72 citations · 231 across the 61 of their papers we have counts for
66 papers
On the L{é}vy concentration function of Gaussian quadratic forms with applications to second order U-statistics
Abhimanyu Choudhary, Arun Kumar Kuchibhotla
We provide an upper-bound for the L{é}vy concentration function: where is a weighted sum…
Berry-Esseen bounds for multivariate martingale difference sequences in the Kolmogorov distance
Weichen Wu, Dung Le, Arun Kumar Kuchibhotla +1
We derive new Gaussian approximations for finite martingale difference sequences in with respect to the Kolmogorov distance. Under appropriate conditions, our bounds…
On a Probability Inequality for Order Statistics with Applications to Bootstrap, Conformal Prediction, and more
Manit Paul, Arun Kumar Kuchibhotla
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.''…
Sharp Debiasing for Smooth Functional Estimation in Banach Spaces
Woonyoung Chang, Arun Kumar Kuchibhotla
This paper studies the estimation of smooth functionals of a mean parameter for a distribution on a general Banach space. We propose a cross-fitted…
Time-uniform conformal and PAC prediction
Kayla E. Scharfstein, Arun Kumar Kuchibhotla
Given that machine learning algorithms are increasingly being deployed to aid in high stakes decision-making, uncertainty quantification methods that wrap around these black box mo…
Statistical Properties of Rectified Flow
Gonzalo Mena, Arun Kumar Kuchibhotla, Larry Wasserman
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, althoug…
Inference for quantile-parametrized families via CDF confidence bands
Srijan Chattopadhyay, Siddhaarth Sarkar, Arun Kumar Kuchibhotla
Quantile-based distribution families are an important subclass of parametric families, capable of exhibiting a wide range of behaviors using very few parameters. These parametric m…
Multiply Robust Conformal Risk Control with Coarsened Data
Manit Paul, Arun Kumar Kuchibhotla, Eric J. Tchetgen Tchetgen
Conformal Prediction (CP) has recently received a tremendous amount of interest, leading to a wide range of new theoretical and methodological results for predictive inference with…
Statistical Inference for Online Algorithms
Selina Carter, Arun K Kuchibhotla
The construction of confidence intervals and hypothesis tests for functionals is a cornerstone of statistical inference. Traditionally, the most efficient procedures - such as the…
Maximal Inequalities for Independent Random Vectors
Supratik Basu, Arun K Kuchibhotla
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric a…
Tail Bounds for Canonical -Statistics and -Processes with Unbounded Kernels
Abhishek Chakrabortty, Arun K. Kuchibhotla
In this paper, we prove exponential tail bounds for canonical (or degenerate) -statistics and -processes under exponential-type tail assumptions on the kernels. Most of the e…
Finite sample valid confidence sets of mode
Manit Paul, Arun Kumar Kuchibhotla
Estimating the mode of a unimodal distribution is a classical problem in statistics. Although there are several approaches for point-estimation of mode in the literature, very litt…
The Berry-Esseen Bound for High-dimensional Self-normalized Sums
Woonyoung Chang, Kenta Takatsu, Konrad Urban +1
This manuscript studies the Gaussian approximation of the coordinate-wise maximum of self-normalized statistics in high-dimensional settings. We derive an explicit Berry-Esseen bou…
Honest Inference for Stochastic Optimization
Kenta Takatsu, Arun Kumar Kuchibhotla
This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statist…
Doubly Robust and Efficient Calibration of Prediction Sets for Right-Censored Time-to-Event Outcomes
Rebecca Farina, Eric J. Tchetgen Tchetgen, Arun Kumar Kuchibhotla
Our objective is to construct well-calibrated prediction sets for a time-to-event outcome subject to right-censoring with guaranteed coverage. Inspired by modern conformal inferenc…
On the Missing Factor in Some Concentration Inequalities for Martingales
Arun Kumar Kuchibhotla
In this note, we improve some concentration inequalities for martingales with bounded increments. These results recover the missing factor in Freedman-style inequalities and are ne…
On the Symmetry of Limiting Distributions of M-estimators
Arunav Bhowmick, Arun Kumar Kuchibhotla
Many functionals of interest in statistics and machine learning can be written as minimizers of expected loss functions. Such functionals are called -estimands, and can be estim…
Algorithmic Forecasting of Extreme Heat Waves
Richard A. Berk, Amy Braverman, Arun Kumar Kuchibhotla
This paper provides some foundations for valid forecasting of rare and extreme heat waves through a better understanding of the similarities and differences between several consecu…
Assumption-Lean Honest Inference for -functionals
Woonyoung Chang, Arun Kumar Kuchibhotla
We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as -functionals. Our ap…
Generalized van Trees inequality: Local minimax bounds for non-smooth functionals and irregular statistical models
Kenta Takatsu, Arun Kumar Kuchibhotla
In a decision-theoretic framework, the minimax lower bound provides the worst-case performance of estimators relative to a given class of statistical models. For parametric and sem…
Inference for Median and a Generalization of HulC
Manit Paul, Arun Kumar Kuchibhotla
It is well-documented in the literature that sample splitting offers significant methodological and theoretical advantages in statistical inference. This, for example, includes cro…
Rectangular Hull Confidence Regions for Multivariate Parameters
Aniket Jain, Arun K Kuchibhotla
We introduce three notions of multivariate median bias, namely, rectilinear, Tukey, and orthant median bias. Each of these median biases is zero under a suitable notion of multivar…
Estimating the Likelihood of Arrest from Police Records in Presence of Unreported Crimes
Riccardo Fogliato, Arun Kumar Kuchibhotla, Zachary Lipton +3
Many important policy decisions concerning policing hinge on our understanding of how likely various criminal offenses are to result in arrests. Since many crimes are never reporte…
Generalized Asymptotic Limit Theory and Inference for Isotonic Regression
Soham Mallick, Siddhaarth Sarkar, Arun Kumar Kuchibhotla
Monotonicity is a natural shape constraint in nonparametric regression problems, arising for instance when predicting factory yield as a monotone function of labor hours. The widel…