Related papers: Rejoinder: The Dantzig selector: Statistical estim…

Discussion of "Statistical Inference: The Big Picture" by R. E. Kass [arXiv:1106.2895]

Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…

Discussion of "Statistical Inference: The Big Picture" by R. E. Kass [arXiv:1106.2895]

Discussion of "Statistical Inference: The Big Picture" by R. E. Kass [arXiv:1106.2895]

Discussion of "Statistical Inference: The Big Picture" by R. E. Kass [arXiv:1106.2895]

Final representation of all those measures $\mu$ for which algebraic polynomials are dense in $L_p(R, d\mu)$ is found. The weighted analogue of the Weierstrass polynomial approximation theorem and a new version of the M. Krein's theorem…

We give an elementary proof of the fact that a binomial random variable $X$ with parameters $n$ and $0.29/n \le p < 1$ with probability at least $1/4$ strictly exceeds its expectation. We also show that for $1/n \le p < 1 - 1/n$, $X$…

Comment on "Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies" [arXiv:1102.2774]

Comment on "Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies" [arXiv:1102.2774]

We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…

This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…

The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function $\Phi_{p,v}$ and investigate some of…

Modern statistical analysis often encounters high-dimensional problems but with a limited sample size. It poses great challenges to traditional statistical estimation methods. In this work, we adopt auxiliary learning to solve the…

We investigate a Bahadur-Kiefer type representation for the p-th empirical quantile corresponding to a sample of n i.i.d. random variables, when 0<p<1 is a sequence which, in particular, may tend to 0 or 1, i.e. we consider the case of…

Rejoinder on Causal Inference Through Potential Outcomes and Principal Stratification: Application to Studies with ``Censoring'' Due to Death by D. B. Rubin [math.ST/0612783]

We use methods of combinatorial number theory to prove that, for each $n>1$ and any prime $p$, some homotopy group $\pi_i(SU(n))$ contains an element of order $p^{n-1+ord_p([n/p]!)}$, where $ord_p(m)$ denotes the largest integer $\alpha$…

We introduce a joint posterior $p$-value, an extension of the posterior predictive $p$-value for multiple test statistics, designed to address limitations of existing Bayesian $p$-values in the setting of continuous model expansion. In…

We establish a recursive relation for the bipartition number $p_2(n)$ which might be regarded as an analogue of Euler's recursive relation for the partition number $p(n)$. Two proofs of the main result are proved in this article. The first…

For $A \subseteq \mathbb{N}$, the question of when $R(A) = \{a/a' : a, a' \in A\}$ is dense in the positive real numbers $\mathbb{R}_+$ has been examined by many authors over the years. In contrast, the $p$-adic setting is largely…

In this paper we have adapted Bahl and Tuteja (1991) estimator in systematic sampling using auxiliary information. Using Bedi (1996) transformation an improved estimator is also proposed under systematic sampling. The expressions of bias…