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Principal Hessian directions revisited (with discussion). (English) Zbl 0922.62057
This article explores the method of principal Hessian directions (pHd), developing new results and refinements that serve to sharpen applications. The author discussed pHd’s ability to deal with linear trends in the data along with an introductory example. This leads to some new results on the distribution of a pHd test statistic and to the conclusion that K.-C. Li’s [ibid. 87, No. 420, 1025-1039 (1992; Zbl 0765.62003)] pHd test normally should not be used in some cases. But with a modified test, pHd provides useful diagnostic methodology when applied to the residuals. Some examples are given.

62J20 Diagnostics, and linear inference and regression
62E15 Exact distribution theory in statistics
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