Related papers: Optimal e-values for testing the mean of a bounded…
Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…
The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalised…
Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the combined test, especially in high-dimensional models…
Based on a recent model of evolving viruses competing with an adapting immune system [1], we study the conditions under which a viral quasispecies can maximize its growth rate. The range of mutation rates that allows viruses to thrive is…
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…
We consider optimal designs for the Kiefer cirteria, which include the E-criterion as a particular case, and the G-criterion in random coefficients regression (RCR) models. We obtain general the Kiefer criteria for approximate designs and…
Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious…
Booth and Cox proposed the E(s^2) criterion for constructing two-level supersaturated designs. Nguyen [Technometrics 38 (1996) 69-73] and Tang and Wu [Canad. J. Statist 25 (1997) 191-201] independently derived a lower bound for E(s^2). This…
Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random…
We show that a class of optimized e-value combinations, arising from a standard construction of e-processes, remains valid even when the tuning parameter is optimized based on the data. This result holds for independent e-values, and, more…
We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we…
Given a stream of Bernoulli random variables, consider the problem of estimating the mean of the random variable within a specified relative error with a specified probability of failure. Until now, the Gamma Bernoulli Approximation Scheme…
Consider two independent exponential populations having different unknown location parameters and a common unknown scale parameter. Call the population associated with the larger location parameter as the "best" population and the…
The problem of simple $M-$ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule…
We consider the problem of robust polynomial regression, where one receives samples $(x_i, y_i)$ that are usually within $\sigma$ of a polynomial $y = p(x)$, but have a $\rho$ chance of being arbitrary adversarial outliers. Previously, it…
An important question in constructing Cross Validation (CV) estimators of the generalization error is whether rules can be established that allow "optimal" selection of the size of the training set, for fixed sample size $n$. We define the…
Testing equality of mean vectors is a very commonly used criterion when comparing two multivariate random variables. Traditional tests such as Hotelling's T-squared become either unusable or output small power when the number of variables…
Rerandomization utilizes modern computing ability to improve covariate balance while adhering to the randomization principle originally advocated by RA Fisher. Affinely invariant rerandomization has the ``Equal Percent Variance Reducing''…
The limitation of permutation tests is that they assume exchangeability. It is shown that in generalized linear models one can construct permutation tests from score statistics in particular cases. When under the null hypothesis the…
Combining the mutual information criterion with a forward feature selection strategy offers a good trade-off between optimality of the selected feature subset and computation time. However, it requires to set the parameter(s) of the mutual…