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To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
Confidence interval of mean is often used when quoting statistics. The same rigor is often missing when quoting percentiles and tolerance or percentile intervals. This article derives the expression for confidence in percentiles of a sample…
Consider testing multiple hypotheses in the setting where the p-values of all hypotheses are unknown and thus have to be approximated using Monte Carlo simulations. One class of algorithms published in the literature for this scenario…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
When the target parameter for inference is a real-valued, continuous function of probabilities in the $k$-sample multinomial problem, variance estimation may be challenging. In small samples or when the function is nondifferentiable at the…
We consider models for which it is important, early in processing, to estimate some variables with high precision, but perhaps at relatively low rates of recall. If some variables can be identified with near certainty, then they can be…
Given p independent normal populations, we consider the problem of estimating the mean of those populations, that based on the observed data, give the strongest signals. We explicitly condition on the ranking of the sample means, and…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often…
Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when the number of components $p$ is of the same asymptotic order as the sample…
A hypothesis testing and an interval estimation are studied for the common mean of several lognormal populations. Two methods are given based on the concept of generalized p-value and generalized confidence interval. These new methods are…
In capture-recapture experiments, individual covariates may be subject to missing, especially when the number of times of being captured is small. When the covariate information is missing at random, the inverse probability weighting method…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
One-sided confidence intervals are presented for the average of non-identical Bernoulli parameters. These confidence intervals are expressed as analytical functions of the total number of Bernoulli games won, the number of rounds and the…
While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…
As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant…
The mid-p-value is a proposed improvement on the ordinary p-value for the case where the test statistic is partially or completely discrete. In this case, the ordinary p-value is conservative, meaning that its null distribution is larger…
Motivated by the questions of risk assessment in climatology (temperature change in North America) and medicine (impact of statin usage and COVID-19 on hospitalized patients), we address the problem of estimating the set in the domain of a…
We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…
For randomized controlled trials to be conclusive, it is important to set the target sample size accurately at the design stage. Comparing two normal populations, the sample size calculation requires specification of the variance other than…