Selected Publications/Talks
2022:
- 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
2021:
- Seminario de Probabilidad Hispanohablante: Ordenación y la aproximación de Dickman para el algoritmo Quickselect
- GRK Seminar, Technische Universität Dortmund, Germany: Relaxing Gaussian Assumptions in High Dimensional Statistical Procedures
2019:
- 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
2018:
- University of British Columbia: Steining the Steiner Formula
- Guanajuato Mexico, CIMAT, XVI Escuela de Probabilidad y Estadistica Minicurso: Charlas de Charles
Selected talks in previous years
- Singapore, Progress using Stein's method for strong embeddings
- Minnesota: IMA workshop on Information Theory and Concentration Phenomena Steining the Steiner formula
- Evanston, Il. 36th Midwest Probability Colloquium, Two tutorial talks on Stein's method: Distributional approximation, Concentration
- Singapore, Concentration of Measures by Bounded Couplings, Stein's Method for the Beta distribution with applications to the Pólya Urn
- Oxford, Concentration of Measures by Bounded Size Bias Couplings
- Istanbul, The Inductive Method, Unbounded Couplings and Stein's Method
- Chalkidiki Greece, Semi-Parametric Efficiency Bounds for the Maximum Partial Likelihood Estimator in Nested Case-Control Sampling
- Rome, Concentration of Measures by Bounded Size Bias Couplings
- Singapore, A Berry-Esseen theorem for the lightbulb Process
- Guanajuato, Mexico, CIMAT Seminar: El Método de Stein y algunas Aplicaciones
- Singapore, Four Tutorial talks on Stein's Method 1,2,3,4
- Rome, Bounds on the constant in the mean central limit theorem
- Oslo, Norway Mantel-Haenszel type estimators and cohort sampling schemes
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?
4. Normal Approximation for Hierarchical Sequences
5. Sampling Case-Control Studies Over Time
Selected Publications
Analysis and asymptotic theory for nested case–control designs under highly stratified proportional hazards models
Goldstein, L. and Langholz, B.
Lifetime Data Analysis (2022) https://doi.org/10.1007/s10985-022-09582-4
Zero Bias Enhanced Stein Couplings
Goldstein, L.
Electronic Communications in Probability (2022), Vol. 27, paper no. 62, 1-13.
[https://arxiv.org/abs/2206.05413][Euclid]
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
[https://doi.org/10.1214/22-AOS2208]
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.
[https://arxiv.org/abs/2002.05335]
The Game of Poker Chips, Dominoes and Survival
Goldstein, L.
Recreational Mathematics Magazine, (2021) vol 8, Issue 14, pp 91-104
[https://sciendo.com/issue/RMM/8/14]
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] [https://arxiv.org/abs/1903.09319]
Dickman approximation in simulation, summations and perpetuities
Bhattacharjee, C. and Goldstein, L.
Bernoulli, (2019) vol 25, No. 4A, pp. 2758–2792
[https://arxiv.org/abs/1706.08192]
Size bias for one and all
Arratia, R., Goldstein, L. and Kochman, F.
Probability Surveys, (2019) vol 16, pp. 1-61
[http://arxiv.org/abs/1308.2729]
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.
[https://arxiv.org/abs/1609.08512]
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
[https://arxiv.org/abs/1703.00505]
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
[https://arxiv.org/abs/1609.01025]
A BKR operation for events occurring for disjoint reasons with high probability
Goldstein, L. and Rinott, Y.
Methodology and Computing in Applied Probability (2018),
[http://arxiv.org/abs/1608.05612][Springer][doi.org/10.1007/s11009-018-9623-6]
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
[http://arxiv.org/abs/1603.05322]
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.
[http://arxiv.org/abs/1510.09188][SPA]
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
[http://arxiv.org/abs/1510.06013]
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.
[http://arxiv.org/abs/1402.6769]
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
[http://arxiv.org/abs/1411.6265]
On Strong Embeddings by Stein's Method
Bhattacharjee, C. and Goldstein, L.
Electronic Journal of Probability, (2016) vol 21, paper no. 15, 30 pp.
[http://arxiv.org/abs/1505.03199][EJP]
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
[http://arxiv.org/abs/1211.0504]
Concentration inequalities via zero bias couplings
Goldstein, L. and Işlak, Ü.
Statistics and Probability Letters, (2014), vol 86, pp. 17-23
[http://arxiv.org/abs/1304.5001][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
[http://arxiv.org/abs/1207.1460]
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.
[http://arxiv.org/abs/1202.0909][EJP]
Clubbed Binomial Approximation for the Lightbulb Process
Goldstein, L, and Xia, A.
Probability Approximations and Beyond, Springer (2012)
Lecture Notes in Statistics, vol. 205, pp. 31-41.
Barbour, A, Chen, L.H.Y. and Siegmund D. (Editors)
[http://arxiv.org/abs/1111.3984][Springer][Amazon]
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.
[arxiv.org/abs/1106.0048][SPL]
Zero Biasing and Jack Measures
Fulman, J., and Goldstein, L.
Combinatorics, Probability and Computing (2011), vol 20, pp. 753-762
[arxiv.org 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.
[arxiv.org/abs/1005.4390] [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.
[arxiv.org/abs/1001.0612]
Applications of size biased couplings for concentration of measures
Ghosh, S., and Goldstein, L.
Electronic Communications in Probability (2011), vol 16, pp. 70-83.
[pdf][ECP]
Size bias, sampling, the waiting time paradox, and infinite divisibility: when is the increment independent?
Arratia, R., and Goldstein, L.
[pdf][arXiv:1007.3910]
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.
[pdf][arXiv:1103.0308]
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][http://arxiv.org/abs/1005.5414][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.
[http://arxiv.org/abs/1007.3025]
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.
[ECP]
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.
[pdf][arXiv:0906.5145]
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
[dvi][pdf][ps][AMM]
L1 Bounds in Normal Approximation
Goldstein, L.
Annals of Probability (2007), vol 35, pp. 1888--1930
[dvi][pdf][ps][Euclid][arXiv:0710.3262]
Total Variation Distance for Poisson Subset Numbers
Goldstein, L, and Reinert, G.
Annals of Combinatorics (2006), vol 10, pp. 333--341
[dvi][pdf][ps][Springer]
Functional BKR Inequalities, and their Duals, with Applications
Goldstein, L, and Rinott, Y.
Jour. Theor. Probab. (2007) , vol 20, pp. 275--293
[arXiv:0710.3262][Springer]
Zero Biasing and a Discrete Central Limit Theorem
Goldstein, L, and Xia, A.
Annals of Probability (2006), vol 34, pp. 1782--1806
[dvi][pdf][ps][Euclid][arXiv:math/0509444]
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
[dvi][pdf][ps]
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
[dvi][pdf][ps]
Optimal Two Choice Stopping on an Exponential Sequence
Goldstein, L., Samuel-Cahn, E.
Sequential Analysis (2006), vol 25, pp. 351--363.
[dvi][pdf][ps]
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.
[dvi][pdf][ps][arxiv:math/0511510]
A Statistical Characterization of Regular Simplices
Abramson, I. and Goldstein, L.
Amer. Math. Monthly (2006) vol. 113, pp. 750-752
[dvi][pdf][ps]
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.
[dvi][pdf][ps][arxiv:math/0503549][Euclid]
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.
[dvi][pdf][russian-pdf][arxiv:math/0510240]
A Permutation Test for Matching
Goldstein, L. and Rinott, Y.
Metron vol 61, (2003), no. 3, pp. 375-388 (2004).
[dvi][pdf][ps][arxiv:math/0511427]
Two Choice Optimal Stopping
Assaf, D., Goldstein, L., Samuel-Cahn, E.
Adv. Appl. Prob. vol 36, (2004), pp. 1116-1147
[dvi][pdf][ps][arxiv:math/0510242]
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.
[dvi][pdf][ps][arxiv:math/0506300][Euclid]
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
[dvi][pdf][ps]
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
[dvi][pdf][ps]
Conditional logistic analysis of case-control studies with complex sampling
Langholz, B., and Goldstein, L.
Biostatistics, vol 2, (2001), pp. 63-84
[pdf]
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.
[dvi][pdf][ps][arxiv:math/0510587]
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.
[dvi][pdf][ps]
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.
Biometrics, vol. 55, (1999), pp. 1129-1136.
[dvi][pdf][ps]
A statistical version of prophet inequalities
Assaf, D., Goldstein, L., Samuel-Cahn, E.
Annals of Statistics, vol. 26, (1998), pp. 1190-1197.
[dvi][pdf][ps][Euclid]
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.
[pdf]
Risk set sampling in epidemiologic cohort studies
Goldstein, L., and Langholz, B.
Statistical Science, vol. 11, (1996), pp. 35-53.
[dvi][Euclid]
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.
[dvi][arxiv:math/0510586]
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.
[Euclid][dvi]
On efficient estimation of smooth functionals
Goldstein, L.,and Khasminskii,R.
Theory of Probability and Applications, vol.40, No.1, (1995), pp. 199-205.
[dvi][pdf]
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.
[pdf]
Approximations to profile score distributions.
Goldstein, L. and Waterman, M.
Journal of Computational Biology, vol. 1, No. 1 (1994), pp. 93-104.
[dvi][pdf]
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
[pdf]