Updatable Estimation in Generalized Linear Models with Missing Response

TL;DR

This paper introduces an online updatable inverse probability weighting method for generalized linear models with missing responses, enabling real-time estimation with theoretical guarantees and comparable performance to batch methods.

Contribution

It proposes a novel two-step online updating algorithm for UIPW estimation in streaming data, relaxing data batch constraints and achieving oracle properties.

Findings

Estimator is consistent and asymptotically normal.

Performs comparably to batch learners in simulations.

Applicable to streaming data with missing responses.

Abstract

This paper develops an updatable inverse probability weighting (UIPW) estimation for the generalized linear models with response missing at random in streaming data sets. A two-step online updating algorithm is provided for the proposed method. In the first step we construct an updatable estimator for the parameter in propensity function and hence obtain an updatable estimator of the propensity function; in the second step we propose an UIPW estimator with the inverse of the updating propensity function value at each observation as the weight for estimating the parameter of interest. The UIPW estimation is universally applicable due to its relaxation on the constraint on the number of data batches. It is shown that the proposed estimator is consistent and asymptotically normal with the same asymptotic variance as that of the oracle estimator, and hence the oracle property is obtained. The finite sample performance of the proposed estimator is illustrated by the simulation and real data analysis. All numerical studies confirm that the UIPW estimator performs as well as the batch learner.