Related papers: Improved Catoni-Type Confidence Sequences for Esti…

Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known…

We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the \textit{sequential predictive conformal inference} (\texttt{SPCI}). We specifically account for the nature that time…

We study properties of confidence intervals (CIs) for the difference of two Bernoulli distributions' success parameters, $p_x - p_y$, in the case where the goal is to obtain a CI of a given half-width while minimizing sampling costs when…

Stochastic approximation (SA) is a classical approach for stochastic convex optimization. Previous studies have demonstrated that the convergence rate of SA can be improved by introducing either smoothness or strong convexity condition. In…

There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…

This note extends the results of classical parametric statistics like Fisher and Wilks theorem to modern setups with a high or infinite parameter dimension, limited sample size, and possible model misspecification. We consider a special…

We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…

The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…

This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for $t$ statistics and coverage error expansions for interval estimators that (i)…

Let $\Phi$ be a random $k$-CNF formula on $n$ variables and $m$ clauses, where each clause is a disjunction of $k$ literals chosen independently and uniformly. Our goal is to sample an approximately uniform solution of $\Phi$ (or…

We consider the Gittins index for a normal distribution with unknown mean $\theta$ and known variance where $\theta$ has a normal prior. In addition to presenting some monotonicity properties of the Gittins index, we derive an approximation…

Compressed Counting (CC) [22] was recently proposed for estimating the ath frequency moments of data streams, where 0 < a <= 2. CC can be used for estimating Shannon entropy, which can be approximated by certain functions of the ath…

In this paper, we study the problem of estimating uniformly well the mean values of several distributions given a finite budget of samples. If the variance of the distributions were known, one could design an optimal sampling strategy by…

Bootstrap smoothed (bagged) estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. Efron, 2014, derived a widely applicable formula for a delta method approximation to the standard…

We propose a novel framework for analyzing convergence rates of stochastic optimization algorithms with adaptive step sizes. This framework is based on analyzing properties of an underlying generic stochastic process, in particular by…

We propose a consistent estimator of sharp bounds on the variance of the difference-in-means estimator in completely randomized experiments. Generalizing Robins [Stat. Med. 7 (1988) 773-785], our results resolve a well-known identification…

Motivated by the pressing need for efficient optimization in online recommender systems, we revisit the cascading bandit model proposed by Kveton et al. (2015). While Thompson sampling (TS) algorithms have been shown to be empirically…

The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced…

Nonparametric two-stage procedures to construct fixed-width confidence intervals are studied to quantify uncertainty. It is shown that the validity of the random central limit theorem (RCLT) accompanied by a consistent and asymptotically…

Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…