Related papers: Jackknife Variance Estimation for H\'ajek-Dominate…
Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is…
We study inference on scalar-valued pathwise differentiable targets after adaptive data collection, such as a bandit algorithm. We introduce a novel target-specific condition, directional stability, which is strictly weaker than previously…
This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…
We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
In Genome-Wide Association Studies (GWAS), heritability is defined as the fraction of variance of an outcome explained by a large number of genetic predictors in a high-dimensional polygenic linear model. This work studies the asymptotic…
Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these…
Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical…
Westling and Carone (2020) proposed a framework for studying the large sample distributional properties of generalized Grenander-type estimators, a versatile class of nonparametric estimators of monotone functions. The limiting distribution…
We study the implications of including many covariates in a first-step estimate entering a two-step estimation procedure. We find that a first order bias emerges when the number of \textit{included} covariates is "large" relative to the…
We analyze bias correction methods using jackknife, bootstrap, and Taylor series. We focus on the binomial model, and consider the problem of bias correction for estimating $f(p)$, where $f \in C[0,1]$ is arbitrary. We characterize the…
We study cluster-robust inference for logistic regression (logit) models. Inference based on the most commonly-used cluster-robust variance matrix estimator (CRVE) can be very unreliable. We study several alternatives. Conceptually the…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
We find that, in a linear model, the James-Stein estimator, which dominates the maximum-likelihood estimator in terms of its in-sample prediction error, can perform poorly compared to the maximum-likelihood estimator in out-of-sample…
Let $(X_{n,t})_{t=1}^{\infty}$ be a stationary absolutely regular sequence of real random variables with the distribution dependent on the number~$n$. The paper presents sufficient conditions for the asymptotic normality (for $n\to\infty$…
This paper investigates Frequentist consistency properties of the posterior distributions constructed via Generalized Variational Inference (GVI). A number of generic and novel strategies are given for proving consistency, relying on the…
Cross validation (CV) and the bootstrap are ubiquitous model-agnostic tools for assessing the error or variability of machine learning and statistical estimators. However, these methods require repeatedly re-fitting the model with different…