A systematic method to deal with the interrelations of systems with multi-index quantities (random variables) is proposed. The method differs of the well-known Polykays. An application of the theoretical results here presented is the calculation of the moments of the sample variance for general populations in a direct way. The main advantage of the proposed methodology is that no conversion for...

A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice of block size allows control over the tradeoff between test power and computation time. In this respect, the B-test family combines favorable properties of p...

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier and we propose an improved estimator of the population frontier. In addition, we provide the exact distribu...

Analysis of molecular variance (AMOVA) is a widely used tool for quantifying the contribution of various levels of population structure to patterns of genetic variation. Implementations of AMOVA use permutation tests to evaluate null hypotheses of no population structure within groups and between groups. With few populations per group, between-group structure might be impossible to detect becau...

We derive the asymptotic distribution of the eigenvalues of a sample covariance matrix with distinct roots. Our theorem can accommodate the situation in which the population covariance matrix is estimated via its sample analogue as well as the more general case in which it is estimated via a √ N -consistent extremum estimator. The sample roots will have a Normal distribution in ∗Address: 2424 M...

Two-phase sampling is often used in a wide variety of surveys. Variance estimation from a two-phase sample has been a subject of active research. The re-sampling method of variance estimation has been used for this problem. However, the method confronts a challenging problem when the first phase sampling fraction is high. In the extreme (but not uncommon) case some first-phase strata are take-a...

We consider the situation in two sample testing when one variance is assumed to be known while the other variance is considered unknown. This situation arises, for example, when one is interested in comparing a standard treatment with a new treatment. Although this situation occurs relatively infrequently, our example discusses the important tool of moment matching and makes the classic two sam...