On the geometry of F, Wald, LR, and LM tests in linear regression models

Siniksaran E.

STATISTICS, cilt.39, sa.4, ss.287-301, 2005 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 4
  • Basım Tarihi: 2005
  • Doi Numarası: 10.1080/02331880500178521
  • Dergi Adı: STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.287-301
  • İstanbul Üniversitesi Adresli: Hayır

Özet

In this article, we examine F, Wald, LR, and LM test statistics in the linear regression model using vector geometry. These four statistics are expressed as a function of one random variable-the angle between the vectors of unrestricted and restricted residuals. The exact and nominal sampling distributions of this angle are derived to illuminate some facts about the four statistics. Alternatively, we offer that the angle itself can be used as a test statistic. A Mathematica program is also written to carry out the approach.