A1279
Title: Sufficient dimension reduction meets two-sample regression estimation
Authors: Masayuki Hirukawa - Ryukoku University (Japan) [presenting]
Di Liu - StataCorp (United States)
Artem Prokhorov - University of Sydney (Australia)
Abstract: When conducting regression analysis using a dataset of anonymous surveys, researchers often face the situations in which important regressors are unavailable. Suppose that there is yet another dataset that contains the missing regressors as well as other variables that overlap across the two datasets. In this environment, regression coefficients may still be estimated consistently by combining data. The plug-in least squares (PILS) has been proposed to do that and its attractive properties in finite samples when compared to other available methods have been demonstrated. However, this estimator attains the parametric convergence rate only if the number of overlapping variables is three or less. To mitigate the curse of dimensionality, the scope of PILS is extended by assuming that the conditional expectation of each missing regressor given the overlapping variables takes the form of a single-index model with an unknown link function. Because the index coefficients are estimated through sufficient dimension reduction (SDR), the new estimator is referred to as PILS-SDR. PILS-SDR is robust to heterogeneity in the underlying population and allows for both continuous and binary missing regressors. It is asymptotically normal with the parametric convergence rate. Monte Carlo simulations confirm desirable finite-sample properties of PILS-SDR, and a real data example from the wage modelling illustrates empirical relevance of PILS-SDR.
