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
 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
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
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
Ann. Probab. 15, (1987), 1395-1418, with Jim Kuelbs and Jorge Samur.
Universal asymptotic normality for conditionally trimmed
Stat. Prob. Lett. 2, (1988), 9-15, with Jim Kuelbs.
A universal law of the iterated logarithm for trimmed and
Springer Lect. Notes in Math 1391, (1989), 82-98.
The asymptotic distribution of self-normalized censored sums
Ann. Probab 18, (1990), 1284-1341, with Jim Kuelbs
and Daniel C. Weiner.
The asymptotic distribution of magnitude-winsorized sums via
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
Ann. Probab. 20, (1992), 455-483, with Daniel C. Weiner.
Asymptotic behavior of self-normalized trimmed sums: nonnormal
J. Theoret. Probab. 5 (1992), 169-196 with Daniel C. Weiner.
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.
The multidimensional central limit theorem for arrays normed
by affine transformations
Ann. Probab. 9, (1981), 611-623, with Michael
Affine normability of partial sums of i.i.d. random vectors:
Z. Wahrscheinlichkeitstheorie 69, (1985), 479-505,
with Michael J. Klass.
Operator stable laws: series representations and domains of normal
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
Z. Wahrscheinlichkeitstheorie 64, (1983), 157-165, with
Max infinitely divisible and max stable sample continuous
Probab. Theor. and Relat. Fields 87, (1990), 139-165,
with Evarist Gine and Pirooz Vatan.
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
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
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
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
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:
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
Probab. Lett. 24 (1995), 121-132, with Yongzhao Shao.
On a distribution-free test of fit for continuous distribution
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
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
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.
Probability in Banach Spaces, 8
Probability Series, vol. 30 (1992), Birkhauser, with Richard Dudley and
Progress in Probability Series,
Vol. 43 (1998), Birkhauser, with Ernst Eberlein and Michel Talagrand.