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Scargle (2000) has discussed Rosenthal and Rubin's (1978) "fail-safe number" (FSN) method for estimating the number of unpublished studies in meta-analysis. He concluded that this FSN cannot possibly be correct because a central assumption…
We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible…
We compare several confidence intervals after model selection in the setting recently studied by Berk et al. [Ann. Statist. 41 (2013) 802-837], where the goal is to cover not the true parameter but a certain nonstandard quantity of interest…
I have three goals in this article: (1) To show the enormous potential of bootstrapping and permutation tests to help students understand statistical concepts including sampling distributions, standard errors, bias, confidence intervals,…
Let $X_1, \ldots, X_n$ be some i.i.d. observations from a heavy tailed distribution $F$, i.e. such that the common distribution of the excesses over a high threshold $u_n$ can be approximated by a Generalized Pareto Distribution…
Several scientific fields including psychology are undergoing a replication crisis. There are many reasons for this problem, one of which is a misuse of p-values. There are several alternatives to p-values, and in this paper we describe a…
INTRODUCTION: Wald's, the likelihood ratio (LR) and Rao's score tests and their corresponding confidence intervals (CIs), are the three most common estimators of parameters of Generalized Linear Models. On finite samples, these estimators…
Prediction intervals are commonly used in meta-analysis with random-effects models. One widely used method, the Higgins-Thompson-Spiegelhalter prediction interval, replaces the heterogeneity parameter with its point estimate, but its…
Meta-analysis can be formulated as combining $p$-values across studies into a joint $p$-value function, from which point estimates and confidence intervals can be derived. We extend the meta-analytic estimation framework based on combined…
The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…
Suppose that X_1,X_2,...,X_n are independent and identically Bernoulli(theta) distributed. Also suppose that our aim is to find an exact confidence interval for theta that is the intersection of a 1-\alpha/2 upper confidence interval and a…
In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of…
For many causal effect parameters of interest, doubly robust machine learning (DRML) estimators $\hat{\psi}_{1}$ are the state-of-the-art, incorporating the good prediction performance of machine learning; the decreased bias of doubly…
Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…
In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a…
This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several…
In Bayesian quantile regression, the most commonly used likelihood is the asymmetric Laplace (AL) likelihood. The reason for this choice is not that it is a plausible data-generating model but that the corresponding maximum likelihood…
We study the asymptotic frequentist coverage of credible sets based on a novel Bayesian approach for a multiple linear regression model under variable selection. We initially ignore the issue of variable selection, which allows us to put a…
Classical confidence intervals after best subset selection are widely implemented in statistical software and are routinely used to guide practitioners in scientific fields to conclude significance. However, there are increasing concerns in…
We show that confidence intervals in a variance component model, with asymptotically correct uniform coverage probability, can be obtained by inverting certain test-statistics based on the score for the restricted likelihood. The results…