Related papers: On the sample mean after a group sequential trial
In this article we have suggested an improved estimator for estimating the population mean in simple random sampling using auxiliary information under the presence of measurement errors. The mean square error (MSE) of the proposed estimator…
The use of historical controls offers a valuable alternative when traditional randomized controlled trials are not feasible. However, such approaches may introduce bias due to temporal changes in patient populations, diagnostic criteria,…
This document presents the statistical methods used to process low-level measurements in the presence of noise. These methods can be classical or Bayesian. The question is placed in the general framework of the problem of nuisance…
Debiased machine learning is a meta algorithm based on bias correction and sample splitting to calculate confidence intervals for functionals, i.e. scalar summaries, of machine learning algorithms. For example, an analyst may desire the…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
Contemporary scientific research is a distributed, collaborative endeavor, carried out by teams of researchers, regulatory institutions, funding agencies, commercial partners, and scientific bodies, all interacting with each other and…
The technique known as group averaging provides powerful machinery for the study of constrained systems. However, it is likely to be well defined only in a limited set of cases. Here, we investigate the possibility of using a `renormalized'…
We propose a new asymptotic test to assess the stationarity of a time series' mean that is applicable in the presence of both heteroscedasticity and short-range dependence. Our test statistic is composed of Gini's mean difference of local…
The choice of sample size in the context of co-primary endpoints for a randomised trial is discussed. Current guidance can leave endpoints with unequal marginal power. A method is provided to achieve equal marginal power by using the…
Treatment effect estimation is a fundamental problem in causal inference. We focus on designing efficient randomized controlled trials, to accurately estimate the effect of some treatment on a population of $n$ individuals. In particular,…
Consider $n$ independent measurements, with the additional information of the times at which measurements are performed. This paper deals with testing statistical hypotheses when $n$ is large and only a small amount of observations…
Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider…
We study optimal sample allocation between treatment and control groups under Bayesian linear models. We derive an analytic expression for the Bayes risk, which depends jointly on sample size and covariate mean balance across groups. Under…
Randomized clinical trials are the gold standard when estimating the average treatment effect. However, they are usually not a random sample from the real-world population because of the inclusion/exclusion rules. Meanwhile, observational…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.
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…
For clinical studies with continuous outcomes, when the data are potentially skewed, researchers may choose to report the whole or part of the five-number summary (the sample median, the first and third quartiles, and the minimum and…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required…