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J. C. Chen, “Testing the Goodness of Fit of Polynomial Models via Spline Smoothing Techniques,” Statistics and Probability Letters, Vol. 19, No. 1, 1994, pp. 65-76. doi:10.1016/0167-7152(94)90070-1

has been cited by the following article:

• TITLE: On Some Procedures Based on Fisher’s Inverse Chi-Square Statistic

  AUTHORS: Kepher H. Makambi

  KEYWORDS: Values; Weighting; Linear Combination; Correlation Coefficient; Estimated Degrees of Freedom

  JOURNAL NAME: Applied Mathematics, Vol.4 No.8, July 23, 2013

  ABSTRACT: We present approximations to the distribution of the weighted combination of independent and dependent p - values, .In case that independence ofPi 's is not assumed, it is argued that the quantity A is implic-itly dominated by positive definite quadratic forms that induce a chi-square distribution. This gives way to the approximation of the associated degrees of freedom using Satterthwaite (1946) or Patnaik (1949) method. An approximation by Brown (1975) is used to estimate the covariance between the log transformed P - values. The performance of the approximations is compared using simulations. For both the independent and dependent cases, the approximations are shown to yield probability values close to the nominal level, even for arbitrary weights, ωi ’s.