise estimation of the positive power of ordered restricted standard deviation of two normal populations with certain restrictions on the means. We propose several improved estimators under…
We study the basic task of mean estimation in the presence of mean-shift contamination. In the mean-shift contamination model, an adversary is allowed to replace a small constant fraction of the clean samples by samples drawn from…
We prove that moderate deviations for empirical measures for countable nonhomogeneous Markov chains hold under the assumption of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chains in Ces\`aro…
Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and…
The coefficient of variation (CV) is commonly used to measure relative dispersion. However, since it is based on the sample mean and standard deviation, outliers can adversely affect the CV. Additionally, for skewed distributions the mean…
The era of big data is coming, and evidence-based medicine is attracting increasing attention to improve decision making in medical practice via integrating evidence from well designed and conducted clinical research. Meta-analysis is a…