TY - JOUR

T1 - Deductive derivation and turing-computerization of semiparametric efficient estimation

AU - Frangakis, Constantine E.

AU - Qian, Tianchen

AU - Wu, Zhenke

AU - Diaz, Ivan

N1 - Funding Information:
We thank the Editor, an Associate Editor, and two referees for helpful comments, and the NIH for partial financial support. The article has its seeds in part in critical discussions with Dr. Spyridon Kotsovilis on the scientific meaning of computability and insight, and has benefited by helpful discussions with Mark van der Laan, Michael Rosenblum, Daniel Scharfstein, Stijn Vansteelandt, and Kyrana Tsapkini.
Publisher Copyright:
© 2015, The International Biometric Society.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - Researchers often seek robust inference for a parameter through semiparametric estimation. Efficient semiparametric estimation currently requires theoretical derivation of the efficient influence function (EIF), which can be a challenging and time-consuming task. If this task can be computerized, it can save dramatic human effort, which can be transferred, for example, to the design of new studies. Although the EIF is, in principle, a derivative, simple numerical differentiation to calculate the EIF by a computer masks the EIF's functional dependence on the parameter of interest. For this reason, the standard approach to obtaining the EIF relies on the theoretical construction of the space of scores under all possible parametric submodels. This process currently depends on the correctness of conjectures about these spaces, and the correct verification of such conjectures. The correct guessing of such conjectures, though successful in some problems, is a nondeductive process, i.e., is not guaranteed to succeed (e.g., is not computerizable), and the verification of conjectures is generally susceptible to mistakes. We propose a method that can deductively produce semiparametric locally efficient estimators. The proposed method is computerizable, meaning that it does not need either conjecturing, or otherwise theoretically deriving the functional form of the EIF, and is guaranteed to produce the desired estimates even for complex parameters. The method is demonstrated through an example.

AB - Researchers often seek robust inference for a parameter through semiparametric estimation. Efficient semiparametric estimation currently requires theoretical derivation of the efficient influence function (EIF), which can be a challenging and time-consuming task. If this task can be computerized, it can save dramatic human effort, which can be transferred, for example, to the design of new studies. Although the EIF is, in principle, a derivative, simple numerical differentiation to calculate the EIF by a computer masks the EIF's functional dependence on the parameter of interest. For this reason, the standard approach to obtaining the EIF relies on the theoretical construction of the space of scores under all possible parametric submodels. This process currently depends on the correctness of conjectures about these spaces, and the correct verification of such conjectures. The correct guessing of such conjectures, though successful in some problems, is a nondeductive process, i.e., is not guaranteed to succeed (e.g., is not computerizable), and the verification of conjectures is generally susceptible to mistakes. We propose a method that can deductively produce semiparametric locally efficient estimators. The proposed method is computerizable, meaning that it does not need either conjecturing, or otherwise theoretically deriving the functional form of the EIF, and is guaranteed to produce the desired estimates even for complex parameters. The method is demonstrated through an example.

KW - Compatibility

KW - Deductive procedure

KW - Gateaux derivative

KW - Influence function

KW - Semiparametric estimation

KW - Turing machine

UR - http://www.scopus.com/inward/record.url?scp=84955347357&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955347357&partnerID=8YFLogxK

U2 - 10.1111/biom.12362

DO - 10.1111/biom.12362

M3 - Article

C2 - 26237182

AN - SCOPUS:84955347357

SN - 0006-341X

VL - 71

SP - 867

EP - 874

JO - Biometrics

JF - Biometrics

IS - 4

ER -