Department of Mathematics
PEOPLE: Faculty

Larry Goldstein

Professor of Mathematics

Contact Information
E-mail: larry@math.usc.edu
Phone: (213) 740-2405
Office: KAP 406D

LINKS
Curriculum Vitae
Faculty Profile on Departmental Website
 

Education

  • Ph.D. Mathematics, University of California, San Diego, 6/1984

Description of Research

Summary Statement of Research Interests
Professor Goldstein's research is focused on distributional approximation and Stein's method, sampling schemes in epidemiology, and optimal stopping.

Funded Research

USC Funding
  • Faculty Development Grant. The characterizing equation method for distributional approximation: Though exact calculation of probabilities in large scale random complex systems is typically difficult, or impossible, tractable approximations are provided by the characterizing equation method. , $2,500, 2009-2010  

Affiliations with Research Centers, Labs, and Other Institutions

  • Center for Applied Mathematical Sciences,http://www.usc.edu/dept/LAS/CAMS/

Conferences and Other Presentations

Conference Presentations
  • "A Gentle Introduction to Stein's Method for normal approximation", Progress in Stein's Method, Lecture/Seminar, , Singapore, National University of Singapore, Invited, Spring 2009   
  • "Bounds on the Constant in the Mean Central Limit Theorem", Progress in Stein's Method, Lecture/Seminar, , Singapore, National University of Singapore, Invited, Spring 2009   
  • "L1 bounds in normal approximation", Progress in Stein's Method, Lecture/Seminar, , Singapore, National University of Singapore, Invited, Spring 2008   
  • "A Curious Connection Between Optimal Stopping and Branching Processes", Conference in honor of Professor Ester Samuel-Cahn, Talk/Oral Presentation, , Jerusalem, Israel, Hebrew University, Jerusalem Israel, Invited, Fall 2006   
  • "Mantel-Haenszel Type Estimators and Cohort Sampling", Analysis of Complex Event History Data, Talk/Oral Presentation, , Oslo, Noway, University of Oslo, Norway, Invited, Fall 2005   
  • "Zero Biasing and Combinatorial Central Limit Theorems", Southern Califormia Probability Symposium, Talk/Oral Presentation, , Irvine, CA, Invited, Fall 2005   
  • "Counter Matching and Genetic Susceptibility to Radiation Induced Breast Cancer", Joint Meeting China Society of Probability and Statistics, Talk/Oral Presentation, , Beijing, China, Invited, Spring 2005   
Other Presentations
  • "El Método de Stein y algunas Aplicaciones", Seminar, Centro de Investigación en Matemáticas, Guanajuato, Mexico, Fall 2008   
  • "L1 bounds in normal approximation", Seminar, Luiss Guido Carli Universita, Rome, Italy, Fall 2008   
  • "Stein's method and some applications", Seminar, University of Bologna, Bologna, Italy, Fall 2008   
  • "Efficiency of the Maximum Partial Likelihood Estimator for", Probability and Statistics seminar, Department of Mathematics, USC, Spring 2008   
  • "Tentative Extensions of a Curious Connection", Statistics Seminar, Department of Mathematics, University of Rome, Rome, Italy, Spring 2007   
  • "Cohort Studies with Complex Sampling", Biostatistics Seminar, UCSD Dept. Biostatistics, La Jolla, CA, Spring 2006   
  • "Odds, Insurance, and Size Biasing in a Promotional Sweepstakes", Seminar, Series in Applied Mathematics, Department of Mathematics, University of Southern California, Spring 2006   
  • "Sampling Case Control Studies over time", Statistics Seminar, Department of Statistics, Oxford University, Oxford, UK, Fall 2005   
  • "Hierarchical Models and the Diamond Lattice", Seminar, Department of Mathematics, East China Normal University, Shanghai, Spring 2005   
  • "Zero Biasing and the Diamond Lattice", Statistics Seminar, Hebrew University of Jerusalem, Jerusalem, Israel, Spring 2005   
  • "Zero Biasing and the Diamond Lattice", Statistics Seminar, Department of Statistics, UC Berkeley, Berkeley, CA, Fall 2004   

Publications

Book
  • Chen, L., Goldstein, L., Qi-Man, S. Normal approximation by Stein's method.
Book Chapter
  • Goldstein, L., Samuel-Cahn, E. (2006). Maximizing expected value with two stage stopping rule. pp. p.1-25. USA, UK, Singapore: Random Walks, Sequential Analysis and Related Topics/World Scientific.
  • Goldstein, L., Reinert, G. (2005). Zero Biasing in One and Higher Dimensions, and Applications. (Vol. 5). pp. 1-18. USA, UK, Singapore: Institute for Mathematical Sciences Lecture Notes/ World Scientific.
Journal Article
  • Goldstein, L., Shao, Q. (2009). Berry-Esseen Bounds for Projections of Coordinate Symmetric Random Vectors. Electronic Communications in Probability. Vol. 14, pp. 474-485.
  • Goldstein, L., Penrose, M. (2009). Normal approximation for coverage models over binomial point processes. Annals of Applied Probability.
  • Goldstein, L., Rinott, Y., Scarsini, M. (2009). Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators. Bernoulli.
  • Bartroff, J., Goldstein, L., Samuel Cahn, E. (2009). Small time asymptotics of the bomber problem. Sequential Analysis.
  • Goldstein, L., Zhang, H. (2009). Efficiency of the Maximum Partial Likelihood Estimator for Nested-Case Control Sampling. Bernoulli. Vol. 15, pp. 569-597. Project Euclid
  • Goldstein, L. (2009). A Probabilistic Proof of the Lindeberg-Feller Central Limit Theorem. American Mathematical Monthly/American Mathematical Society. Vol. 116, pp. 45-60.
  • Goldstein, L., Rinott, Y. (2007). Functional BRK Inequalities, and their Duals, with Applications. Journal of Theoretical Probability. Vol. 20, pp. 275--293.
  • Goldstein, L. (2007). L^1 Bounds in Normal Approximation. Annals of Probability. Vol. 35, pp. 1888-1930.
  • Goldstein, L., Langholz, B. (2007). Cohort Sampling Schemes for the Mantel-Haenszel Estimator. Scandinavian Journal of Statistics/Blackwell Publishers. Vol. 34, pp. 137--154..
  • Goldstein, L., Samuel-Cahn, E. (2006). Optimal Two Choice Stopping on an Exponental Sequence. Sequential Analysis/Marcel Dekker. (25), pp. 351--363.
  • Goldstein, L., Xia, A. (2006). Zero Biasing and a Discrete Central Limit Theorem. Annals of Probability. Vol. 34, pp. 1782-1806.
  • Goldstein, L., Reinert, G. (2006). Total Variation Distance for Poisson Subset Numbers. Annals of Combinatorics. Vol. 10, pp. 333-341..
  • Assaf, D., Goldstein, L., Samuel Cahn, E. (2006). Maximizing expected value with two stage stopping rules.
  • Abramson, I., Goldstein, L. (2006). A Statistical Characterization of Regular Simplices. American Mathematical Monthly/American Mathematical Society. Vol. 113, pp. 750-752.
  • Goldstein, L. (2005). Berry Esseen Bounds for Combinatorial Central Limit Theorems and Pattern Occurrences, using Zero and Size Biasing. Journal of Applied Probability. Vol. 42, pp. 661-683.
  • Arratia, R., Goldstein, L., Langholz, B. (2005). Local Central Limit Theorems, the High Order Correlations of Rejective Sampling, and Applications to Conditional Logistic Likelihood Asymptotics. Annals of Statistics. Vol. 33, pp. 871-914.
  • Goldstein, L., Reinert, G. (2005). Distributional Transformations, Orthogonal Polynomials, and Stein Characterizations. Journal of Theoretical Probability. Vol. 18, pp. 185-208..
  • Goldstein, L., Assaf, D., Samuel-Cahn, E. (2004). Two Choice Optimal Stopping. Advances in Applied Probability. Vol. 36, pp. 1116-1147.
  • Goldstein, L. (2004). Normal Approximation for Hierarchical Sequences. Annals of Applied Probability. Vol. 14, pp. 1950-1969.
  • Goldstein, L., Rinott, Y. (2003). A Permutation Test for Matching. Metron - International Journal of Statistics. Vol. vol 61 (no. 3), pp. pp. 375-388.
  • Goldstein, L., Zhang, H. (2003). Information and Asymptotic Efficiency of the Case-Cohort Sampling Design in Cox's Regression Model. Journal of Multivariate Analysis/Academic Press. Vol. 85, pp. 292-317.
  • Goldstein, L., Assaf, D., Samuel-Cahn, E. (2002). Ratio Prophet Inequalities when the Mortal has Several Choices. Annals of Applied Probability. Vol. 12, pp. 972-984.
  • Goldstein, L., Langholz, B. (2001). Conditional logistic analysis of case-control studies with complex sampling. Biostatistics/Oxford University Press. Vol. 2, pp. 63-84.
  • Ghosh, S., Goldstein, L. (2000). Concentration of measures via size biased couplings. Probability Theory and Related Fields.
  • Assaf, D., Goldstein, L., Samuel-Cahn, E. (2000). An Unexpected Connection between Branching Processes and Optimal Stopping. J. Appl. Probab.. Vol. 37 (3), pp. 613-626.
  • Borgan, O., Langholz, B., Samuelsen, S. O., Goldstein, L., Pagoda, J. (2000). Exposure stratified case-cohort studies. Lifetime Data Analysis. Vol. 6, pp. 39-58.
  • Langholz, B., Thomas, D., Faucett, C., Huberman, M., Goldstein, L. (1999). Ascertainment correction in rate ratio estimation from case-sibling control studies of variable age-at-onset diseases. Biometrics. Vol. 55, pp. 1129-1136.
  • Goldstein, L., Reinert, G. (1997). Stein's Method and the Zero Bias Transformation with Application to Simple Random Sampling. Ann. Appl. Probab.. Vol. 7 (4), pp. 935--952.
  • Steel, M., Goldstein, L., Waterman, M. (1996). A central limit theorem for the parsimony length of trees. Advances in Applied Probability. Vol. 28, pp. 1051-1071.
  • Goldstein, L., Gordon, L. (1996). Asymptotics for the maximum of half-normal plots. Annals of Statistics. Vol. 24, pp. 2250-2265.
  • Goldstein, L., Rinott, Y. (1996). Multivariate normal approximations by Stein's method and size bias couplings. Journal of Applied Probability, vol 33, (1996), pp. 1-17.. Vol. 33, pp. 1-17. arXiv link
  • Goldstein, L., Langholz, B. (1996). Risk Set Sampling in Epidemiologic Cohort Studies. Institute of Mathematical Statistics. Vol. 11, pp. 35-53.
  • Assaf, D., Goldstein, L., Samuel-Cahn, E. (1996). A Statistical Version of Prophet Inequalities. Ann. Statist. Vol. 26 (3), pp. 1190-1197.
  • Goldstein, L., Khasminskii, R. (1995). On efficient estimation of smooth functionals. Theory of Probability and Applications. Vol. 40 (1), pp. 199-205.
  • Borgan, O., Goldstein, L., Langholz, B. (1995). Methods for the Analysis of Sampled Cohort Data in the Cox Proportional Hazards Model. Annals of Statistics. Vol. vol. 23 (no. 5), pp. pp. 1749-1778.
  • Goldstein, L., Waterman, M. (1994). Approximations to profile score distributions. Journal of Computational Biology. Vol. 1 (1), pp. 93-104.
  • Goldstein, L., Waterman, M. (1992). Poisson, Compound Poisson and Process approximations for testing statistical significance in sequence comparisons. Bulletin of Mathematical Biology. Vol. 54 (5), pp. 785-812.
  • Abramson, I., Goldstein, L. (1991). Efficient nonparametric testing by functional estimation. Journal of Theoretical Probability. Vol. 4 (1), pp. 137-159.
  • Arratia, R., Goldstein, L., Gordon, L. (1989). Two Moments Suffice for Poisson Approximations: The Chen-Stein Method. The Annals of Probability. Vol. 17 (1), pp. 9-25.
  • Goldstein, L. (1988). On the choice of step size in the Robbins Monro procedure. Statistics and Probability Letters. Vol. 6, pp. 299-303.
  • Goldstein, L. (1988). Mean square rates of convergence in the continuous time simulated annealing algorithm in Rd. Advances in Applied Mathematics. Vol. 9, pp. 35-39.
  • Goldstein, L. (1988). Minimizing noisy functionals in Hilbert space: An extension of the Kiefer Wolfowitz procedure. Journal of Theoretical Probability. Vol. 1 (2), pp. 189-204.
  • Goldstein, L., Waterman, M. (1987). Mapping DNA by stochastic relaxation. Advances in Applied Mathematics. Vol. 8, pp. 194-207.

Honors and Awards

  • Fellow, the Institute of Mathematics Statistics (IMS), 2003  

Service to the Profession

Professional Memberships
  • Institue of Mathematical Statistics, 1984-2009  
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