Unifying Design-based Inference: A New Variance Estimation Principle

TL;DR

This paper introduces two new classes of variance estimators that do not rely on parametric assumptions, offering improved properties and a conservative approach for variance estimation in statistical inference.

Contribution

It proposes the Oblozene Chlebizky (OC) variance estimators as a novel alternative to generalized sandwich estimators, filling a 40-year gap since White (1980).

Findings

OC estimators match the expected value of generalized sandwich estimators.

The second estimator class is guaranteed conservative for variance.

Both estimators replace random matrices with nonrandom or expected matrices.

Abstract

This paper presents two novel classes of variance estimators with superior properties, in the absence of parametric or semi-parametricassumptions. The first new class of estimator is the Oblozene Chlebizky (OC) variance estimators as a novel alternative to the generalized sandwich in Paper 1 of 4. That the OC concept is unlikely to arise from other, more standard, frameworks is manifestly true in light of the 40 year lacuna since White (1980). For any member of the generalized sandwich variance estimator class, there is an OC with the same expected value. The this alternative replaces a random matrix at the center with a nonrandom one. The second type of estimator is guaranteed conservative for the variance of the estimator and is based upon a similar principle of replacing a random matrix with its expectation.