摘要(英) |
Base on multiple linear regression, the statistic, Cp, is usually used to do model selection. In this thesis, we use the robust likelihood technique introduced by Royall and Tsou (2003) to construct a roubust Cp (ATp) under the normal working model. By way of simulations, ATp not only adjusts some defects on Cp, but also is better than RCp (Ronchetti and Staudte, 1994) and RTp (Sommer and Huggins, 1996) which are the other roubust Cp statistics if the normal assumption is wrong. In addition, we use two real examples to demonstate.
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參考文獻 |
[1] Hempel, F.R., Ronchetti, E. M., Rousseeuw, P.J. and Stahel, W.A. (1986), Robust Statistics: the Approach Based on Influence Functions, John Wiley,New York.
[2] Kutner, M.H, Nachtsheim, C.J., Neter, J. and Li, W. (2005), Applied Linear Statistical Models, 5th. ed, McGraw-Hill/Irwin, New York.
[3] Mallows, C.L. (1973), “Some comments on ”, Technometrics, 15, pp.661-675.
[4] Royall, R.M. and Tsou, T-S (2003), “Interpreting statistical evidence using imperfect models: Robust adjusted likelihood functions”, Journal of the Royal Statistical Society, Series B, 65, pp. 391-404.
[5] Ronchetti, E. and Staudte, R.G. (1994), “A robust version of Mallows’ ”, J. Am. Statist. Ass, 89, pp. 550-559.
[6] Sommer, S. and Huggins, R.M. (1996), “Variables selection using the Wald test and a robust ”, Journal of the Royal Statistical Society, Series C, 45, pp. 15-29.
[7] Tsou, T-S and Chien, L-C (2005), “Parametric robust tests for multiple regression parameters under generalized linear models”, Advances and Applications in Statistics, 5, pp. 51-86.
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