The Effect of Truncation on the Identifiability of Regression Coefficients
研究了因变量截断导致回归系数不可识别的条件，发现当误差分布为指数分布或双指数分布时，截断会使似然函数平坦，无法推断回归系数。
Abstract When data are truncated and hence partly unobservable, parameters identifiable under the complete observation may not be identifiable. A class of distributions is characterized, under which regression coefficients are unidentifiable by truncation of a dependent variable in the regression model. In a class of strongly unimodal densities regression coefficients are shown to be unidentifiable only when the underlying distribution is proportional to the exponential distribution in support of the truncated observation. The exponential, double exponential, and Huber's least-informative distribution for a location parameter are apparent examples of the distributions under which the unidentifiability can occur. In a more restrictive class of symmetric and strongly unimodal densities the unidentifiability arises only when the error distribution has exponential tails and the degree of truncation is at least 50%. The likelihood function becomes completely flat with respect to the regression coefficients and hence does not provide any power for the inference of the parameters here. Key Words: Exponential tailStrong unimodalityTruncated dependent variable