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Unified framework for inference using confidence sets for the CDF

Abstract Number:

3795 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Paper 

Participants:

Siddhaarth Sarkar (1), Arun Kuchibhotla (2)

Institutions:

(1) Carnegie Mellon University, N/A, (2) Carnegie Mellon University, Pittsburgh, PA

Co-Author:

Arun Kuchibhotla  
Carnegie Mellon University

First Author:

Siddhaarth Sarkar  
Carnegie Mellon University

Presenting Author:

Siddhaarth Sarkar  
Carnegie Mellon University

Abstract Text:

Traditional statistical inference methods often face limitations due to their reliance on strict assumptions. Moreover, these methods are typically tailored to specific assumptions, restricting their adaptability to any alternative set of assumptions. In this work, we present a unified framework for deriving confidence intervals for various functionals (e.g., mean or median) under a broad class of user-specified assumptions (e.g., finite variance or tail behavior). Leveraging confidence sets for cumulative distribution functions (CDFs), this framework offers a principled and flexible inference strategy, reducing dependence on stringent assumptions and providing applicability in diverse contexts.

Keywords:

Confidence intervals|Assumption-lean inference|Confidence sets for CDF|Semi-infinite programming|Non-parametric methods|

Sponsors:

IMS

Tracks:

Statistical Methodology

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