BOUNDED SUPPORT IN LINEAR RANDOM COEFFICIENT MODELS: IDENTIFICATION AND VARIABLE SELECTION
研究了线性随机系数模型中当解释变量有有限支撑时的识别问题，证明了在特定条件下随机系数的均值和方差协方差可由条件矩识别，并展示了自适应LASSO在有限维和中高维下对方差协方差变量选择的一致性。
We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identification, and show that the means and the variances and covariances of the random coefficients are identified from the first two conditional moments of the response given the covariates if the support of the covariates, excluding the intercept, contains a Cartesian product with at least three points in each coordinate. We also discuss identification of higher-order mixed moments, as well as partial identification in the presence of a binary regressor. Next, we show the variable selection consistency of the adaptive LASSO for the variances and covariances of the random coefficients in finite and moderately high dimensions. This implies that the estimated covariance matrix will actually be positive semidefinite and hence a valid covariance matrix, in contrast to the estimate arising from a simple least squares fit. We illustrate the proposed method in a simulation study.