# Abram M. Kagan

## Professor

Department of Mathematics

 University of Maryland College Park, MD 20742-4015 Room 2306 phone: 1-301-405-5476 fax: 1-301-314-0827

[ Teaching | Research Areas | Publications | Student's Corner ]

I got my M. S. in Mathematics from University of Tashkent (now it is National University of Uzbekistan). Both my Ph. D. and D. Sc. in mathematical statistics are from Leningrad (now St. Petersburg) State University.
In 1965 – 1988 I was a senior researcher at the Leningrad Branch of Steklov Mathematical Institute (known by its Russian acronym LOMI), Russian Academy of Sciences.
Since April 1, 1988 I have been with Department of Mathematics (Statistics Program), University of Maryland.
My hobby since the high school was playing chess. As a high school student, I played in many official tournaments in the former Soviet Union. After a few decades break, I played in a few tournaments in the United States. My official US Chess federation rating is 2111 in regular chess and 2283 in speed chess. However, I have not played recently in tournaments so that my actual rating is probably lower. My other hobbies are swimming all the year around and downhill skiing in winter. My fervent desire is seeing my grandchildren (now aged 18, 16, 12 and 9) enjoying mountain-skiing, swimming and playing soccer.

## Teaching

### Research Areas

• Parameter Estimation
• Fisher Information
• Characterization Problems
• Sufficiency and Exponential Families
• Generalized Linear Models

### Publications

• 2016
On the structure of UMVUEs (with Ya. Malinovsky). Sankhya, Ser. A, 78 ( 2016), 124-132
• 2015
An analytic generalization of independence and identical distributiveness (with G. Szekely). Stat. Probab. Letters (2015), 7-10
• 2014
i. Partially complete sufficient statistics are jointly complete (with Ya. Malinovsky and L. Mattner). Theory Probab. Appl.,59, 3 (2014), 542-561.
• 2013
i. On the Nile problem by Sir Ronald Fisher (with Ya. Malinovsky).Electronic J. Statistics, 7 (2013), 1968-1982.
ii. Monotonicity in the sample size of the length of classical confidence intervals (with Ya. Malinovsky). Stat. Probab. Letters, 83 (2013), 78-82.
• 2012
i. Contribution to the theory of Pitman estimators (with T. Yu, A. Barron, and M. Madiman). Zapiski Nauchnukh Seminarov PDMI, 408 (2012), 245-267. (reprinted in J. Math. Sci., 199 (2014), 202-214).
• 2010
i. A class of multivariate distributions related to distributions with a Gaussian component (with L. Klebanov). IMS Collections, 7 (2010), 105-112.
• 2009
i. Geometric properties of the sample mean and vector of residuals (with T. Yu) . Statist. Probab. Letters, 79(2009), 1409-1413.
• 2008
i. An identity for the Fisher information and Mahalanobis distance (with Bing Li) . J. Statist. Plan. Inference, 138 (2008), 3950–3959.
ii. Bivariate distributions with Gaussian-like dependence structure (with S. Bar-Lev). Comm. Statistics – Theory and Methods, 38 (2008), 2669-2676
iii. Some inequalities related to the Stam inequality (with T. Yu). J. Math. Analysis, 53(2008), 195-205.
• 2007
i. Sub- and superadditivity a la Carlen of matrices related to the Fisher information (with Z. Landsman and C. R. Rao). J. Statist. Planning and Inference, 137, 291-298.
ii. A lemma on stochastic majorization and properties of the Student distribution (with A. V. Nagaev). Theory Probab. Applications, 52, no. 1.
iii. Strong decomposition of random variables (with J. Hoffman –Jorgensen, L. Pitt and L. Shepp) J. Theoret. Probab.
• 2006
i. Quasi-independence of random variables and a property of normal and gamma distributions. J. Statist. Planning and Inference, 136, 199-208.
ii. Profile sufficiency . Austrian J. Statistics, 35, 121-130.
• 2005
i. A sufficiency paradox: an insufficient statistic preserving the Fisher information (with L. Shepp). American Statistician, 59, No. 1.
ii. On estimation of a location parameter in presence of an ancillary component (with C. R. Rao). Theory Probab. and Its Applications, 50, 172-176.
iii. The structure of the UMVUEs from categorical data (with M. Konikov). Theory Probab. and Its Applications, 50, No. 3.
• 2004
i. On the maximum correlation coefficient (with W. Bryc and A. Dembo). Theory Probab. and Its Applications, 49, 191-197.
• 2003
i. Some properties and applications of the efficient Fisher score (with C. R. Rao). J. Statist. Planning and Inference, 116, 343-352.
ii. Statistical approach to some mathematical problems. Austrian J. of Statistics, 32, 71-83.
• 2002
i. Sufficiency and ancillarity in characterization problems. J. Statist. Planning and Inference, 102, 223-228.
ii. Transfer theorems in exponential families. Statist. and Probab. Letters, 57, 225-228.
iii. An inequality for the Pitman estimators related to the Stam inequality. Sankhya .A64, 282-292
• 2001
i. A discrete version of the Stam inequality and a characterization of the Poisson distribution. J. Statist. Planning and Inference, 92, 7-12.
ii. A property of linear forms of independent random variables related to uniqueness of linear structure (with R.G. Laha). J. Statist. Planning and Inference, 92, 13-20.
iii. Multivariate normal distributions, Fisher information and matrix inequalities (with P. J. Smith). Internat. J. of Mathem. Education in Science and Technology, 32, 91-96.
iv. A note on the logistic link function. Biometrika, 88, 599-601.
v. Remarks on the maximum correlation coefficient (with A. Dembo and L. Shepp). Bernoulli, 7, 343-350.
vi. Another look at the Cramer-Rao inequality. American Statistician, 55, 211-212. vii. How many moments can be estimated from a large sample? (with S. Nagaev). Statist. and Probab. Letters, 55, 99-105.
• 2000
i. An extension of Darmois-Skitovich theorem to a class of dependent random variables (with J. Wesolowski). Statist. and Probab. Letters, 47, 69-73
• 1999
i. Symmetrization of binary random variables (with C. Mallows, L. Shepp, R. Vanderbei, and Y. Vardi). Bernoulli, 5, 1013-1020.
ii. Relation between the covariance and Fisher information matrices (with Z. Landsman). Statist. and Probab. Letters, 42, 7-13.
iii. Characterization of the Weibull distribution by properties of the Fisher information under type I censoring (with I. Gertsbakh). Statist. and Probab. Letters, 42, 99-105.
iv. Characterization of the normal distribution through the power of a one-way ANOVA (with G. Letac). J. Statist. Planning and Inference, 77, 1-9.
v. Tail hypotheses in the signal plus noise model (with L. Shepp). Statist. and Probab. Letters, 43, 317-319.
• 1998
i. Some linear models are necessarily parametric (with L. Shepp). Statist. and Probab. Letters, 37, 77-80.
ii. Why the variance? (with L Shepp). Statist. and Probab. Letters
iii. A stronger version of matrix convexity as applied to functions of Hermitian matrices (with P.J. Smith). J. of Inequalities and Applications
• 1997
i. Statistical meaning of Carlen's superadditivity of the Fisher information (with Z. Landsman). Statist. and Probab. Letters, 32, 175-179.
ii. A class of polynomials with an invariance property (with V. Rohatgi). .J. Statist. Planning and Inference, 63, 215-222.
iii. Independence of the sum and absolute difference of independent random variables does not imply their normality (with R. G. Laha and V. Rohatgi). Mathem. Methods of Statist., 6, 263-265.
• 1996
i. Normality via conditional normality of linear forms (with J. Wesolowski). Statist. and Probab. Letters, 29, 229-232

### In University

Statistics Seminar Organizer, 2010 - 2015.

### In Math Community

Co-organizer of the 5th Lukacs Symposium in Probability and Statistics (Bowling Green, Spring 1995)
Co-organizer of Special Session of the Amer. Math. Soc. Regional Meeting (College Park, Spring 1997)

### Student's Corner

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