Selected Publications/Talks

  • Stein’s Method: The Golden Anniversary, National University of Singapore, Zero Bias Enhanced Stein Couplings 
  • Collegio Carlo Alberto, Turin Italy, Relaxing Gaussian Assumptions in High Dimensional Statistical Procedures
  • University of Minnesota Data Science Seminar: Relaxing Gaussian Assumptions in High Dimensional Statistical Procedures




  • Chulalongkorn University, Bangkok Thailand: Dickman Approximation for Quickselect sorting, and by Stein's Method in Number theory
  • Coumbia  University, New York: Nonlinear Compressed Non-Gaussian Sensing via Stein Discrepancies
  • CUNY, New York: Dickman Approximation for Quickselect sorting, and by Stein's Method in Number theory
  • UCSD, La Jolla: Dickman Approximation for Quickselect sorting, and by Stein's Method in Number theory
  • International Conference on Machine Learning, Long Beach: The many faces of a simple identity
  • Symposium in Memory of Charles Stein [1920 - 2016], National Univeristy of Singapore: Dickman approximation in quickselect sorting and probabilistic number theory
  • Symposium in Memory of Charles Stein [1920 - 2016], National Univeristy of Singapore: Single index models and non-linear compressed sensing in the non-Gaussian case via Stein type discrepancies


Selected talks in previous years

  Five Talks in Melbourne


1. A Curious Connection Between Optimal Stopping and Branching Processes

2. Two Choice Stopping: How much is an extra chance worth?

3. Berry Esseen Bounds for Local Extremes and Combinatorial Central Limit Theorems, using Size and Zero Biasing

4. Normal Approximation for Hierarchical Sequences

5. Sampling Case-Control Studies Over Time 

Selected Publications

        Papers on the arxiv server

        Analysis and asymptotic theory for nested case–control designs under highly stratified proportional hazards models
        Goldstein, L. and Langholz, B.
        Lifetime Data Analysis (2022)

        Zero Bias Enhanced Stein Couplings
        Goldstein, L.     
        Electronic Communications in Probability (2022), Vol. 27, paper no. 62, 1-13.


        Relaxing the Gaussian assumption in Shrinkage and SURE in high dimension
        Fathi, M., Goldstein, L., Reinert, G. and Saumard, A.       
        Annals of Statistics, (2022) vol 50, No 4, 2732--2766


        M-estimation in a diffusion model with application to biosensor transdermal blood alcohol monitoring
        Allayioti, M., Bartroff, J., Goldstein, L., Luczak, S. and Rosen, G.       

        The Game of Poker Chips, Dominoes and Survival
        Goldstein, L.       
        Recreational Mathematics Magazine, (2021) vol 8, Issue 14, pp 91-104


        Stein's method via induction
        Chen, L., Goldstein, L. and Röllin, A.       
        Electronic Journal of Probability, (2020) vol 25, paper no. 132, pp. 1-49

        [Euclid] []

        Dickman approximation in simulation, summations and perpetuities
        Bhattacharjee, C. and Goldstein, L.       
        Bernoulli, (2019) vol 25, No. 4A, pp. 2758–2792


        Size bias for one and all
        Arratia, R., Goldstein, L. and Kochman, F.
        Probability Surveys, (2019) vol 16, pp. 1-61

         Non-Gaussian Observations in Nonlinear Compressed Sensing via Stein Discrepancies
         Goldstein, L. and Wei, X
         Information and Inference: A Journal of the IMA, (2019) vol 8.1, pp. 125-159. iay006.

         Non asymptotic distributional bounds for the Dickman approximation of the running time of the Quickselect algorithm
         Goldstein, L.
         Electronic Journal of Probability, (2018) vol. 23, pp. 1--13 DOI: 10.1214/18-EJP227

        Structured signal recovery from non-linear and heavy-tailed measurements
        Goldstein, L., Minsker, S. and Wei, X.
        IEEE Transactions on Information Theory, (2018) vol 64, No. 8, pp. 5513-5530

        A BKR operation for events occurring for disjoint reasons with high probability

        Goldstein, L. and Rinott, Y.
        Methodology and Computing in Applied Probability (2018), 

        Stein's method for positively associated random variables with applications to Ising, percolation and voter models
        Goldstein, L. and Wiroonsri, N.
        Annales de l’Institut Henri Poincaré, (2018) vol 54, 385–421
        Bounds to the normal for proximity region graphs
        Goldstein, L., Johnson, T. and Lachièze-Rey, R.
        Stochastic Processes and Applications, (2018) no. 4, 1208-1237.

        Size biased couplings and the spectral gap for random regular graphs
        Cook, N., Goldstein, L. and Johnson, T.
        Annals of Probability, (2018), vol 46, No.1, 72-125

        Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models
        Bartroff, J., Goldstein, L. and Işlak, Ü.
        Bernoulli, (2018) vol  24, No. 4B, pp. 3283-3317.
        The sequential probability ratio test: An efficient alternative to exact binomial testing for clean water act 303(d) evaluation 
Chen, C., Gribble, M., Bartroff, J., Bay, S. and Goldstein, L.
        Journal of Environmental Management, (2017) vol. 192, pp. 89–-93
        [Elsevier Link][Science Direct]

        Gaussian Phase Transitions and Conic Intrinsic Volumes:  Steining the Steiner Formula
        Goldstein, L., Nourdin, I. and Peccati, G.
        Annals of Applied Probability (2017), vol 27, pp. 1-47

       On Strong Embeddings by Stein's Method
        Bhattacharjee, C. and Goldstein, L.
        Electronic Journal of Probability, (2016) vol 21, paper no. 15, 30 pp.

        Stein's method and the rank distribution of random matrices over finite fields
        Fulman, J. and Goldstein, L.
        Annals of Probability, (2015) vol 43, pp. 1274-1314

        Concentration inequalities via zero bias couplings

        Goldstein, L. and Işlak, Ü. 
        Statistics and Probability Letters, (2014), vol 86, pp. 17-23
        [][Elsevier] [10.1016/j.spl.2013.12.001]

        Stein's method for the Beta distribution and the Pòlya-Eggenberger Urn

        Goldstein, L. and Reinert, G.
        Journal of Applied Probability, (2013), vol 50, pp. 1187–1205
        A Berry-Esseen bound for the uniform multinomial occupancy model
   Bartroff, J. and Goldstein, L.
        Electronic Journal of Probability, (2013), vol 18, paper no. 27, 29 pp.

        Clubbed Binomial Approximation for the Lightbulb Process
   Goldstein, L, and Xia, A.
        Probability Approximations and Beyond, Springer (2012)
        Lecture Notes in Statisticsvol. 205,  pp. 31-41. 
        Barbour, A, Chen, L.H.Y. and Siegmund D. (Editors) 

       Stochastic comparisons of symmetric sampling designs
Goldstein, L., Rinott, Y., and Scarsini, M. 
       Methodology and Computing in Applied Probability (2012), vol  14, pp. 407-420
       [Springer Link][pdf]
       Concentration of measure for the number of isolated vertices in the Erdős-Rényi random graph by size bias couplings.
Ghosh, S., Goldstein, L. and Raič, M. 
        Statistics and Probability Letters (2011) vol 81, pp.1565-1570.

       Zero Biasing and Jack Measures
       Fulman, J., and Goldstein, L. 
       Combinatorics, Probability and Computing (2011), vol 20, pp. 753-762
       [ technical report][CPC]

       Normal Approximation by Stein's Method
Chen, L., Goldstein, L., and Shao, Q.M. 
       Springer Verlag, 2010 [errata][links]

       A Berry-Esseen bound with applications to vertex degree counts in the Erdős-Rényi random graph
       Goldstein, L.
       Annals of Applied Probability (2013), vol 23, pp. 617-636.
       [] [AAP][Euclid]

       A Berry Esseen Theorem for the Lightbulb Process
Goldstein, L., and Zhang, H. 
       Advances in Applied Probability (2011) vol 43.3, pp. 875-898.

       Applications of size biased couplings for concentration of measures

       Ghosh, S., and Goldstein, L.
       Electronic Communications in Probability (2011), vol 16, pp. 70-83.

       Size bias, sampling, the waiting time paradox, and infinite divisibility: when is the increment independent?
       Arratia, R., and Goldstein, L. 

       On Optimal Allocation of a Continuous Resource Using an Iterative Approach and Total Positivity
Bartroff, J., Goldstein, L., Rinott, Y., and Samuel-Cahn, E. 
       Advances in Applied Probability (2010), vol 42, pp. 795-815.

      Concentration of measures via size biased couplings
Ghosh, S., and Goldstein, L.
       Probability Theory and Related Fields,  (2011), vol 149, pp. 271-278.
       [10.1007/s00440-009-0253-3], tech report: [arXiv:0906.3886]  

      Stochastic comparisons of stratified sampling techniques for some Monte Carlo estimators
Goldstein, L., Rinott, Y., and Scarsini, M. 
      Bernoulli, (2011) vol 17, pp. 592-608. 
      [pdf][][Project Euclid][Bernoulli]

       The Spend-it-all Region and Small Time results for the Continuous Bomber Problem
 Bartroff, J., Goldstein, L., and Samuel-Cahn, E.
       Sequential Analysis (2010), vol 29, pp. 275-291.

Berry-Esseen Bounds for Projections of Coordinate Symmetric Random Vectors
  Goldstein, L., and Shao, Q.
       Electronic Communications in Probability (2009), vol 14, pp. 474-485.

      Normal approximation for coverage models over binomial point processes
      Goldstein, L., and Penrose, M. D.
      Annals of Applied Probability (2010), vol 20, pp. 696-721.
      [pdf][arXiv:0812.3084][project Euclid]

  Bounds on the Constant in the Mean Central Limit Theorem
      Goldstein, L.
      Annals of Probability (2010)vol 38, pp. 1672-1689. 
      Efficiency of the Maximum Partial Likelihood Estimator in Nested-Case Control Sampling
      Goldstein, L., and Zhang, H.
      Bernoulli (2009), vol 15, pp. 569-597.
      [pdf][arXiv:0809.0445][Euclid][technical report]

      A Probabilistic Proof of the Lindeberg-Feller Central Limit Theorem
      Goldstein, L.
      American Mathematical Monthly (2009), vol 116, pp. 45--60

1 Bounds in Normal Approximation
      Goldstein, L.
      Annals of Probability (2007), vol 35, pp. 1888--1930

      Total Variation Distance for Poisson Subset Numbers
      Goldstein, L, and Reinert, G.
      Annals of Combinatorics (2006), vol 10,  pp. 333--341

      Functional BKR Inequalities, and their Duals, with Applications
Goldstein, L, and Rinott, Y.
      Jour. Theor. Probab. (2007) , vol 20, pp. 275--293

      Zero Biasing and a Discrete Central Limit Theorem
Goldstein, L, and Xia, A. 
      Annals of Probability (2006), vol 34, pp. 1782--1806

      Cohort Sampling Schemes for the Mantel-Haenszel Estimator
Goldstein, L, and Langholz, B.
      Scandanavian Journal of Statistics (2007), vol. 34,  pp. 137--154.   
      [pdf][Scand. Jour. Stat.][arXiv:math/0609333(tech report)]

      Zero Biasing in One and Higher Dimensions, and Applications
Goldstein, L, and Reinert, G.
      Stein's method and applications 
      Institute for Mathematical Sciences Lecture Notes Series No. 5 (2005), 
     World Scientific Press, Singapore, pp. 1--18
      Maximizing expected value with two stage stopping rules
      Assaf, D., Goldstein, L., Samuel-Cahn, E.    
      Random Walks, Sequential Analysis and Related Topics,  World Scientific Press, Singapore, pp. 1--25

      Optimal Two Choice Stopping on an Exponential Sequence
      Goldstein, L., Samuel-Cahn, E. 
      Sequential Analysis (2006), vol 25, pp. 351--363.

      Berry Esseen Bounds for Combinatorial Central Limit Theorems and Pattern Occurrences, using Zero and Size Biasing

      Goldstein, L.
      Journal of Applied Probability, (2005), vol 42, pp. 661--683.

      A Statistical Characterization of Regular Simplices
Abramson, I.  and Goldstein, L.
      Amer. Math. Monthly (2006) vol. 113, pp. 750-752
      Correction: [dvi][pdf][ps], corrected version [arxiv:math/0612163v2]

      Normal Approximation for Hierarchical Sequences 
      Goldstein, L.
      Ann. Appl. Probab. (2004), vol 14, pp. 1950-1969.

      Distributional transformations, orthogonal polynomials, and Stein characterizations
      Goldstein, L. and Reinert, G.
      Jour. Theor. Probab. (2005), vol 18, pp. 237-260. 
      (In Russian) Obozr. Prikl. Prom. Mat., (OP&PM Surveys in Applied and Industrial Mathematics) 2006, v. 13, No. 1, pp. 28--50.

      A Permutation Test for Matching
      Goldstein, L. and Rinott, Y.
      Metron  vol 61, (2003), no. 3, pp. 375-388 (2004). 

      Two Choice Optimal Stopping 
      Assaf, D., Goldstein, L., Samuel-Cahn, E. 
      Adv. Appl. Prob. vol 36, (2004), pp. 1116-1147

      Local Central Limit Theorems, the High Order Correlations of Rejective Sampling, 
      and Applications to Conditional Logistic Likelihood Asymptotics 
      Annals of Statistics vol 33, (2005), pp. 871-914
      Arratia, R., Goldstein, L., Langholz, B. 

      Information and Asymptotic Efficiency of the Case-Cohort Sampling Design in Cox's Regression Model 
      Zhang, H., Goldstein, L. 
      Journal of Multivariate Analysis vol 85, (2003), pp. 292-317

      Ratio Prophet Inequalities when the Mortal has Several Choices 
      Assaf, D., Goldstein, L., Samuel-Cahn, E. 
      Ann. Appl. Probab. vol 12, (2002), pp. 972-984

      Conditional logistic analysis of case-control studies with complex sampling 
      Langholz, B., and Goldstein, L. 
      Biostatistics, vol 2, (2001), pp. 63-84 

      An unexpected connection between branching processes and optimal stopping. 
      Assaf, D., Goldstein, L., Samuel-Cahn, E. 
      Journal of Applied Probability, vol. 37, (2000), pp. 613-626. 

      Exposure stratified case-cohort studies 
      Borgan, O., Langholz, B., Samuelson, S.O., Goldstein, L., Pogoda, J. 
      Lifetime Data Analysis
vol. 6, (2000), pp. 39-58. 

      Ascertainment correction in rate ratio estimation from case-sibling control studies of variable age-at-onset diseases 
      Langholz, B., Thomas, D.C., Faucett, C., Huberman, M., Goldstein, L. 
      Biometricsvol. 55, (1999), pp. 1129-1136. 

      A statistical version of prophet inequalities 
      Assaf, D., Goldstein, L., Samuel-Cahn, E. 
      Annals of Statistics
, vol. 26, (1998), pp. 1190-1197. 

     Stein's Method and the Zero Bias Transformation with Application to Simple Random Sampling 
     Goldstein, L.,and Reinert, G. 
     Annals of Applied Probability, vol. 7, (1997), pp. 935-952. 
     [dvi][pdf][ps][arxiv:math/0510619][technical report][Euclid]

     A central limit theorem for the parsimony length of trees 
     Steel, M., Goldstein, L., and Waterman, M. 
     Advances in Applied Probability, vol. 28, (1996), pp. 1051-1071.

     Risk set sampling in epidemiologic cohort studies 
     Goldstein, L., and Langholz, B. 
     Statistical Science, vol. 11, (1996), pp. 35-53. 

     Multivariate normal approximations by Stein's method and size bias couplings 
     Goldstein, L. and Rinott, Y. 
     Journal of Applied Probability, vol 33, (1996), pp. 1-17. 

     Asymptotics for the maximum of half-normal plots 
     Goldstein, L., and Gordon, L. 
     Annals of Statistics, vol 24, (1996), pp. 2250-2265.

     Methods for the analysis of sampled cohort data in the Cox proportional hazards model. 
     Borgan, O., Goldstein, L. and Langholz, B. 
     Annals of Statistics, vol 23, No. 5, (1995), pp.1749-1778. 

     On efficient estimation of smooth functionals 
     Goldstein, L.,and Khasminskii,R. 
     Theory of Probability and Applications, vol.40, No.1, (1995),  pp. 199-205. 

     Poisson, Compound Poisson and Process approximations for testing statistical significance in sequence comparisons
     Goldstein, L. and Waterman, M.
     Bulletin of Mathematical Biology,  vol. 54, No. 5, (1992)  pp. 785-812.

     Approximations to profile score distributions. 
     Goldstein, L. and Waterman, M. 
     Journal of Computational Biology, vol. 1, No. 1 (1994),  pp. 93-104. 

     Asymptotic Theory for Nested Case-Control Sampling in the Cox Regression Model
     Goldstein, L. and Langholz, B.
     The Annals of Statistics, Vol. 20, No. 4. (Dec., 1992), pp. 1903-1928.

     Efficient nonparametric testing by functional estimation

     Abramson, I. and Goldstein, L.
     Journal of Theoretical Probability, vol. 4, No. 1 (1991) pp. 137-159.

     Poisson Approximation and the Chen-Stein Method 
Arratia; R., Goldstein, L. and Gordon, L. 
     Statistical Science, Vol. 5, No. 4. (Nov., 1990), pp. 403-424.
   [MR1092983]  [pdf]

     [Poisson Approximation and the Chen-Stein Method]: Rejoinder
     Arratia, R., Goldstein, L., and Gordon, L.
     Statistical Science, Vol. 5, No. 4. (Nov., 1990), pp. 432-434.

     Two Moments Suffice for Poisson Approximations: The Chen-Stein Method
Arratia, R., Goldstein, L., and Gordon, L. 
     The Annals of Probability, Vol. 17, No. 1. (Jan., 1989), pp. 9-25.
     [MR0972770]  [pdf]

      Mean square rates of convergence in the continuous time simulated annealing algorithm in Rd

      Goldstein, L.
      Advances in Applied Mathematics,  vol. 9, (1988) , pp. 35-39.

     On the choice of step size in the Robbins Monro procedure

     Goldstein, L.
      Statistics and Probability Letters,  vol. 6, (1988),  pp. 299-303.

     Minimizing noisy functionals in Hilbert space:  An extension of the Kiefer Wolfowitz procedure

     Goldstein, L.
     Journal of Theoretical Probability,  vol. 1, No. 2,  (1988),  pp. 189-204. 

     Mapping DNA by stochastic relaxation
     Goldstein, L., Waterman, M. 
      Advances in Applied Mathematics, 
vol. 8, (1987), pp. 194-207