Marjorie Hahn


Office: Bromfield-Pearson Building, Room 202
Phone: 72363


Research Interests

[1] Probability and stochastic processes: approximation of partial sums, central limit theorems and other weak convergence theorems in finite and infinite-dimensional spaces, empirical central limit theorems, probability in Banach spaces, isoperimetric inequalities and concentration of measure, large deviations, random sets, decoupling methods, dependence [2] Statistics: Asymptotics, approximation theorems, maximum likelihood and generalizations including the maximum product of spacings method, exponential families

Publications in Probability Grouped by Topic (partial listing):

Approximation of Partial Sums

Uniform local probability approximations: improvements on Berry-Esseen
Ann. Probab. 23, (1995), 446-463, with Michael J. Klass.
Approximation of partial sums of arbitrary i.i.d. random variables and the precision of the usual exponential upper bound
Ann. Probab. 25, No.3, (1997), 1451-1470, with Michael J. Klass.
Optimal upper and lower bounds for the upper tails of compound Poisson processes
J. Theoret. Probab. 11, No.2, (1998), 535-559, with Michael J. Klass.

Empirical or Self-Normalized Central Limit Theorems:

Distinctions between the regular and empirical central limit theories for exchangeable random variables
Progress in Probability Series, Vol. 43 (1998), 111--144, Birkhauser, with Gang Zhang.

Trimmed Sums With and Without Self-normalization:

Asymptotic normality of trimmed sums of phi-mixing random variables
Ann. Probab. 15, (1987), 1395-1418, with Jim Kuelbs and Jorge Samur.
Universal asymptotic normality for conditionally trimmed sums
Stat. Prob. Lett. 2, (1988), 9-15, with Jim Kuelbs.
A universal law of the iterated logarithm for trimmed and censored sums
Springer Lect. Notes in Math 1391, (1989), 82-98.
The asymptotic distribution of self-normalized censored sums and sums-of-squares
Ann. Probab 18, (1990), 1284-1341, with Jim Kuelbs and Daniel C. Weiner.
The asymptotic distribution of magnitude-winsorized sums via self-normalization
J. Theoret. Probab. 3, (1990), 137-168, with Jim Kuelbs and Daniel C. Weiner.
Asymptotic behavior of partial sums: A more robust approach via trimming and self-normalization
In: Sums, Trimmed Sums, and Extremes, Progress in Probability 23, (1991), 1-54, Birkhauser, with Jim Kuelbs and Daniel C. Weiner.
Asymptotic behavior of self-normalized trimmed sums: nonnormal limits
Ann. Probab. 20, (1992), 455-483, with Daniel C. Weiner.
Asymptotic behavior of self-normalized trimmed sums: nonnormal limits II
J. Theoret. Probab. 5 (1992), 169-196 with Daniel C. Weiner.

Matching Theorems:

An Exposition of Talagrand's Mini-course on Matching Theorems
In: Proceedings of the Eighth International Conference on Probability in Banach Spaces, Progress in Probability Series 30, (1992), 3-38, Birkhauser, with Yongzhao Shao.

Operator-Stable Laws:

The multidimensional central limit theorem for arrays normed by affine transformations
Ann. Probab. 9, (1981), 611-623, with Michael J. Klass.
Affine normability of partial sums of i.i.d. random vectors: a characterization
Z. Wahrscheinlichkeitstheorie 69, (1985), 479-505, with Michael J. Klass.
Operator stable laws: series representations and domains of normal attraction
J. Theoretical Probability 2, (1988), 3-36, with William N. Hudson and Jerry A. Veeh.

Stables and Max-Stables:

On stability of probability laws with univariate stable marginals
Z. Wahrscheinlichkeitstheorie 64, (1983), 157-165, with Evarist Gine.
Max infinitely divisible and max stable sample continuous processes
Probab. Theor. and Relat. Fields 87, (1990), 139-165, with Evarist Gine and Pirooz Vatan.

Random Sets:

Limit theorems for random sets: an application of probability in Banach space results
Lec. Notes in Math. 990, (1983), 112-135, with Evarist Gine and Joel Zinn.
Characterization and domains of attraction of p-stable random compact convex sets
Ann. Probab. 13, (1985), 447-468, with Evarist Gine.
The Levy-Khinchin representation for random compact convex subsets which are infinitely divisible under Minkowski addition
Z. Wahrscheinlichkeitstheorie 70, (1985), 271-287, with Evarist Gine.
M-infinitely divisible random compact convex sets
Lec. Notes in Math. 1153, (1985), 226-248, with Evarist Gine.

Central Limit Theorems in C or D:

Conditions for sample-continuity and the central limit theorem
Ann. Probab. 5, (1977), 351-360.
Sample-continuity of square-integrable processes
Ann. Probab. 5, (1977), 361-370, with Michael J. Klass.
A note on the central limit theorem for square-integrable processes
Proc. Amer. Math. Soc. 69, (1977), 331-334.
Central limit theorems in D[0,1]
Z. Wahrscheinlichkeitstheorie 44, (1978), 89-101.

Reconstruction of Laws from Projections; Radon Transform

A characterization of the families of finite-dimensional distributions associated with countably additive stochastic processes whose sample paths are in D
Z. Wahrscheinlichkeithstheorie (1978), with Lester E. Dubins.
The pointwise translation problem for the Radon transform in Banach spaces
Lect. Notes in Math. 828, (1980), 176-186, with Peter Hahn.
Distances between measures from 1-dimensional projections as implied by continuity of the inverse Radon transform
Z. Wahrscheinlichkeitstheorie 70, (1985), 361-380, with Eric Todd Quinto.

Publications In Statistics Grouped by Topic:

Spacings:

Maximum spacing estimates: A generalization and improvement of maximum likelihood estimates I
Progress in Probab. Vol. 35, Birkhauser, (1994), 417-431, with Yongzhao Shao.
Limit theorems for the logarithm of sample spacings
Statist. Probab. Lett. 24 (1995), 121-132, with Yongzhao Shao.
On a distribution-free test of fit for continuous distribution functions
Scand. J. Statist. 23,(1996), 63-73, with Yongzhao Shao.
Strong consistency of maximum product of spacings estimates with applications in nonparametrics and in estimation of unimodal densities
Ann. Inst. Statist. Math. 51(1) (1999), with Yongzhao Shao.
Maximum product of spacings method: a unified formulation with illustration of strong consistency
Illinois J. Math. 43(3) (1999), with Y. Shao.

Maximum Likelihood Estimators:

Existence and strong consistency of maximum likelihood estimates for 1-dimensional exponential families
Statist. Probab. Lett. 28, (1996), 9-21, with Weiwen Miao.
Existence of maximum likelihood estimates for multi-dimensional exponential families
Scand. J. Statist. 24, (1997), 1-16, with Weiwen Miao.

Estimation for Thick Tails:

On joint estimation of an exponent of regular variation and an asymmetry parameter for tail distributions
In: Sums, Trimmed Sums, and Extremes, Progress in Probability 30 (1991), 82-111, Birkhauser, with Daniel C. Weiner

Volumes Edited:

Probability in Banach Spaces V
Lecture Notes in Math, vol. 1153 (1985), Springer-Verlag, with Anatole Beck, Richard Dudley, Jim Kuelbs, and Michael Marcus.
Sums, Trimmed Sums and Extremes
Progress in Probability Series, vol. 23 (1991), Birkhauser, with David M. Mason and Daniel C. Weiner.
Probability in Banach Spaces, 8
Progress in Probability Series, vol. 30 (1992), Birkhauser, with Richard Dudley and Jim Kuelbs.
High-dimensional Probability
Progress in Probability Series, Vol. 43 (1998), Birkhauser, with Ernst Eberlein and Michel Talagrand.