Statistics seminar - Dr Kosuke Morikawa - Iowa State University

A seminar by Dr Kosuke Morikawa from Iowa State University

Title: Semiparametric Inference under Complex Survey Designs

Abstract: Survey sampling is a classical field with a history of more than seventy years, and many inferential problems have been extensively studied. Nevertheless, a general theory of semiparametric efficiency under complex survey designs remains comparatively underdeveloped. One obstacle is dependence among sampling indicators: even simple random sampling without replacement, in which n units are selected from a finite population of size N, induces dependence among the inclusion indicators.

In the first part of this talk, I show that local asymptotic normality, convolution theorems, and semiparametric efficiency can still be developed for a broad class of non-informative complex survey designs, including simple random sampling without replacement, stratified sampling, probability-proportional-to-size sampling, rejective sampling, and cluster sampling. Under conditions that rule out excessively strong dependence, the limiting observed-data experiment has the same tangent-space geometry as a reference Poisson experiment with the same limiting first-order inclusion probabilities. Consequently, efficient influence functions and efficiency bounds can be derived using essentially the same projection arguments as under independent Poisson sampling.

In the second part, I consider informative sampling, where the inclusion probability depends on the outcome even after conditioning on observed covariates. The key idea is to treat the observed survey weight—the inverse of the inclusion probability—as a random variable rather than conditioning on it as a fixed design quantity. This perspective allows us to derive the efficient influence function and construct an estimator that attains the semiparametric efficiency bound while leaving the outcome distribution largely unrestricted.

If time permits, I will conclude with an application of survey sampling techniques to large language model evaluation, where posterior sampling learns how to allocate costly human ratings across strata.

For further information, please contact RSFAS Seminars.

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