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Abstract:
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In the analysis of a high-dimensional data, a technique commonly used in practice is to fit univariate (i.e., predictor specific) linear models while adjusting for some of the remaining predictors. However, such univariate methods are still biased unless strong assumptions apply and multivariate approaches (i.e., penalized regression or Bayesian methods) are encouraged. The popularity of the univariate approach stems from the ease of implementation and the power of the approach if the adjustment approximation is correct. In this paper, we propose an innovative approach to performing univariate high-dimensional linear regression. Our approach considers the unknown adjustment variable (i.e., the impact of the remaining variables) as missing data and estimates the regression parameter via an implementation of a quasi-expectation-maximization (EM) algorithm. This UNivariate approach to HIgh-Dimensional linear regression via the EM algorithm (UNHIDEM) results in covariate-wide estimates of the regression parameter along with predictions and standard errors of future values. We compare the empirical properties from UNHIDEM to common techniques with simulated and real data.
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