Related papers: Optimal e-values for testing the mean of a bounded…
Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a…
In this article we derive the best possible upper bound for $E[\max{X_i}-\min_i{X_i}]$ under given means and variances on $n$ random variables $X_i$. The random vector $(X_1,...,X_n)$ is allowed to have any dependence structure, provided $E…
Replicability issues -- referring to the difficulty or failure of independent researchers to corroborate the results of published studies -- have hindered the meaningful progression of science and eroded public trust in scientific findings.…
Optimal reinsurance when Value at Risk and expected surplus is balanced through their ratio is studied, and it is demonstrated how results for risk-adjusted surplus can be utilized. Simplifications for large portfolios are derived, and this…
We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error…
Given two populations from which independent binary observations are taken with parameters $p_1$ and $p_2$ respectively, estimators are proposed for the relative risk $p_1/p_2$, the odds ratio $p_1(1-p_2)/(p_2(1-p_1))$ and their logarithms.…
We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including genomics and medical imaging, it is natural to assume that…
Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained…
We theoretically and computationally compare the strength of the three main upper bounds from the literature on the optimal value of the Edge-Weighted Maximum Clique Problem (EWMCP). We provide a set of instances for which the ratio between…
In this paper, we provide extended convolution bounds for the Fr\'{e}chet problem and discuss related implications in quantitative risk management. First, we establish a new form of inequality for the Range-Value-at-Risk (RVaR). Based on…
We use the exact finite sample likelihood and statistical decision theory to answer questions of ``why?'' and ``what should you have done?'' using data from randomized experiments and a utility function that prioritizes safety over…
Various events in the nature, economics and in other areas force us to combine the study of extremes with regression and other methods. A useful tool for reducing the role of nuisance regression, while we are interested in the shape or…
Equivalence testing compares the hypothesis that an effect $\mu$ is large against the alternative that it is negligible. Here, `large' is classically expressed as being larger than some `equivalence margin' $\Delta$. A longstanding problem…
In the paper the maximum and the minimum of the ratio of the difference of the arithmetic mean and the geometric mean, and the difference of the power mean and the geometric mean of $n$ variables, are studied. A new optimization argument…
Motivated by the construction of tractable robust estimators via convex relaxations, we present conditions on the sample size which guarantee an augmented notion of Restricted Eigenvalue-type condition for Gaussian designs. Such a notion is…
We consider the problem of mean estimation under quantization and adversarial corruption. We construct multivariate robust estimators that are optimal up to logarithmic factors in two different settings. The first is a one-bit setting,…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of the ES scheme from…
This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable,…
Running machine learning algorithms on large and rapidly growing volumes of data is often computationally expensive, one common trick to reduce the size of a data set, and thus reduce the computational cost of machine learning algorithms,…