Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sufficient Covariate, Propensity Variable and Doubly Robust Estimation   Statistical causal inference from observational studies often requires
adjustment for a possibly multi-dimensional variable, where dimension reduction
is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a
popular approach to such reduction. We address causal inference within Dawid's
decision-theoretic framework, where it is essential to pay attention to
sufficient covariates and their properties. We examine the role of a propensity
variable in a normal linear model. We investigate both population-based and
sample-based linear regressions, with adjustments for a multivariate covariate
and for a propensity variable. In addition, we study the augmented inverse
probability weighted estimator, involving a combination of a response model and
a propensity model. In a linear regression with homoscedasticity, a propensity
variable is proved to provide the same estimated causal effect as multivariate
adjustment. An estimated propensity variable may, but need not, yield better
precision than the true propensity variable. The augmented inverse probability
weighted estimator is doubly robust and can improve precision if the propensity
model is correctly specified.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex