Automated selection of post‐strata using a model‐assisted regression tree estimator

Abstract

Despite having desirable properties, model‐assisted estimators are rarely used in anything but their simplest form to produce official statistics. This is due to the fact that the more complicated models are often ill suited to the available auxiliary data. Under a model‐assisted framework, we propose a regression tree estimator for a finite‐population total. Regression tree models are adept at handling the type of auxiliary data usually available in the sampling frame and provide a model that is easy to explain and justify. The estimator can be viewed as a post‐stratification estimator where the post‐strata are automatically selected by the recursive partitioning algorithm of the regression tree. We establish consistency of the regression tree estimator and a variance estimator, along with asymptotic normality of the regression tree estimator. We compare the performance of our estimator to other survey estimators using the United States Bureau of Labor Statistics Occupational Employment Statistics Survey data.

A Tutorial on Model-Assisted Estimation with Application to Forest Inventory

“…Although here we describe building the post-stratified estimator based on a single categorical variable, the strata can be created by binning a mix of quantitative and categorical variables. McConville and Toth [49] explore the theoretical properties of a post-stratified estimator where the bins are created by a regression tree. In the context of forest inventory, Pulkkinen et al [50] and Myllymäki et al [51] explore the utility of post-strata generated by regression trees.…”

Design-Unbiased Statistical Learning in Survey Sampling

“…Still, an unbiased estimator is consistent, provided its sampling variance tends to 0 under a suitable asymptotic setting. As mentioned in Section 1, below we develop stability conditions first for the delete-one RB estimator (12) under the special case of SRS and, then, under general unequal probability sampling design.…”

“…Breidt and Opsomer (2017) review the "general recipe", and give examples of many Machine Learning (ML) techniques that can be or have been embedded in the model-assisted framework, such as Kernel methods, splines or neural networks. McConville and Toth (2019) observe that many of these sophisticated estimators "are rarely ever used by statistical agencies to produce official statistics", because the underlying "models are often ill suited to the available auxiliary data. "…”

“…Toth and Eltinge (2011) extend their result, allowing for finite-population sampling in addition to the IID superpopulation model. McConville and Toth (2019) adapt the method of proof of Toth and Eltinge (2019) to establish the design-consistency of the post-stratification estimator corresponding to the sample-trained regression tree.…”

Model-assisted estimation through random forests in finite population sampling

“…In contrast, nonparametric procedures are robust to model missp-eficiation, which is a desirable property. A number of nonparametric model-assisted estimation procedures have been studied in the last two decades: local polynomial regression (Breidt and Opsomer, 2000), B-splines (Goga, 2005) and penalized B-splines , penalized splines (Breidt et al, 2005); (McConville and Breidt, 2013), neural nets (Montanari and Ranalli, 2005), generalized additive models (Opsomer et al, 2007), nonparametric additive models (Wang and Wang, 2011) and regression trees McConville and Toth, 2019). Except for neural networks, the other aforementioned nonparametric methods suffer from the curse of dimensionality.…”