Evaluating the Maximum MSE of Mean Estimators with Missing Data

Manski, Charles F.; Tabord-Meehan, Max

doi:10.1177/1536867x1701700311

Cited by 5 publications

(6 citation statements)

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“…The maximum regret of the ES rule can be approximated by computing regret on a grid that discretizes the state space. An algorithm akin to that of Manski and Tabord-Meehan (2017) can be developed to perform the computations.…”

Section: Maximum Regret Of the Es Rule With Trial Datamentioning

confidence: 99%

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Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald

Manski¹

2021

ECTA

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Haavelmo (1944) proposed a probabilistic structure for econometric modeling, aiming to make econometrics useful for decision making. His fundamental contribution has become thoroughly embedded in econometric research, yet it could not answer all the deep issues that the author raised. Notably, Haavelmo struggled to formalize the implications for decision making of the fact that models can at most approximate actuality. In the same period, Wald (1939, 1945) initiated his own seminal development of statistical decision theory. Haavelmo favorably cited Wald, but econometrics did not embrace statistical decision theory. Instead, it focused on study of identification, estimation, and statistical inference. This paper proposes use of statistical decision theory to evaluate the performance of models in decision making. I consider the common practice of as‐if optimization: specification of a model, point estimation of its parameters, and use of the point estimate to make a decision that would be optimal if the estimate were accurate. A central theme is that one should evaluate as‐if optimization or any other model‐based decision rule by its performance across the state space, listing all states of nature that one believes feasible, not across the model space. I apply the theme to prediction and treatment choice. Statistical decision theory is conceptually simple, but application is often challenging. Advancing computation is the primary task to complete the foundations sketched by Haavelmo and Wald.

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Section: Maximum Regret Of the Es Rule With Trial Datamentioning

confidence: 99%

“…In this way, statistical decision theory embraces use of both correct and incorrect models to make decisions. I use prediction of a real-valued outcome to illustrate, summarizing recent work in Dominitz and Manski (2017) and Manski and Tabord-Meehan (2017).…”

Section: Introduction: Joining Haavelmo and Waldmentioning

confidence: 99%

Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald

Manski¹

2021

ECTA

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“…Monte Carlo integration methods. Manski and Tabord-Meehan (2017) give an application that will be discussed in Section 5.…”

Section: Practicalitiesmentioning

confidence: 99%

“…Computation of state-dependent expected welfare, the inner operation in problems ( 4) through ( 6), can now be accomplished numerically by Monte Carlo integration methods. Manski and Tabord-Meehan (2017) give an application that will be discussed in Section 5.…”

Section: Practicalitiesmentioning

confidence: 99%

Remarks on statistical inference for statistical decisions

Manski¹

2019

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The Wald development of statistical decision theory addresses decision making with sample data. Wald's concept of a statistical decision function (SDF) embraces all mappings of the form [data 6 decision]. An SDF need not perform statistical inference; that is, it need not use data to draw conclusions about the true state of nature. Inference-based SDFs have the sequential form [data 6 inference 6 decision]. This paper motivates inference-based SDFs as practical procedures for decision making that may accomplish some of what Wald envisioned. The paper first addresses binary choice problems, where all SDFs may be viewed as hypothesis tests. It next considers as-if optimization, which uses a point estimate of the true state as if the estimate were accurate. It then extends this idea to as-if maximin and minimax-regret decisions, which use point estimates of some features of the true state as if they were accurate. The paper primarily uses finite-sample maximum regret to evaluate the performance of inference-based SDFs. To illustrate abstract ideas, it presents specific findings concerning treatment choice and point prediction with sample data. I am grateful to

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“…Because this assessment is done before any actual sample data are drawn, does not take any data as input. Readers interested in may also be interested in the command, which computes the maximum mean squared error of user-specified point predictors of real random variables (Manski and Tabord-Meehan 2017).…”

Section: Introductionmentioning

confidence: 99%

Evaluating the maximum regret of statistical treatment rules with sample data on treatment response

Litvin

Manski

2021

The Stata Journal: Promoting communications on statistics and S

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In this article, we present the wald_tc command, which computes the maximum regret (MR) of a user-specified statistical treatment rule that uses sample data on realized treatment response (and optionally an instrumental variable) to determine a treatment choice for a population. Because the outcomes of counterfactual treatments are not observed and treatment selection in the study population may not be random, decision makers may be able only to partially identify average treatment effects. wald_tc allows users to compute the MR of a proposed statistical treatment rule under a flexible specification of the data-generating process and determines the state that generates MR.

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Evaluating the Maximum MSE of Mean Estimators with Missing Data

Cited by 5 publications

References 4 publications

Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald

Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald

Remarks on statistical inference for statistical decisions

Evaluating the maximum regret of statistical treatment rules with sample data on treatment response

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