Homojen Olmayan Varyans Varsayımı Altında Ortalamaların Eşitliği için Skor ve Wald İstatistiğine Dayalı Alternatif Testler

Yıl 2020, Cilt: 1 Sayı: 1-2, 78 - 100, 30.12.2020

Sevgi Aksoy Fikri Gökpınar

https://doi.org/10.5281/zenodo.4398842

Öz

Bu çalışmada, normal dağılımın ortalamalarının eşitliği hipotezinin testi için, Skor ve Wald istatistiklerine
dayalı yeni test istatistikleri önerilmiştir. Skor ve Wald istatistikleri asimptotik olarak ki-kare dağıldığından
küçük örnek çaplarında p-değerleri yanlı çıkmaktadır. Dolayısıyla bu testler için ki-kare yaklaşımı yerine,
Hesaplamalı Yaklaşım Testi olarak adlandırılan Parametrik Bootstrap Yönteminin özel bir hali kullanılmıştır.
Bu testlerin literatür de yaygın olarak kullanılan bazı testlere göre etkinliğini değerlendirmek için
simülasyonlar yaparak deneysel I. tip hata ve güç bakımından karşılaştırmaları yapılmıştır. Bu çalışmada
Skor testine dayalı Hesaplamalı Yaklaşım Testi yaklaşımının özellikle küçük örnek çaplarında iyi sonuçlar
verdiği görülmüştür.

Anahtar Kelimeler

Hesaplamalı yaklaşım testi, Skor istatistiği, Wald istatistiği, Normal dağılım, Konum parametresi

Kaynakça

• [1] Pal, N., Lim, W. K., and Ling, C. H. (2007). A computational approach to statistical inferences. Journal of Applied Probability and Statistics, 2(1), 13–35.
• [2] Davison, A. C. and Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge: Cambridge University Press, 115-125.
• [3] Chang, C. H., Pal, N., and Lin, J. J. (2017). A Revisit to Test the Equality of Variances of Several Populations. Communications in Statistics-Simulation and Computation, 46(8), 6360-6384.
• [4] Chang, C. H. and Pal, N. (2008). A revisit to the Behren-Fisher problem: Comparison of five test methods. Communications in Statistics-Simulation and Computation, 37(6), 1064-1085.
• [5] Chang, C. H., Pal, N., Lim, W. K., and Lin, J. J. (2010). Comparing several population means:A parametric bootstrap method and its comparison with usual ANOVA F test as well as ANOM. Computational Statistics, 25(1), 71-95.
• [6] Chang, C. H., Lin, J. J., and Pal, N. (2011). Testing the equality of several gamma means: A parametric boostrap method with applications. Computational Statistics, 26(1), 55-76.
• [7] Negahdari, F., Abdollahnezhad, K., and Jafari, A. A. (2011). A comparison of hypothesis testing methods for the mean of a log-normal distribution. World Applied Sciences Journal, 12(6), 845-849.
• [8] Gokpinar, E. Y. and Gokpinar, F. (2012). A test based on the computational approach for equality of means under the unequal variance assumption. Hacettepe journal of Mathematics and Statistics, 41(4), 605-613.
• [9] Gokpinar, E. Y., Polat, E., Gokpinar, F., and Gunay, S. (2013). A new computational approach for testing equality of inverse gaussian means under heterogeneity. Hacettepe journal of Mathematics and Statistics, 42(5), 581-590.
• [10] Jafari, A. A. and Abdollahnezhada, K. (2015). Inferences on the means of two log-normal distributions; A computational approach test. Communications in Statistic-Simulation and Computation, 44(7), 1659-1672.
• [11] Abdollahnezhada, K. and Jafari, A. A. (2015). Inferences on the Parameters of Power Law Distribution. ProbStat Forum, 08, 130-139.
• [12] Gokpinar, E. Y. and Gokpinar, F. (2015). A computational approach for testing equality of coefficients of variation in k normal populations. Hacettepe journal of Mathematics and Statistics, 44 (5), 1197–1213.
• [13] Mutlu, H. T., Gökpinar, F., Gökpinar, E., Gül, H. H. and Güven, G. (2017). A new computational approach test for one-way ANOVA under heteroscedasticity. Communications in Statistics-Theory and Methods, 46(16), 8236- 8256.
• [14] Jafari, A.A. and Abdollahnezhad, K. (2017). Testing the equality means of several log-normal distributions. Communications in Statistics-Simulation and Computation, 46(3), 2311–2320.
• [15] Gokpinar, F. and Gokpinar, E. (2017). Testing the equality of several log-normal means based on a computational approach Communications in Statistics-Simulation and Computation, 46(3), 1998–2010.
• [16] Engle, R. F. (1984). Wald, likelihood ratio and Lagrange multiplier tests in econometrics. Handbook of Econometrics. (2). Amsterdam: Elsevier, 775–826.
• [17] Welch, B.L. (1951). On the comparison of several mean values: An alternative approach. Biometrica, 38, 330- 336.
• [18] Weerahandi, S. (1995). ANOVA under unequal error variances. Biometrics, 51(2), 589-599.
• [19] Krishnamoorthy, K., Lu, F. and Mathew, T. (2007). A parametric boostrap approach for ANOVA with unequal variances: Fixed and random models. Computational Statistics and Data Analysis, 51(12), 5731-5742.
• [20] Gökpınar, E., Y. and Gökpınar, F. (2012). A test based on the computational approach for equality of means under the unequal variance assumption. Hacettepe journal of Mathematics and Statistics, 41(4), 605-613.