A0701
Title: High dimensional LASSO variable selection for correlated covariates
Authors: Kaimeng Zhang - Chonnam National University (Korea, South) [presenting]
Chi Tim Ng - Hang Seng University of Hong Kong (Hong Kong)
Abstract: A regression model is considered that regress the response against the idiosyncratic factors obtained from the factor analysis of the covariates. Such a model is particularly useful in the high-dimensional variable selection problems in certain econometrics applications where all covariates are correlated due to systematic economic factors. In such cases, it is shown both theoretically and empirically that the usual penalized regression of the response against the covariates tends to select either all or none of the covariates. On the contrary, the proposed hybrid approach of factor analysis and penalized regression can select relevant covariates consistently under $p=O(e^n)$ and other mild conditions on the factor loading matrix, where $p$ and $n$ are the number of covariates and the sample size respectively. To illustrate the ideas, two empirical data analysis examples are considered, (i) the gross domestic production of a chosen country against capital inputs and labor inputs of all countries and (ii) the stock returns of a chosen stock against the trading volumes of all stocks in the financial market.
