On the Optimality of Differentiated SPR Tests of Composite Hypotheses.
On the Optimality of Sample-Based Estimates of the Expectation of the Empirical Minimizer***
We study sample-based estimates of the expectation of the function produced by the empirical minimization algorithm. We investigate the extent to which one can estimate the rate of convergence of the empirical minimizer in a data dependent manner. We establish three main results. First, we provide an algorithm that upper bounds the expectation of the empirical minimizer in a completely data-dependent manner. This bound is based on a structural result due to Bartlett and Mendelson, which relates...
On the optimality of the empirical risk minimization procedure for the convex aggregation problem
We study the performance of empirical risk minimization (ERM), with respect to the quadratic risk, in the context of convex aggregation, in which one wants to construct a procedure whose risk is as close as possible to the best function in the convex hull of an arbitrary finite class . We show that ERM performed in the convex hull of is an optimal aggregation procedure for the convex aggregation problem. We also show that if this procedure is used for the problem of model selection aggregation,...
On the optimality of the max-depth and max-rank classifiers for spherical data
The main goal of supervised learning is to construct a function from labeled training data which assigns arbitrary new data points to one of the labels. Classification tasks may be solved by using some measures of data point centrality with respect to the labeled groups considered. Such a measure of centrality is called data depth. In this paper, we investigate conditions under which depth-based classifiers for directional data are optimal. We show that such classifiers are equivalent to the Bayes...
On the optimum sequential test of two hypotheses for statistically dependent observations
On the order equivalence relation of binary association measures
Over a century of research has resulted in a set of more than a hundred binary association measures. Many of them share similar properties. An overview of binary association measures is presented, focused on their order equivalences. Association measures are grouped according to their relations. Transformations between these measures are shown, both formally and visually. A generalization coefficient is proposed, based on joint probability and marginal probabilities. Combining association measures...
On the outstanding elements and record values in the exponential and gamma populations.
Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the nk-th record value in the k-th set is made in terms of ni-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution...
On the performance of small-area estimators: fixed vs. random area parameters.
On the Performance of the Ordinary Least Squares Method under an Error Component Model.
On the Poisson difference distribution inference and applications.
On the power of an asymptotically optimal test for the case of Laplace distribution
In the paper we prove a formula for the limit of the difference between the power of the asymptotically optimal test and the power of the asymptotically most powerful test for the case of Laplace distribution.
On the Power of Nonparametric Changepoint-Tests.
On the predictability of long-range dependent series.
On the principle of equivariance: concepts and applications.
On the probability of reaching a barrier in an Erlang(2) risk process.
In this paper the process of aggregated claims in a non-life insurance portfolio as defined in the classical model of risk theory is modified. The Compound Poisson process is replaced with a more general renewal risk process with interocurrence times of Erlangian type. We focus our analysis on the probability that the process of surplus reaches a certain level before ruin occurs, χ(u,b). Our main contribution is the generalization obtained in the computation of χ(u,b) for the case of interocurrence...
On the problem of the means of weighted normal populations.
An analytical problem, which arises in the statistical problem of comparing the means of two normal distributions, the variances of which -as well as their ratio- are unknown, is well known in the mathematical statistics as the Behrens-Fisher problem. One generalization of the Behrens-Fisher problem and different aspect concerning the estimation of the common mean of several independent normal distributions with different variances are considered and one solution is proposed.
On the product of triangular random variables
We derive the probability density function (pdf) for the product of three independent triangular random variables. It involves consideration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables.
On the properties of the Generalized Normal Distribution
The target of this paper is to provide a critical review and to enlarge the theory related to the Generalized Normal Distributions (GND). This three term (position, scale shape) distribution is based in a strong theoretical background due to Logarithm Sobolev Inequalities. Moreover, the GND is the appropriate one to support the Generalized entropy type Fisher's information measure.
On the Property of Dullness of Pareto Distribution.
On the quadratic derivative of exponential probabilities
In the paper it is shown that exponential families of probabilities have the quadratic derivative of the likelihood ratio, and explicit formulas for this derivative are derived.