20 citations · 42 across the 13 of their papers we have counts for
14 papers
M-estimation with e-statistics
Hongjian Wang, Aaditya Ramdas
We present a theory of point estimation with e-statistics (e-values and e-processes) by introducing the "ME-estimator": the parameter that minimizes the corresponding e-statistic,…
E-values and sequential power-one tests for monotonicity and unimodality
Hongjian Wang, Aaditya Ramdas
We develop e-values and e-processes testing the null hypothesis that a distribution over nonnegative integers is monotone, and that a distribution over integers is unimodal given a…
Almost sure null bankruptcy of testing-by-betting strategies
Hongjian Wang, Shubhada Agrawal, Aaditya Ramdas
The bounded mean betting procedure serves as a crucial interface between the domains of (1) sequential, anytime-valid statistical inference, and (2) online learning and portfolio s…
Anytime-valid FDR control with the stopped e-BH procedure
Hongjian Wang, Sanjit Dandapanthula, Aaditya Ramdas
The recent e-Benjamini-Hochberg (e-BH) procedure for multiple hypothesis testing is known to control the false discovery rate (FDR) under arbitrary dependence between the input e-v…
Sharp Matrix Empirical Bernstein Inequalities
Hongjian Wang, Aaditya Ramdas
We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unk…
Testing by Betting while Borrowing and Bargaining
Hongjian Wang, Wouter M. Koolen, Aaditya Ramdas
Testing by betting has been a cornerstone of the game-theoretic statistics literature. One bets against the null hypothesis, and the accumulated wealth quantifies the evidenc…
Positive Semidefinite Matrix Supermartingales
Hongjian Wang, Aaditya Ramdas
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These a…
Time-Uniform Confidence Spheres for Means of Random Vectors
Ben Chugg, Hongjian Wang, Aaditya Ramdas
We study sequential mean estimation in . In particular, we derive time-uniform confidence spheres -- confidence sphere sequences (CSSs) -- which contain the mean of r…
Anytime-valid t-tests and confidence sequences for Gaussian means with unknown variance
Hongjian Wang, Aaditya Ramdas
In 1976, Lai constructed a nontrivial confidence sequence for the mean of a Gaussian distribution with unknown variance . Curiously, he employed both an improper (right Ha…
The extended Ville's inequality for nonintegrable nonnegative supermartingales
Hongjian Wang, Aaditya Ramdas
Following the initial work by Robbins, we rigorously present an extended theory of nonnegative supermartingales, requiring neither integrability nor finiteness. In particular, we d…
Huber-Robust Confidence Sequences
Hongjian Wang, Aaditya Ramdas
Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences f…
A unified recipe for deriving (time-uniform) PAC-Bayes bounds
Ben Chugg, Hongjian Wang, Aaditya Ramdas
We present a unified framework for deriving PAC-Bayesian generalization bounds. Unlike most previous literature on this topic, our bounds are anytime-valid (i.e., time-uniform), me…
Catoni-style confidence sequences for heavy-tailed mean estimation
Hongjian Wang, Aaditya Ramdas
A confidence sequence (CS) is a sequence of confidence intervals that is valid at arbitrary data-dependent stopping times. These are useful in applications like A/B testing, multi-…
Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance
Hongjian Wang, Mert Gürbüzbalaban, Lingjiong Zhu +2
Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy…