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Abstract:
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Many variable selection algorithms include variable ranking as a principle because of its scalability and efficiency in data mining. Most of the ranking methods, however, are derived from an independence assumption of the observations, which is not necessarily true in reality, and may cause some misleading results by reason of the misspecified models. But some times observations can be grouped into blocks, each block of which is independent of the other blocks. We will look into two approaches to analyze such data: the sandwich covariance matrix estimator, which works well for linear models; and a method of Tukey, which is easier and possibly more general. Here we assume the design matrix is stochastic and blocks independently follow the same distribution, under which we provide extended interpretations and asymptotical equivalence of the two approaches.
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