1 / 15

Statistical Inference from Small Samples

. Speakers:. Professor Konstantinos Fokianos, Department of Mathematics and Statistics, University of Cyprus. ?The Density Ratio Model and Its applications."Professor Jana Jureckova, Department of Probability and Statistics, Charles University, Prague, ?Estimators and their score functions".Pro

aurorette
Download Presentation

Statistical Inference from Small Samples

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Statistical Inference from Small Samples In honor of Professor Abram Kagan, who is celebrating his 70th birthday

    2. Speakers: Professor Konstantinos Fokianos, Department of Mathematics and Statistics, University of Cyprus. “The Density Ratio Model and Its applications.” Professor Jana Jureckova, Department of Probability and Statistics, Charles University, Prague, “Estimators and their score functions”. Professor Abram Kagan, Department of Mathematics (Statistics Program), University of Maryland. "An identity for the Fisher information and Mahalanobis distance" Professor Lev Klebanov, Department of Probability and Statistics, Charles University, Prague, "N-distances and their applications to genomic”. Professor Zinoviy Landsman, Department of Statistics, University of Haifa, “Exponential dispersion models: second order optimal estimation of mean.” Professor Ernst Presman, Central Economics and Mathematics Institute, Academy of Sciences of Russia, "Randomly Evolving Graphs and Gittins Type Index Theorem“. Professor Yosef Rinott, Department of Statistics, Hebrew University, “Some probability inequalities and games." Professor Marco Scarsini, Department of Economics, Luiss Rome and HEC Paris. “Stochastic order relations and lattices of probability measures “ Professor Shelley Zacks, Department of Mathematical Sciences, Binghamton University, "Sequential Estimation of the Odds of Two Independent Sequences of Bernoulli trials.“

    3. Zinoviy Landsman, Department of Statistics, Actuarial Research Center, University of Haifa Phone: 972+(0)4+8249003, Internal: 3003 e-mail: landsman@stat.haifa.ac.il Ehud Makov, Department of Statistics, Actuarial Research Center, University of Haifa Phone: 972+(0)4+8249620, Internal: 3620              IBM: 972+(0)4+8288284/5 e-mail: makov@stat.haifa.ac.il Program and organizing Committee:

    4. Schedule: 9:00- 9:30 Reception. 9:30-9:45 Zinoviy Landsman. Opening.. 9:45-10:00 Udi Makov. Welcome speech. Section 1: Chair Shaul Bar-Lev. 10:00-10:30 Shelley Zacks. 10:30-11:00 Konstantinos Fokianos. 11:00-11:15 Coffee break. 11:15-11:45 Jana Jureckova. 11:45-12:15 Zinoviy Landsman. 12:15-13:30 Lunch. Section 2: Chair David Perry. 13:30-14:00 Ernst Presman. 14:00-14:30 Yosef Rinott. 14:30-14:45 Coffee break. 14:45-15:15 Marco Scarsini. 15:15-15:45 Abram Kagan.

    5. Location:

    6. Sponsors: The President, University of Haifa The Rector, University of Haifa Faculty of Social Sciences Actuarial Research Center Caesarea Rothschild Institute

    7. Speaker: Konstantinos Fokianos Title: The Density Ratio Model and Its Applications The density ratio model is specified by assuming that the log-likelihood of two unknown densities is of some parametric form. The model has been extended to cover multiple sample problems while its theoretical properties have been investigated using large sample theory.  A main application of the density ratio model is testing whether two, or more, distributions are equal. We review some work in this area and show how the methodology associated with the density ratio model can be extended to small sample problems.

    8. Speaker: Jana Jureckova. Title: Estimators and their score functions. We shall consider characterizations of the score functions in the location and linear regression models by means of a constant regression to a maximal invariant.These results have various interesting applications to equivariant, asymptotically linear estimators. Moreover, the score function of a statistic Sn can be expressed as a conditional expectation of the score function of the sample, given Sn; also this phenomenon has various interesting consequences, e.g. it leads to a local expansion of a power of a test. It turns out that some (e.g. rank) tests of ? =?0 against two-sided alternatives may not be locally unbiased, unless the basic distribution is symmetric.

    9. Speaker: Abram Kagan Title: An identity for the Fisher information and Mahalanobis distance. An observable random vector X is related to an unobservable categorical random variable Y with P(Y = i) = pi by Pi(A) = P(X ? A|Y = i), i = 1, … , k. Assuming the distributions Pi having a common covariance matrix, elegant identities are presented that connect the matrix of Fisher information in Y on the parameters p1,…, pk, the matrix of linear information in X, and the Mahalanobis distances between the pairs of P's. Since the parameters are not free, the information matrices are singular and the technique of generalized inverses is used. It is a joint work with Bing Li of PennState University.

    10. Speaker: Lev Klebanov Title: "N-distances and their apllications to genomic". We introduce a wide class of distances between probability distributions. The class is based on the notation of negative definite kernel on a set of probability measures. Each distance from this class generates multidimensional two-sample distribution free test in multidimensional (or Hilbert) space. We give also some application to the search of differentially expressed gene combinations.

    11. Speaker: Zinoviy Landsman Title: Exponential dispersion models: second order optimal estimation of the mean. The talk is devoted to the second order (s. o.) minimax improvement in the estimation of the mean value of the Exponential Dispersion Family (EDF). The necessary and sufficient condition for the possibility of such an improvement, for a unbounded space of mean values, is obtained. As a result of the joint work with S. Bar-Lev and D. Bshouty, the s. o. estimation theory for regularly varying at zero and infinite variance functions of EDF is developed . The broadly popular Tweedie class of distributions fits well in this theory.

    12. Speaker: Yosi Rinott Title : Some probability inequalities and games. I will discuss some inequalities related to the dependence structure of finitely exchangeable random variables and some games with strategies determined by such inequalities.

    13. Speaker: Marco Scarsini Title: Stochastic order relations and lattices of probability measures We study various partially ordered spaces of probability measures and we determine which of them are lattices. This has important consequences for optimization problems with stochastic dominance constraints. In particular we show that the space of probability measures on R is a lattice under most of the known partial orders, whereas the space of probability measures on Rd typically is not. Nevertheless, some subsets of this space, defined by imposing strong conditions on the dependence structure of the measures, are lattices.

    14. Speaker: Shelley Zacks Title: Sequential Estimation of the Odds of Two Independent Sequences of Bernoulli trials. We develop the exact distribution of the stopping variable of a sequential procedure that was originally given by Robbins and Siegmund (1974). The stopping variable was designed for estimating the log-odds in a sequence of Bernoulli trials. Using our exact distribution of the stopping variable, we also give explicit formulae for the expected value and mean-squared-error for the estimator of the odds at stopping. An alternative two-stage procedure is then given and some of its important characteristics are exactly evaluated. It is shown that if the probability of success p is not too small or too large, the two-stage procedure is nearly as efficient as the purely sequential procedure. The results of this paper are then applied for designing an appropriate stopping time in a reliability experiment for estimating the ratio of the mean time between failures of two independent systems with exponential life times (joint work with N. Mukhopadhyay).

    15. Accommodations: Nof Hotel, Haifa 101 Hanassi Ave  (Central Carmel) Haifa 34642 Israel http://travel.yahoo.com/p-hotel-325590-nof_hotel-i

More Related