Related papers: Confidence intervals for average success probabili…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
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…
For a regression problem with a binary label response, we examine the problem of constructing confidence intervals for the label probability conditional on the features. In a setting where we do not have any information about the underlying…
We give a classical confidence belt construction which unifies the treatment of upper confidence limits for null results and two-sided confidence intervals for non-null results. The unified treatment solves a problem (apparently not…
For discrete-time survival data, conditional likelihood inference in Cox's hazard odds model is theoretically desirable but exact calculation is numerical intractable with a moderate to large number of tied events. Unconditional maximum…
Given a composite null hypothesis H, test supermartingales are non-negative supermartingales with respect to H with initial value 1. Large values of test supermartingales provide evidence against H. As a result, test supermartingales are an…
We connect the power of Confidence Intervals in different Frequentist methods to their reliability. We show that in the case of a bounded parameter a biased method which near the boundary has large power in testing the parameter against…
Recently there has been much interest in data that, in statistical language, may be described as having a large crossed and severely unbalanced random effects structure. Such data sets arise for recommender engines and information retrieval…
Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a…
We investigate generically applicable and intuitively appealing prediction intervals based on $k$-fold cross validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training…
This paper presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval…
We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…
In the context of selective inference, confidence envelopes for the false discoveries allow the user to select any subset of null hypotheses while having a statistical guarantee on the number of false discoveries in the selected set. Many…
Using normal approximation (NA) to construct a kernel-smoother-based confidence interval faces a fundamental challenge: the normalization makes a small estimation bias become a non-negligible inferential bias. This paper takes a different…
We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable…
Simple Monte Carlo is a versatile computational method with a convergence rate of $O(n^{-1/2})$. It can be used to estimate the means of random variables whose distributions are unknown. Bernoulli random variables, $Y$, are widely used to…
In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…
Consider a linear regression model with independent and identically normally distributed random errors. Suppose that the parameter of interest is a specified linear combination of the regression parameters. We prove that the usual…
We consider the Roe-Woodroofe construction of confidence intervals for the case of a Poisson distributed variate where the mean is the sum of a known background and an unknown non-negative signal. We point out that the intervals do not have…
A result of Chebyshev (1864) and Hoeffding1956}, on bounding an expectation of a given function with respect to a Bernoulli convolution (also called Poisson binomial law, or law of the number of successes in independent trials) with any…