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2003 | 23 | 2 | 123-145
Tytuł artykułu

On small sample inference for common mean in heteroscedastic one-way model

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we consider and compare several approximate methods for making small-sample statistical inference on the common mean in the heteroscedastic one-way random effects model. The topic of the paper was motivated by the problem of interlaboratory comparisons and is also known as the (traditional) common mean problem. It is also closely related to the problem of multicenter clinical trials and meta-analysis. Based on our simulation study we suggest to use the approach proposed by Kenward & Roger (1997) as an optimal choice for construction of the interval estimates of the common mean in the heteroscedastic one-way model.
Rocznik
Tom
23
Numer
2
Strony
123-145
Opis fizyczny
Daty
wydano
2003
otrzymano
2003-01-09
poprawiono
2003-12-09
Twórcy
  • Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská cesta 9, 841 04 Bratislava, Slovakia
  • Institute of Measurement Science, Slovak Academy of Sciences, Dúbravská cesta 9, 841 04 Bratislava, Slovakia
autor
  • Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia
  • Mathematical Institute, Slovak Academy of Sciences, Stefánikova 49, 814 73 Bratislava, Slovakia
Bibliografia
  • [1] W.G. Cochran, Problems arising in the analysis of a series of similar experiments, Journal of the Royal Statistical Society, Supplement 4 (1937), 102-118.
  • [2] K.R. Eberhardt, C.P. Reeve and C.H. Spiegelman, A minimax approach to combining means, with practical examples, Chemometrics Intell. Lab. Systems 5 (1989), 129-148.
  • [3] W.R. Fairweather, A method of obtaining an exact confidence interval for the common mean of several normal populations, Applied Statistics 21 (1972), 229-233.
  • [4] F.A. Graybill and R.D. Deal, Combining unbiased estimators, Biometrics 3 (1959), 1-21.
  • [5] J. Hartung and K.H. Makambi, Alternative test procedures and confidence intervals on the common mean in the fixed effects model for meta-analysis, Technical Report of the Department of Statistics, University of Dortmund 2000.
  • [6] J. Hartung, A. Böckenhoff and G. Knapp, Generalized Cochran-Wald statistics in combining of experiments, Journal of Statistical Planning and Inference 113 (2003), 215-237.
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  • [8] H.K. Iyer, C.M. Wang and T. Mathew, Models and confidence intervals for true values in interlaboratory trials, Manuscript submitted for publication 2002.
  • [9] S.M. Jordan and K. Krishnamoorthy, Exact confidence intervals for the common mean of several normal populations, Biometrics 52 (1996), 77-86.
  • [10] A.N. Kackar and D.A. Harville, Approximations for standard errors of estimators of fixed and random effects in mixed linear models, Journal of the American Statistical Association 79 (1984), 853-862.
  • [11] M.G. Kenward and J.H. Roger, Small sample inference for fixed effects from restricted maximum likelihood, Biometrics 53 (1997), 983-997.
  • [12] A.I. Khuri, T. Mathew and B.K. Sinha, Statistical Tests for Mixed Linear Models, J. Wiley & Sons, New York 1998.
  • [13] R.C. Paule and J. Mandel, Consensus values and weighting factors, Journal of Research of the National Bureau of Standards 87 (5) (1982), 377-385.
  • [14] A.L. Rukhin, B.J. Biggerstaff and M.G. Vangel, Restricted maximum likelihood estimation of a common mean and the Mandel-Paule algorithm, Journal of Statistical Planning and Inference 83 (2000), 319-330.
  • [15] A.L. Rukhin and M.G. Vangel, Estimation of a common mean and weighted means statistics, Journal of the American Statistical Association 93 (441) (1998), 303-308.
  • [16] A. Savin, G. Wimmer and V. Witkovský, On Kenward-Roger confidence intervals for common mean in interlaboratory trials, Measurement Science Review 3 Section 1, (2003), 53-56. http://www.measurement.sk/.
  • [17] S.R. Searle, G. Casella and C.E. McCulloch, Variance Components, J. Wiley & Sons, New York 1992.
  • [18] K.W. Tsui and S. Weerahandi, Generalized p values in significance testing of hypotheses in the presence of nuisance parameters, Journal of the American Statistical Association 84 (1989), 602-607.
  • [19] S. Weerahandi, Generalized confidence intervals, Journal of the American Statistical Association 88 (1993), 899-905.
  • [20] S. Weerahandi, Exact Statistical Methods for Data Analysis, Springer-Verlag, New York 1995.
  • [21] G. Wimmer and V. Witkovský, Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model, Journal of Statistical Computation and Simulation 73 (2003a), 333-346.
  • [22] G. Wimmer and V. Witkovský, Consensus mean and interval estimators for the common mean, ProbaStat 2002, Submitted to Tatra Mountains Mathematical Publications, (2003b).
  • [23] V. Witkovský, On the exact computation of the density and of the quantiles of linear combinations of t and F random variables, Journal of Statistical Planning and Inference 94 (2001), 1-13.
  • [24] L.H. Yu, Y.Sun and B.K. Sinha, On exact confidence intervals for the common mean of several normal populations, Journal of Statistical Planning and Inference 81 (1999), 263-277.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1040
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