Related papers: Statistical inference for piecewise normal distrib…
For an unknown continuous distribution on a real line, we consider the approximate estimation by the discretization. There are two methods for the discretization. First method is to divide the real line into several intervals before taking…
In this paper, we develop interval estimation methods for means of bounded random variables based on a sequential procedure such that the sampling is continued until the sample sum is no less than a prescribed threshold.
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
We consider a non-proportional hazards model where the regression coefficient is not constant but piecewise constant. Following Andersen and Gill (1982), we know that a knowledge of the changepoint leads to a relatively straightforward…
A confidence distribution is a distribution for a parameter of interest based on a parametric statistical model. As such, it serves the same purpose for frequentist statisticians as a posterior distribution for Bayesians, since it allows to…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in medical research. Unfortunately that confidence interval has a poor coverage probability: it is significantly smaller…
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…
Traditional statistical inference in cluster randomized trials typically invokes the asymptotic theory that requires the number of clusters to approach infinity. In this article, we propose an alternative conformal causal inference…
We examine the problem of construction of confidence intervals within the basic single-parameter, single-iteration variation of the method of quasi-optimal weights. Two kinds of distortions of such intervals due to insufficiently large…
We consider interval estimation of the difference between two binomial proportions. Several methods of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly…
This note points out how confidence interval estimates for standard deviation transform into confidence interval estimates for the power of F-tests at fixed alternative means. An application is shown for the test of a two-sided hypothesis…
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…
In this article, we consider the problem of constructing the confidence interval and testing hypothesis for the common coefficient of variation (CV) of several normal populations. A new method is suggested using the concepts of generalized…
In econometrics, many parameters of interest can be written as ratios of expectations. The main approach to construct confidence intervals for such parameters is the delta method. However, this asymptotic procedure yields intervals that may…
This paper concerns the construction of confidence intervals in standard seroprevalence surveys. In particular, we discuss methods for constructing confidence intervals for the proportion of individuals in a population infected with a…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…