Reliabilities of chi(2)- and F tests in Gauss-Markov model


HEKİMOĞLU Ş.

JOURNAL OF SURVEYING ENGINEERING-ASCE, cilt.125, ss.109-135, 1999 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 125 Konu: 3
  • Basım Tarihi: 1999
  • Dergi Adı: JOURNAL OF SURVEYING ENGINEERING-ASCE
  • Sayfa Sayısı: ss.109-135

Özet

Power and level breakdown points are used in robust statistics to determine the global reliability of a test. A method for calculating the finite-sample versions of these for tests such as chi(2) Or F is given here when observations have the Gauss-Markov model. Outliers are compared with the generating model using a coordinate transformation and simulated samples. Outliers are considered in two groups, namely, "doubtful" and "clear." The reliability of a chi(2)- or F test changes with the magnitude, number, and kind of outliers (i.e., random outliers or influential outliers), and also with the level of significance, alpha. The chi(2)- and F tests are generally insensitive to both doubtful and clear outliers. The chi(2) test can reliably reject the null hypothesis at alpha = 0.05, when the observations contain multiple clear random outliers, only if the magnitude of one of them is at least greater than 5 sigma. Also, the F test can reliably reject the null hypothesis at alpha = 0.05, when the observations contain multiple clear random outliers, only if the magnitude of one of them is at least greater than 6 sigma. The greater the magnitude and number of clear outliers that are contained in the observations, the more successful is the chi(2)- or F test in rejecting the null hypothesis. The reliabilities of the chi(2)- and F tests decrease as the number of unknowns increases. For this case, the power and level finite-sample breakdown points of the chi(2)- and F tests are estimated here to be approximately 1/2.