International Statistical Review

Regression Analysis with a Stochastic Design Variable

Hakan S. Sazak,, Moti L. Tiku, and M. Qamarul Islam

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Abstract

In regression models, the design variable has primarily been treated as a nonstochastic variable. In numerous situations, however, the design variable is stochastic. The estimation and hypothesis testing problems in such situations are considered. Real life examples are given.

Article information

Source
Internat. Statist. Rev., Volume 74, Number 1 (2006), 77-88.

Dates
First available in Project Euclid: 29 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.isr/1143654388

Zentralblatt MATH identifier
1131.62060

Keywords
Stochastic design Non-normality Modified likelihood Least squares Correlation coefficient Hypothesis testing

Citation

Sazak,, Hakan S.; Tiku, Moti L.; Qamarul Islam, M. Regression Analysis with a Stochastic Design Variable. Internat. Statist. Rev. 74 (2006), no. 1, 77--88. https://projecteuclid.org/euclid.isr/1143654388


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References

  • [1] Abramowitz, M. & Stegun, I.A. (1965). Handbook of Mathematical Functions. New York: Dover.
  • [2] Barnett, V.D. (1966). Evaluation of the maximum likelihood estimators when the likelihood equation has multiple roots. Biometrika, 53, 151-165.
  • [3] Bhattacharyya, G.K. (1985). The asymptotics of maximum likelihood and related estimators based on type II censored data. J. Amer. Stat. Assoc., 80, 398-404.
  • [4] Daniel, W.W. (1978). Applied Nonparametric Statistics. Boston: Houghton Mifflin Company.\
  • [5] Gayen, A.K. (1951). The frequency distribution of the product moment correlation coefficient in random samples from non-normal universes. Biometrika, 38, 219-231.
  • [6] Hamilton, L.C. (1992). Regression With Graphics. California: Brooks/Cole Publishing Campany.
  • [7] Hutchinson, T.P. & Lai, C.D. (1990). Continuous Bivariate Distributions Emphasising Applications. Adelaide: Rumsby Scientific.
  • [8] Islam, M.Q., Tiku, M.L. & Yildirim, F. (2001). Non-normal regression, I: Skew distributions. Commun. Statist.-Theory Meth., 30, 993-1020.
  • [9] Islam, M.Q. & Tiku, M.L. (2004). Multiple linear regression model under non-normality. Commun. Statist.-Theory Meth., 33, 2443-2467.
  • [10] Lee, A.F.S., Kapadia, C.H. & Dwight, B.B. (1980). On estimating the scale parameter of the Rayleigh distribution from doubly censored samples. Statist. Hefte, 21, 14-29.
  • [11] Puthenpura, S. & Sinha, N.K. (1986). Modified maximum likelihood method for the robust estimation of system parameters from noisy data. Automatica, 22, 231-235.
  • [12] Sazak, H.S. (2003). Estimation and Hypothesis Testing in Stochastic Regression. Ph.D. Thesis: Middle East Technical University, Ankara (December).
  • [13] Schneider, H. (1986). Truncated and Censored Samples from Normal Populations. New York: Marcel Dekker.
  • [14] Senoglu, B. & Tiku, M.L. (2002). Linear contrast in experimental design with non-identical error distributions. Biometrical J., 44, 359-374.
  • [15] Tiku, M.L. (1967). Estimating the mean and standard deviation from a censored normal sample. Biometrika, 54, 155-165.
  • [16] Tiku, M.L. (1989). Modified maximum likelihood estimation. In Encylopedia of Statistical Sciences, Eds. S. Kotz and N.L. Johnson, Supplement Volume. New York: John Wiley.
  • [17] Tiku, M.L. & Suresh, R.P. (1992). A new method of estimation for location and scale parameters. J. Statist. Plann. Inf., 30, 281-292.
  • [18] Tiku, M.L. & Vaughan, D.C. (1997). Logistic and nonlogistic density functions in binary regression with nonstochastic covariates. Biometrical J., 39, 883-898.
  • [19] Tiku, M.L. & Akkaya, A.D. (2004). Robust Estimation and Hypothesis Testing. New Delhi: New Age International (P) Ltd., Publishers.
  • [20] Tiku, M.L., Tan, W.Y. & Balakrishnan, N. (1986). Robust Inference. New York: Marcel Dekker.
  • [21] Tiku, M.L., Wong, W.K. & Bian, G. (1999). Time series models with asymmetric innovations. Commun. Statist.-Theory Meth., 28, 1331-1360.
  • [22] Tiku, M.L., Islam, M.Q. & Selcuk, A. (2001). Non-normal regression, II. Symmetric distributions. Commun. Statist.-Theory Meth., 30, 1021-1045.
  • [23] Vaughan, D.C. (1992). On the Tiku-Suresh method of estimation. Commun. Statist.-Theory Meth., 21, 451-469.
  • [24] Vaughan, D.C. (2002). The Generalized Secant Hyperbolic distribution and its properties. Commun. Statist.-Theory Meth., 31, 219-238.
  • [25] Vaughan, D.C. & Tiku, M.L. (2000). Estimation and hypothesis testing for a non-normal bivariate distribution with applications. J. Mathematical and Computer Modelling, 32, 53-67.