Adjusted likelihood approach to estimate the proportion of true null hypotheses in multiple tests
Keywords:
Multiple testing, likelihood approach, false discovery ratesAbstract
A number of methods have been established to estimate the proportion true null hypotheses in multiple testing
under the assumption of independency. On other hand, the test statistics are either discrete or continuous. In this
paper, we will review an existing likelihood approach for estimating the proportion of true nulls
controlling the false discovery rates when the test statistics are continuous (see Hualing and Hanfeng, 2021). We
therefore present an extension of these method that can successfully make some improvement of the
performance. Simulation study demonstrates that the new estimator performs very well.
Downloads
References
[1]. Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control; 19(6): 716 – 723.
[2]. Cheng Y, Gao D, Tong T. 2015. Boas and variance reduction in estimating the proportion of true null hypotheses. Biostatistics; 16: 189-204.
[3]. Hualing Z, Hanfeng C. 2021. Estimating the Proportion of True Null Hypotheses: a Likelihood Approach. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences; 21(5): 2249-4626
[4]. Jiang H, Doerge R. 2008. Estimating the proportion of true null hypotheses for multiple comparisons. Cancer Informatics; 6: 26-32.
[5]. Langaas M, Lindqvist BH, Ferkingstad E. 2005. Estimating the proportion of true null hypotheses with application to DNA microarray data. J. R. Stat. Soc B; 67: 555-572.
[6]. Oluyemi O, Hanfeng C. 2016. Estimating the proportion of true null hypotheses in multiple testing problems. Journal of Probability statistics, Article ID 3937056.
[7]. Mosig MO, Lipkin E, Galina K, et al. 2001. A whole genome scan for quantitative trait loci affecting milk protein percentage in Israeli-Holstein cattle, by means of selective milk DNA pooling in a Daughter design, using an adjusted false discovery rate criterion. Genetics; 157: 1683-1698.
[8]. Nettleton D, Hwang JTG, Galdo RA, Wise RP. 2006. Estimating the number of true null hypotheses from a histogram of p-values. Journal of Agricultural, Biological, and Environmental Statistics; 11: 337-356.
[9]. Shimazaki H, Shinomoto S. 2007. A Method for Selecting the Bin Size of a Time Histogram. Neural computation; 19(6):1503-27.
[10]. Storey JD, 2002. A direct approach to false discovery rates. J. R. Stat. Soc B; 64: 479-498.
[11]. Tong T, Feng Z, Hilton JS, Zhao H. 2013. Estimating the proportion of true null hypotheses using the pattern of observed p-value. J. Appl. Stat.; 40: 1949-1964.
[12]. Wu B, Guan Z, Zhao H. 2006. Parametric and nonparametric FDR estimation revisited. Biometrics; 62: 735- 744.
[13]. Zhao H, Wu X, Zhang H, Chen H. 2012. Estimating the proportion of true null hypotheses in nonparametric exponential mixture model with application to the leukemia gene expression data. Communication in statistics-simulation and Computation; 41: 1580- 1592.