Statistical Inference from Small Samples

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Statistical Inference from Small Samples
Workshop on
(fine properties of statistics , inequalities,
characterization , exponential families,
applications).

• In honor of Professor Abram Kagan,
  who is celebrating his 70th birthday

December 21, 2006
Speakers
Program Committee
Schedule
Location and Contacts
Sponsors
Department of Statistics Actuarial Research
Center University of Haifa
Accommodation
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.

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Program and organizing Committee

• Zinoviy Landsman,
• Department of Statistics, Actuarial
  Research Center, University of Haifa
• Phone [phone], Internal 3003e-mail
  landsman_at_stat.haifa.ac.il
• Ehud Makov,
• Department of Statistics, Actuarial
  Research Center, University of HaifaPhone
  972(0)48249620, Internal 3620            
  IBM 972(0)48288284/5e-mail
  makov_at_stat.haifa.ac.il

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Schedule

• 900- 930 Reception.
• 930-945 Zinoviy Landsman. Opening..
• 945-1000 Udi Makov. Welcome speech.
• Section 1 Chair Shaul Bar-Lev.
• 1000-1030 Shelley Zacks.
• 1030-1100 Konstantinos Fokianos.
• 1100-1115 Coffee break.
• 1115-1145 Jana Jureckova.
• 1145-1215 Zinoviy Landsman.
• 1215-1330 Lunch.
• Section 2 Chair David Perry.
• 1330-1400 Ernst Presman.
• 1400-1430 Yosef Rinott.
• 1430-1445 Coffee break.
• 1445-1515 Marco Scarsini.
• 1515-1545 Abram Kagan.

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Location
Observatory (?????) of Rabin Building University
of Haifa Mount Carmel, Haifa 31905 Tel
972-4-8240563, Fax [phone]
Contact persons
Zinoviy Landsman e-mail landsman_at_stat.haifa.ac.
il Elena Radu e-mail eradu_at_stat.haifa.ac.il
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Sponsors

• The President, University of Haifa
• The Rector, University of Haifa
• Faculty of Social Sciences
• Actuarial Research Center
• Caesarea Rothschild Institute

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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.

Speakers
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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.

Speakers
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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 ? AY 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.

Speakers
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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.

Speakers
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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.

Speakers
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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.

Speakers
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Speaker Marco Scarsini

• Title Stochastic order relations and lattices of
  probability measures
• We study various partially ordered spaces of
  probabilitymeasures 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.

Speakers
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).

Speakers
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• Accommodations
• Nof Hotel, Haifa101 Hanassi Ave  (Central
  Carmel)Haifa 34642 Israelhttp//travel.yahoo.com
  /p-hotel-325590-nof_hotel-i

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