ywh19860616 发表于 2011-3-21 13:09 
我的疑问在于，两幅截图中都提到了分法，即对数据进行segment，为什么第一幅图提到的分法不对，而第二幅提到的分法又是正确的，两者具体区别在哪？
We have occasionally encountered the faulty notion that something like quantile regression could be achieved by segmenting the response variable into subsets according to its unconditional distribution and then doing least squares fitting on these subsets. Clearly, this form of "
truncation on the dependent variable" would yield disastrous results in the present example. In general, such strategies are doomed to failure for all the reasons so carefully laid out in Heckman (1979). It is thus worth emphasizing that even for the extreme quantiles
all the sample observations are actively in play in the process of quantile regression fitting.
Each fit depicted in Figure 2.2 is ultimately determined by only a pair of sample points, but all n points are needed to determine which pair of points are selected. With p parameters to be estimated, p points determine the fit, but which p points depend on the entire sample.
In contrast, segmenting the sample into subsets defined
according to the conditioning covariates is always a valid option. Indeed such local fitting underlies
all non-parametric quantile regression approaches. In the most extreme cases we have p distinct cells corresponding to
different settings of the covariate vector, x, and quantile regression reduces to simply computing ordinary univariate quantiles for each of these cells. In
intermediate cases we may wish to project these cell estimates onto a more parsimonious (linear) model. See e.g. Chamberlain (1994) and Knight, Bassett, and Tam (2000).
注意红色字部分。
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