Related papers: On randomized confidence intervals for the binomia…
Based on the physical randomization of completely randomized experiments, Rigdon and Hudgens (2015) propose two approaches to obtaining exact confidence intervals for the average causal effect on a binary outcome. They construct the first…
The approximate Bernstein polynomial model, a mixture of beta distributions, is applied to obtain maximum likelihood estimates of the regression coefficients, and the baseline density and survival functions in an accelerated failure time…
We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…
In this manuscript we review two methods to construct exact confidence bounds for an unknown real parameter in a general class of discrete statistical models. These models include the binomial family, the Poisson family as well as…
There are over 55 different ways to construct a confidence respectively credible interval (CI) for the binomial proportion. Methods to compare them are necessary to decide which should be used in practice. The interval score has been…
Confidence interval of mean is often used when quoting statistics. The same rigor is often missing when quoting percentiles and tolerance or percentile intervals. This article derives the expression for confidence in percentiles of a sample…
Given a sample from a multivariate distribution $F$, the uniform random variates generated independently and rearranged in the order specified by the componentwise ranks of the original sample look like a sample from the copula of $F$. This…
We consider the problem of estimating the mean of a distribution supported by the $k$-dimensional probability simplex in the setting where an $\varepsilon$ fraction of observations are subject to adversarial corruption. A simple particular…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…
The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses…
While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…
We propose modified frequentist definitions for the determination of confidence intervals for the case of Poisson statistics. We require that 1-\beta^{'} \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha^{'}. We show that this definition…
Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the…
An iterative randomness extraction algorithm which generalized the Von Neumann's extraction algorithm is detailed, analyzed and implemented in standard C++. Given a sequence of independently and identically distributed biased Bernoulli…
New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on…
We propose modified frequentist definition for the determination of confidence intervals for the case of Poisson statistics. Namely, we require that 1-\beta' \geq \sum_{n=o}^{n_{obs}+k} P(n|\lambda) \geq \alpha'. We show that this…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…