Related papers: Generalized Confidence Interval for the Common Coe…
The properties of the generalized Waring distribution defined on the non negative integers are reviewed. Formulas for its moments and its mode are given. A construction as a mixture of negative binomial distributions is also presented. Then…
In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi (1969). This solves a long-standing open problem…
We propose a novel computationally low-cost method for estimating a general predictive measure of generalised Bayesian inference. The proposed method utilises posterior covariance and provides estimators of the Gibbs and the plugin…
It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
A/B tests are typically analyzed via frequentist p-values and confidence intervals; but these inferences are wholly unreliable if users endogenously choose samples sizes by *continuously monitoring* their tests. We define *always valid*…
This paper suggests a generalized class of estimators for population mean of the qualitative study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of bias and mean square error of the…
Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment…
Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach…
Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation $\, X \sim {\cal{N}}(\mu , \, \sigma^2) \,$. Here we extend this result to obtaining 1-sample confidence…
A confidence sequence (CS) is a sequence of confidence intervals that is valid at arbitrary data-dependent stopping times. These are useful in applications like A/B testing, multi-armed bandits, off-policy evaluation, election auditing,…
In this research, inferential theory for hypothesis testing under general convex cone alternatives for correlated data is developed. While there exists extensive theory for hypothesis testing under smooth cone alternatives with independent…
This paper introduces a new version of the smoothly trimmed mean with a more general version of weights, which can be used as an alternative to the classical trimmed mean. We derive its asymptotic variance and to further investigate its…
Monte Carlo methods are used to approximate the means, $\mu$, of random variables $Y$, whose distributions are not known explicitly. The key idea is that the average of a random sample, $Y_1, ..., Y_n$, tends to $\mu$ as $n$ tends to…
We propose a general purpose confidence interval procedure (CIP) for statistical functionals constructed using data from a stationary time series. The procedures we propose are based on derived distribution-free analogues of the $\chi^2$…
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…
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…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
We consider universal inference in variance components models, focusing on settings where the parameter is near or at the boundary of the parameter set. Two cases, which are not handled by existing state-of-the-art methods, are of…
In the analysis of survey data it is of interest to estimate and quantify uncertainty about means or totals for each of several non-overlapping subpopulations, or areas. When the sample size for a given area is small, standard confidence…