Semi-Supervised Linear Regression

We study a regression problem where for some part of the data we observe both label variable (Y) and predictors (X), while other only are given. Such arises, example, when observations costly may require skilled human agent. When conditional expectation E[Y|X] is not exactly linear, one can consider best linear approximation to expectation, which be estimated consistently by least-square estimates (LSE). The latter depends on labeled data. suggest improved alternative LSE that use also unlabeled Our estimation method easily implemented has simply described asymptotic properties. new asymptotically dominate usual standard procedures under certain non-linearity condition E[Y|X]; otherwise, they equivalent. performance estimator small sample size investigated in an extensive simulation study. A real example inferring homeless population used illustrate methodology.