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The “Paper of the Month” for February 2018 is selected to be W. Hoeffding’s 1948 paper “A Class of Statistics with Asymptotically Normal Distribution” where he introduced the concept of U-statistics and built much of the heavy-duty machineries. It was published on The Annals of Mathematical Statistics Vol. 19, No. 3 (1948), pp. 293-325.
For further information about this paper, please check Recommendation Note prepared by the recommender of “Paper of the Month” Professor Nitis Mukhopadhyay.
December 2017–January 2018
Controlling the probability of falsely rejecting the null hypothesis is critical for valid and meaningful statistical analysis. But how should this probability be defined and calculated when there are multiple, simultaneous hypotheses? For many years, this question was mostly investigated in the analysis of variance (ANOVA) setting, in which the number of comparisons is typically small or moderate. Until 1995, the common approach to this problem was to control the family-wise error rate (FWER) which ensures that the probability of falsely rejecting at least one of the hypotheses is smaller than a user-specified bound. However, the advent of high-throughput methods, such as in genetics, resulted in a much larger number of simultaneous hypotheses and rendered the FWER approach impractical, in the sense that it was too stringent and lacked power to reject any hypothesis.
In 1995, Benjamini and Hochberg published their breakthrough paper “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing” in which they defined the False Discovery Rate (FDR) as the expected proportion of falsely rejected hypotheses, out of the total number of rejected hypotheses. The paper proposed a very simple procedure to estimate the FDR, and showed that indeed, the procedure controls the FDR at the desired level. This approach enabled significant advances in many areas, and is particularly useful in this age of “Big Data”.
The paper appeared in the Journal of the Royal Statistical Society, Series B, Vol. 57, No. 1. (1995), pp. 289-300. For additional reading, we also suggest reading about the q-value in the paper “A direct approach to false discovery rates“, by John Storey, which appeared in 2002, in the Journal of the Royal Statistical Society, Series B, 64: 479-498.
Notes Preparer: Haim Bar
Once a month during the academic year our faculty will select a paper which we encourage our students to read and discuss. Papers featured in this section should be generally understood by graduate students, and will be selected either because of their impact, or historical value, or because they contain a useful (perhaps overlooked) techniques or results.
The inaugural “Paper of the Month” (November 2017) was selected to be Brad Efron’s paper titled “Bootstrap Methods: Another Look at the Jackknife”, published in 1979 in the Annals of Statistics (Vol. 7, No. 1, pages 1-26). It is hard to overstate the impact of this paper. It allows researchers to construct confidence intervals in many settings, even when there is no closed-form derivation of the standard deviation.
A glance at Efron’s Google scholar page shows that this work was already cited tens of thousands of times. In his column in the IMS Bulletin from November 17, 2016, Professor Xiao-Li Meng included this paper among his five selected “Nobel-Prize (NP) Worthy i.i.d Ideas in Statistics” and wrote: “[the bootstrap] certainly has made many researchers’ lives much easier”, and that it “has literally generated an industry of research on proving when it works, when it doesn’t, and how to make it work when its vanilla version fails.” For example, we may refer to the paper “Two Guidelines for Bootstrap Hypothesis Testing” by Peter Hall and Susan R. Wilson (Biometrics, Vol. 47, No. 2 (Jun., 1991), pp. 757-762)
Notes Preparer: Haim Bar