Statistical Papers

, Volume 54, Issue 3, pp 605–617 | Cite as

Testing base load with non-sample prior information on process load

Regular Article

Abstract

Inference about population parameters could be improved using non- sample prior information (NSPI) from reliable sources along with the available data. This paper studies the problem of testing the intercept parameter of a simple regression model when NSPI is available on the value of the slope. The information on the slope may have the three different scenarios: (i) unknown (unspecified), (ii) known (certain or specified), and (iii) uncertain if the suspected value is unsure, for which we define the unrestricted test (UT), restricted test (RT) and pre-test test (PTT) for the intercept parameter. The test statistics, their sampling distributions, and power functions are derived. Comparison of the power functions and size of the tests are used to search and recommend a best test. The study reveals that the PTT has a reasonable dominance over the UT and RT both in terms of achieving highest power and lowest size.

Keywords

Linear regression Test of intercept Power function Normal and bivariate Student-t distributions 

Mathematics Subject Classification

Primary 62F03 Secondary 62J05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bancroft TA (1944) On biases in estimation due to the use of the preliminary tests of singnificance. Ann Math Stat 15: 190–204MathSciNetMATHCrossRefGoogle Scholar
  2. Bancroft TA (1964) Analysis and inference for incompletely specified models involving the use of the preliminary test(s) of singnificance. Biometrics 20(3): 427–442MathSciNetMATHCrossRefGoogle Scholar
  3. Han CP, Bancroft TA (1968) On pooling means when variance is unknown. J Am Stat Assoc 63: 1333–1342MathSciNetCrossRefGoogle Scholar
  4. Judge GG, Bock ME (1978) The statistical implications of pre-test and stein-rule estimators in econoetrics. North-Holland, New YorkGoogle Scholar
  5. Kent R (2009) Energy miser-know your plants energy, Fingerprint. http://www.ptonline.com/articles/know-your-plants-energy-fingerprint. Accesed 23 May 2011
  6. Khan S (2003) Estimation of the parameters of two parallel regression lines under uncertain prior information. Biom J 44: 73–90CrossRefGoogle Scholar
  7. Khan S (2008) Shrinkage estimators of intercept parameters of two simple regression models with suspected equal slopes. Commun Stat Theory Methods 37: 247–260MATHCrossRefGoogle Scholar
  8. Khan S, Saleh AKMdE (1997) Shrinkage pre-test estimator of the intercept parameter for a regression model with multivariate Student-t errors. Biom J 39: 1–17MathSciNetCrossRefGoogle Scholar
  9. Khan S, Saleh AKMdE (2001) On the comparison of the pre-test and shrinkage estimators for the univariate normal mean. Stat Pap 42(4): 451–473MathSciNetMATHCrossRefGoogle Scholar
  10. Khan S, Hoque Z, Saleh AKMdE (2002) Improved estimation of the slope parameter for linear regression model with normal errors and uncertain prior information. J Stat Res 31(1): 51–72MathSciNetGoogle Scholar
  11. Khan S, Saleh AKMdE (2005) Estimation of intercept parameter for linear regression with uncertain non-sample prior information. Stat Pap 46: 379–394MathSciNetMATHCrossRefGoogle Scholar
  12. Khan S, Saleh AKMdE (2008) Estimation of slope for linear regression model with uncertain prior information and Student-t error. Commun Stat Theory Methods 37(16): 2564–2581MathSciNetMATHCrossRefGoogle Scholar
  13. Kotz S, Nadarajah S (2004) Multivariate t distributions and their applications. Cambridge University Press, New YorkMATHCrossRefGoogle Scholar
  14. Saleh AKMdE (2006) Theory of preliminary test and Stein-type estimation with applications. Wiley, New JerseyMATHCrossRefGoogle Scholar
  15. Saleh AKMdE, Sen PK (1978) Nonparametric estimation of location parameter after a preliminary test on regression. Ann Stat 6: 154–168MathSciNetMATHCrossRefGoogle Scholar
  16. Saleh AKMdE, Sen PK (1982) Shrinkage least squares estimation in a general multivariate linear model. Procedings of the Fifth Pannonian Symposium on Mathematical Statistics, pp 307–325Google Scholar
  17. Tamura R (1965) Nonparametric inferences with a preliminary test. Bull Math Stat 11: 38–61Google Scholar
  18. Yunus RM (2010) Increasing power of M-test through pre-testing. Unpublished PhD Thesis, University of Southern Queensland, AustraliaGoogle Scholar
  19. Yunus RM, Khan S (2008) Test for intercept after pre-testing on slope: a robust method. In: 9th Islamic Countries Conference on Statistical Sciences (ICCS-IX): Statistics in the Contemporary World: Theories, Methods and Applications, pp 81–90Google Scholar
  20. Yunus RM, Khan S (2011a) Increasing power of the test through pre-test - a robust method. Commun Stat Theory Methods 40: 581–597MathSciNetMATHCrossRefGoogle Scholar
  21. Yunus RM, Khan S (2011b) M-tests for multivariate regression model. J Nonparamatric Stat 23: 201–218MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Computing, Australian Centre for Sustainable CatchmentsUniversity of Southern QueenslandToowoombaAustralia

Personalised recommendations