Conditional inference with a complex sampling: exact computations and Monte Carlo estimations

TL;DR

This paper introduces a method for survey population estimation using conditional inference with complex sampling, employing exact calculations and Monte Carlo simulations for improved weighting and adjustment techniques.

Contribution

It proposes using inverse conditional inclusion probabilities as weights and demonstrates exact and Monte Carlo methods for their computation in complex survey sampling.

Findings

Exact computation of conditional weights is feasible with auxiliary information.

Monte Carlo simulations effectively estimate conditional weights when auxiliary data is available.

The methods improve outlier and strata adjustment in survey analysis.

Abstract

In survey statistics, the usual technique for estimating a population total consists in summing appropriately weighted variable values for the units in the sample. Different weighting systems exit: sampling weights, GREG weights or calibration weights for example. In this article, we propose to use the inverse of conditional inclusion probabilities as weighting system. We study examples where an auxiliary information enables to perform an a posteriori stratification of the population. We show that, in these cases, exact computations of the conditional weights are possible. When the auxiliary information consists in the knowledge of a quantitative variable for all the units of the population, then we show that the conditional weights can be estimated via Monte-Carlo simulations. This method is applied to outlier and strata-Jumper adjustments.