Testing powers of the ratio of variances of two normal populations with a common mean

References

• Graybill FA, Deal RB. Combining unbiased estimators. Biometrics. 1959;15(4):543–550. doi: 10.2307/2527652
   Web of Science ®Google Scholar
• Brown LD, Cohen A. Point and confidence estimation of a common mean and recovery of inter-block information. Ann Stat. 1974;2(5):963–976. doi: 10.1214/aos/1176342817
   Web of Science ®Google Scholar
• Moore B, Krishnamoorthy K. Combining independent normal sample means by weighting with their standard errors. J Stat Comput Simul. 1997;58(2):145–153. doi: 10.1080/00949659708811827
   Web of Science ®Google Scholar
• Pal N, Lin JJ, Chang CH, et al. A revisit to the common mean problem: comparing the maximum likelihood estimator with the graybill–Deal estimator. Comput Stat Data Anal. 2007;51(12):5673–5681. doi: 10.1016/j.csda.2007.04.004
   Web of Science ®Google Scholar
• Tripathy MR, Kumar S. Equivariant estimation of common mean of several normal populations. J Stat Comput Simul. 2015;85(18):3679–3699. doi: 10.1080/00949655.2014.995658
   Web of Science ®Google Scholar
• Rukhin AL. Estimation of the common mean from heterogeneous normal observations with unknown variances. J R Stat Soc Ser B (Stat Methodol). 2017;79(5):1601–1618. doi: 10.1111/rssb.12227
   Google Scholar
• Chang CH, Pal N. Testing on the common mean of several normal distributions. Comput Stat Data Anal. 2008;53(2):321–333. doi: 10.1016/j.csda.2008.07.024
   Web of Science ®Google Scholar
• Cohen A, Sackrowitz H. Testing hypotheses about the common mean of normal distributions. J Stat Plan Inference. 1984;9(2):207–227. doi: 10.1016/0378-3758(84)90022-3
   Web of Science ®Google Scholar
• Fairweather WR. A method of obtaining an exact confidence interval for the common mean of several normal populations. J R Stat Soc Ser C Appl Stat. 1972;21(3):229–233.
   Google Scholar
• Krishnamoorthy K, Lu Y. Inferences on the common mean of several normal populations based on the generalized variable method. Biometrics. 2003;59(2):237–247. doi: 10.1111/biom.2003.59.issue-2
   PubMed Web of Science ®Google Scholar
• Li X, Williamson PP. Testing on the common mean of normal distributions using Bayesian methods. J Stat Comput Simul. 2014;84(6):1363–1380. doi: 10.1080/00949655.2012.744838
   Web of Science ®Google Scholar
• Malekzadeh A, Kharrati Kopaei M. Inferences on the common mean of several normal populations under heteroscedasticity. Comput Stat. 2018;33(3):1367–1384. doi: 10.1007/s00180-017-0789-0
   Web of Science ®Google Scholar
• Jena P, Tripathy MR, Kumar S. Point and interval estimation of powers of scale parameters for two normal populations with a common mean. Stat Pap. 2022;1–30. https://doi.org/10.1007/s00362–022–01361–5
   PubMed Web of Science ®Google Scholar
• Gelfand AE, Dey DK. On the estimation of a variance ratio. J Stat Plan Inference. 1988;19(1):121–131. doi: 10.1016/0378-3758(88)90057-2
   Web of Science ®Google Scholar
• Brown L. Inadmissibility of the usual estimators of scale parameters in problems with unknown location and scale parameters. Ann Math Stat. 1968;39(1):29–48. doi: 10.1214/aoms/1177698503
   Google Scholar
• Stein C. Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean. Ann Inst Stat Math. 1964;16(1):155–160. doi: 10.1007/BF02868569
   Web of Science ®Google Scholar
• Madi MT. On the invariant estimation of a normal variance ratio. J Stat Plan Inference. 1995;44(3):349–357. doi: 10.1016/0378-3758(94)00082-7
   Web of Science ®Google Scholar
• Brewster JF, Zidek JV. Improving on equivariant estimators. Ann Stat. 1974;2(1):21–38. doi: 10.1214/aos/1176342610
   Web of Science ®Google Scholar
• Ghosh M, Kundu S. Decision theoretic estimation of the variance ratio. Stat Decisions. 1996;14(2):161–175.
   Google Scholar
• Kubokawa T. A unified approach to improving equivariant estimators. Ann Stat. 1994;22(1):290–299. doi: 10.1214/aos/1176325369
   Web of Science ®Google Scholar
• Bobotas P, Kourouklis S. On the estimation of a normal precision and a normal variance ratio. Stat Methodol. 2010;7(4):445–463. doi: 10.1016/j.stamet.2010.01.001
   Google Scholar
• Bobotas P, Iliopoulos G, Kourouklis S. Estimating the ratio of two scale parameters: a simple approach. Ann Inst Stat Math. 2012;64(2):343–357. doi: 10.1007/s10463-010-0308-3
   Web of Science ®Google Scholar
• Kubokawa T. General dominance properties of double shrinkage estimators for ratio of positive parameters. J Stat Plan Inference. 2014;147:224–234. doi: 10.1016/j.jspi.2013.11.009
   Web of Science ®Google Scholar
• Kim DH, Kang SG, Lee WD. Noninformative priors for the normal variance ratio. Stat Pap. 2009;50(2):393–402. doi: 10.1007/s00362-007-0065-4
   Web of Science ®Google Scholar
• Sharma D, Kibria BG. On some test statistics for testing homogeneity of variances: a comparative study. J Stat Comput Simul. 2013;83(10):1944–1963. doi: 10.1080/00949655.2012.675336
   Web of Science ®Google Scholar
• Scheffé H. On the ratio of the variances of two normal populations. Ann Math Stat. 1942;13(4):371–388. doi: 10.1214/aoms/1177731535
   Google Scholar
• Nagata Y. Improvements of interval estimations for the variance and the ratio of two variances. J Japan Stat Soc Japan Issue. 1989;19(2):151–161.
   Google Scholar
• Rajić V.Ć, Stanojević J. Confidence intervals for the ratio of two variances. J Appl Stat. 2013;40(10):2181–2187. doi: 10.1080/02664763.2013.808319
   Web of Science ®Google Scholar
• Sugiura N, Gupta AK. Maximum likelihood estimates for Behrens-Fisher problem. J Japan Stat Soc Japan Issue. 1987;17(1):55–60.
   Google Scholar
• Tripathy MR, Kumar S. Estimating a common mean of two normal populations. J Stat Theory Appl. 2010;9(2):197–215.
   Google Scholar
• Diciccio TJ, Martin MA, Stern SE. Simple and accurate one-sided inference from signed roots of likelihood ratios. Canad J Stat. 2001;29(1):67–76. doi: 10.2307/3316051
   Web of Science ®Google Scholar
• Chang CH, Pal N, Lin JJ. A note on comparing several poisson means. Commun Stat Simul Comput. 2010;39(8):1605–1627. doi: 10.1080/03610918.2010.508860
   Web of Science ®Google Scholar
• Pal N, Lim WK, Ling CH. A computational approach to statistical inferences. J Appl Probab Stat. 2007;2(1):13–35.
   Google Scholar
• Tsui KW, Weerahandi S. Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J Am Stat Assoc. 1989;84(406):602–607.
   Web of Science ®Google Scholar
• Cressie N. Jackknifing in the presence of inhomogeneity. Technometrics. 1997;39(1):45–51. doi: 10.1080/00401706.1997.10485438
   Web of Science ®Google Scholar
• Heyl PR, Cook GS. The value of gravity at washington. J Res U.S. Bureau Stand. 1936;17(6):805–839. doi: 10.6028/jres.017.047
   Google Scholar
• Eberhardt KR, Reeve CP, Spiegelman CH. A minimax approach to combining means, with practical examples. Chemomet Intell Lab Syst. 1989;5(2):129–148. doi: 10.1016/0169-7439(89)80009-7
   Web of Science ®Google Scholar