Related papers: Statistical inference for piecewise normal distrib…
This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…
In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it…
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…
The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
We study nonasymptotic (finite-sample) confidence intervals for treatment effects in randomized experiments. In the existing literature, the effective sample sizes of nonasymptotic confidence intervals tend to be looser than the…
Estimating the mode of a unimodal distribution is a classical problem in statistics. Although there are several approaches for point-estimation of mode in the literature, very little has been explored about the interval-estimation of mode.…
This paper utilizes the modified signed log-likelihood ratio method for the problem of inference about the common coefficient of variation in several independent normal populations. This method is applicable for both the problem of…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
In this paper, we consider the problem of constructing confidence interval for the correlation coefficient in a bivariate normal distribution. For this problem, we found fifteen approaches in literatures. Also, we have proposed a…
Confidence intervals are central to statistical inference as a tool to evaluate the type I error risk at a given significance level. We devise a method to construct confidence intervals using a single run of a permutation test. This…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Post-selection inference consists in providing statistical guarantees, based on a data set, that are robust to a prior model selection step on the same data set. In this paper, we address an instance of the post-selection-inference problem,…
The current standard for confidence interval construction in the context of a possibly misspecified model is to use an interval based on the sandwich estimate of variance. These intervals provide asymptotically correct coverage, but…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…