21 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…
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…
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…
From Isotonic to Lipschitz Regression: A New Interpolative Perspective on Shape-restricted Estimation
Kenta Takatsu, Tianyu Zhang, Arun Kumar Kuchibhotla
This manuscript bridges nonparametric smoothness-based and shape-restricted estimation, which may appear as two disjoint paradigms in the field. The proposed approach is motivated…
Berry-Esseen bounds for multivariate martingale difference sequences in the Kolmogorov distance
Weichen Wu, Dung Le, Arun Kumar Kuchibhotla +1
We derive new Gaussian approximation 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.''…