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Abstract The classical multiple testing model remains an important practical area of statistics with new approaches still being developed. In this paper we develop a new multiple testing procedure inspired by a method sometimes used in a problem with a different focus. Namely, the inference after model selection problem. We note that solutions to that problem are often accomplished by making use of a penalized likelihood function. A classic example is the Bayesian information criterion (BIC) method. In this paper we construct a generalized BIC method and evaluate its properties as a multiple testing procedure. The procedure is applicable to a wide variety of statistical models including regression, contrasts, treatment versus control, change point, and others. Numerical work indicates that, in particular, for sparse models the new generalized BIC would be preferred over existing multiple testing procedures. 

The jackknife is a reliable tool for reducing the bias of a wide range of estimators. This note demonstrates that even such versatile tools have regularity conditions that can be violated even in relatively simple cases, and that caution needs to be exercised in their use. In particular, we show that the jackknife does not provide the expected reliability for bias-reduction for the sample median, because of subtle changes in behavior of the sample median as one moves between even and odd sample sizes. These considerations arose out of class discussions in a MS-level nonparametrics course. 

We discuss inference after data exploration, with a particular focus on inference after model or variable selection. We review three popular approaches to this problem: sample splitting, simultaneous inference, and conditional selective inference. For each approach, we explain how it works, and highlight its advantages and disadvantages. We also provide an illustration of these post-selection inference approaches. 

Statistical inference has strongly relied on the use of p-values to draw conclusions. For over a decade this reliance on the p-value has been questioned by researches and academics. The question of whether p-values are truly the best standard, and what other possible statistics could replace p-values l has been discussed deeply. We set out to understand the amount of variation within p-values, and to find if they really are as reliable as the frequency of their use would suggest. To answer this question, we studied a set of clinical trials over the past two years. We also aim to describe the variety of information included in drag labels, and determine whether this information conforms to FDA guidelines. We found a large variation in the presentation of clinical trial data, much of which was not in line with the guidelines of the FDA. Our findings also show that among the clinical trials we studied there is more variation among the p-values than among the estimates. From this, we can conclude that the estimates from clinical trials should hold a heavy weight in the decision of whether or not to approve the drug. This finding suggests that there is validity to the skepticism of the reliance on p-values, and that further studies need to be done to find a new, more reliable, standard in statistical inference. 

This paper illustrates how to calculate the moments and cumulants of the two-stage Mann-Whitney statistic. These results may be used to calculate the asymptotic critical values of the two-stage Mann-Whitney test. In this paper, a large amount of deductions will be showed.