Herbert Robbins

Q: What Schools Are Affiliated With Herbert Robbins

Herbert Robbins is affiliated with the following schools: Rutgers University, Imperial College London, University of Michigan, University of North Carolina at Chapel Hill, Columbia University, New York University, Harvard University

Herbert Robbins's AcademicInfluence.com Rankings

Herbert Robbins

Mathematics

#111

World Rank

#289

Historical Rank

#43

USA Rank

Measure Theory

#31

World Rank

#55

Historical Rank

#18

USA Rank

mathematics Degrees

Download Badge

Mathematics

Why Is Herbert Robbins Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Herbert Ellis Robbins was an American mathematician and statistician. He did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of What is Mathematics?, a popularization that is still in print. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem .

(See a Problem?)

Herbert Robbins's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

A Stochastic Approximation Method (1951) (7422)
Some aspects of the sequential design of experiments (1952) (2152)
An Empirical Bayes Approach to Statistics (1956) (1053)
Complete Convergence and the Law of Large Numbers. (1947) (918)
A Remark on Stirling’s Formula (1955) (795)
Asymptotically efficient adaptive allocation rules (1985) (718)
The Empirical Bayes Approach to Statistical Decision Problems (1964) (627)
ON THE ASYMPTOTIC THEORY OF FIXED-WIDTH SEQUENTIAL CONFIDENCE INTERVALS FOR THE MEAN. (1965) (549)
A Convergence Theorem for Non Negative Almost Supermartingales and Some Applications (1985) (515)
Great expectations: The theory of optimal stopping (1971) (458)
Sequential medical trials. (1980) (322)
The Central Limit Theorem for Dependent Random Variables (1948) (291)
A Theorem on Graphs, with an Application to a Problem of Traffic Control (1939) (289)
Minimum Variance Estimation Without Regularity Assumptions (1951) (269)
Minimum Variance Estimation Without Regularity Assumptions (1951) (269)
Statistical Methods Related to the Law of the Iterated Logarithm (1970) (243)
Asymptotically Subminimax Solutions of Compound Statistical Decision Problems (1985) (235)
Strong consistency of least squares estimates in multiple regression. (1979) (204)
Boundary Crossing Probabilities for the Wiener Process and Sample Sums (1970) (184)
Optimal selection based on relative rank (the “secretary problem”) (1964) (183)
Sequential Estimation of the Mean of a Normal Population (1985) (176)
On the Measure of a Random Set (1944) (176)
On the Asymptotic Distribution of the Sum of a Random Number of Random Variables. (1948) (170)
Some Thoughts on Empirical Bayes Estimation (1983) (151)
Adaptive Design and Stochastic Approximation (1979) (145)
Application of the Method of Mixtures to Quadratic Forms in Normal Variates (1949) (143)
Sequential choice from several populations. (1995) (129)
Strong consistency of least squares estimates in multiple regression (1978) (128)
Estimating the Total Probability of the Unobserved Outcomes of an Experiment (1968) (115)
Moments of Randomly Stopped Sums (1965) (114)
The theory of optimal stopping (1991) (111)
Mixture of Distributions (1948) (100)
Maximally dependent random variables. (1976) (94)
A SEQUENTIAL DECISION PROBLEM WITH A FINITE MEMORY. (1956) (90)
A Sequential Analogue of the Behrens-Fisher Problem (1967) (82)
A CONVERGENCE THEOREM FOR NON NEGATIVE ALMOST SUPERMARTINGALES AND SOME APPLICATIONS**Research supported by NIH Grant 5-R01-GM-16895-03 and ONR Grant N00014-67-A-0108-0018. (1971) (82)
The Expected Sample Size of Some Tests of Power One (1974) (72)
Confidence sequences for mean, variance, and median. (1967) (72)
A class of dependent random variables and their maxima (1978) (71)
Consistency and asymptotic efficiency of slope estimates in stochastic approximation schemes (1981) (66)
A Martingale System Theorem and Applications (1961) (64)
Sequential Tests Involving Two Populations (1974) (64)
ON SUMS OF INDEPENDENT RANDOM VARIABLES WITH INFINITE MOMENTS AND "FAIR" GAMES. (1961) (64)
Iterated least squares in multiperiod control (1982) (56)
Asymptotic Solutions of the Compound Decision Problem for Two Completely Specified Distributions (1955) (55)
A Class of Stopping Rules for Testing Parametric Hypotheses (1985) (55)
The Distribution of a Definite Quadratic Form (1948) (55)
Iterated logarithm inequalities. (1967) (53)
Clinical and prophylactic trials with assured new treatment for those at greater risk: I. A design proposal. (1996) (52)
Clinical and prophylactic trials with assured new treatment for those at greater risk: II. Examples. (1996) (47)
On optimal stopping rules (1963) (46)
Prediction and estimation for the compound Poisson distribution. (1977) (45)
The Empirical Bayes Approach to Testing Statistical Hypotheses (1963) (44)
A Sequential Procedure for Selecting the Largest of $k$ Means (1968) (44)
Optimal Selection Based on Relative Rank (1985) (39)
Ergodic Property of the Brownian Motion Process. (1953) (39)
On the law of the iterated logarithm for maxima and minima (1972) (38)
The sequence of sums of independent random variables (1954) (38)
Strong consistency of least-squares estimates in regression models. (1977) (37)
On the equidistribution of sums of independent random variables (1953) (36)
The U,V Method of Estimation (1988) (35)
On optimal stopping rules for $S_{n}/n$ (1965) (34)
The candidate problem with unknown population size (1975) (33)
Some nonparametric sequential tests with power one. (1968) (32)
The Problem of the Greater Mean (1950) (31)
On Distribution-free Tolerance Limits in Random Sampling (1944) (29)
Adaptive design in regression and control. (1978) (28)
Statistical Tests of Power One and the Integral Representation of Solutions of Certain Partial Differential Equations (1985) (27)
A Renewal Theorem for Random Variables which are Dependent or Non-Identically Distributed (1963) (27)
An empirical Bayes estimation problem. (1980) (27)
Estimating a treatment effect under biased sampling. (1988) (26)
Stochastic search in a convex region (1988) (25)
Two-stage procedures for estimating the difference between means (1954) (24)
Selecting the highest probability in binomial or multinomial trials. (1981) (24)
Some further remarks on inequalities for sample sums. (1968) (23)
Reducing the number of inferior treatments in clinical trials. (1972) (23)
Finding the Size of a Finite Population (1967) (22)
THE STRONG LAW OF LARGE NUMBERS WHEN THE FIRST MOMENT DOES NOT EXIST. (1955) (22)
On the „Parking“ Problem (1985) (21)
A Remark on the Joint Distribution of Cumulative Sums (1954) (21)
THE LIMITING DISTRIBUTION OF THE LAST TIME s(n) >/= nin. (1968) (21)
Estimating the superiority of a drug to a placebo when all and only those patients at risk are treated with the drug. (1989) (20)
Urn Models for Regression Analysis, With Applications to Employment Discrimination Studies (1983) (17)
A sequential test for two binomial populations. (1974) (17)
Sequential Medical Trials (Stopping Rules/Asymptotic Optimality). (1980) (16)
Some complements to Brouwer’s fixed point theorem (1967) (15)
Estimating a multiplicative treatment effect under biased allocation (1991) (15)
Sequential Estimation of p with Squared Relative Error Loss. (1975) (15)
Inequalities for the sequence of sample means. (1967) (14)
An extension of a lemma of Wald (1966) (14)
Probability distributions related to the law of the iterated logarithm. (1969) (14)
Limit theorems for weighted sums and stochastic approximation processes. (1978) (13)
Estimating Many Variances (1982) (12)
SEQUENTIAL DESIGN OF COMPARATIVE CLINICAL TRIALS (1983) (11)
Jerzy Neyman Memorial Lecture Some Thoughts on Empirical Bayes Estimation (1985) (11)
The Distribution of Student's $t$ When the Population Means are Unequal (1948) (10)
On a class of recurrent sequences (1937) (10)
On values associated with a stochastic sequence (1967) (10)
ADAPTIVE DESIGN AND THE MULTIPERIOD CONTROL PROBLEM (1982) (10)
Adaptive choice of mean or median in estimating the center of a symmetric distribution. (1983) (9)
Some problems of optimal sampling strategy (1964) (9)
Linear empirical Bayes estimation of means and variances. (1985) (8)
Acknowledgment of Priority: On the Measure of a Random Set, [Parts I and II] (1947) (8)
A Note on Gambling Systems and Birth Statistics (1952) (8)
An Interview with Herbert Robbins (1984) (7)
Remarks on the Secretary Problem (1991) (7)
Convergence of Distributions (1948) (7)
Asymptotically minimax stochastic search strategies in the plane. (1987) (7)
Efficiency of the u,v method of estimation. (2000) (7)
Estimation and prediction for mixtures of the exponential distribution. (1980) (7)
Optimal sequential sampling from two populations. (1984) (6)
SEQUENTIAL DECISION ABOUT A NORMAL MEAN (1977) (6)
A Note on the Riemann Integral (1943) (6)
Report of the Chapel Hill Meeting of the Institute (1950) (6)
Maximum likelihood estimation in regression with uniform errors (1986) (5)
Weight Adjustment Rule of Neural Networks for Computing Discrete 2-D Gabor Transforms (1990) (5)
TESTING STATISTICAL HYPOTHESES. THE COMPOUND APPROACH (1961) (5)
On the classification of the mappings of a 2-complex (1941) (5)
A note on the ‘underadjustment phenomenon’ (1983) (5)
Mathematical Probability in Election Challenges (1973) (5)
Local convergence theorems for adaptive stochastic approximation schemes. (1979) (4)
SOME NUMERICAL RESULTS ON A COMPOUND DECISION PROBLEM (1961) (4)
Two properties of the function $\cos x$ (1944) (3)
A Bayes Test of “p≤½” versus “p≤½” (1985) (3)
On the Expected Values of Two Statistics (1944) (2)
Some Breakthroughs in Statistical Methodology (1984) (2)
Sequential rank and the Pólya urn (1979) (2)
Stochastic Search in a Square and on a Torus (1988) (2)
Recurrent Games and the Petersburg Paradox (1961) (2)
ASYMPTOTICALLY SUBMINIMAX SOLUTIONS OF COMPOUND STATISTICAL (2005) (2)
Problems for Solution: 4215-4219 (1946) (2)
On the $\left( {C,\,1} \right)$ summability of certain random sequences (1946) (1)
A Note on the ‘Under adjustment Phenomenon’ (1985) (1)
Mathematical aspects of estimating two treatment effects and a common variance in an assured allocation design (2002) (1)
Adaptive statistical procedures and related topics : proceedings of a symposium in honor of Herbert Robbins, June 7-11, 1985, Brookhaven National Laboratory, Upton, New York (1986) (1)
A class of optimal stopping problems (1967) (1)
[Who Solved the Secretary Problem?]: Comment (1989) (1)
Order statistics and the Pólya urn process (1977) (1)
Comments on a Paper by James Albertson (1959) (1)
An Empirical Bayes Approarch to Statistics (1955) (0)
Review: A. Wald, Statistical decision functions (1951) (0)
Linear empirical Bayesestimation ofmeansandvariances (1985) (0)
Correction to "The Problem of the Greater Mean" (1951) (0)
A BAYES TEST OF P LESS THAN OR EQUAL TO 1/2 VERSUS P >1/2 (1961) (0)
Problems for Solution: 4171-4175 (1945) (0)
Advanced Problems: 5530-5539 (1967) (0)
Topics in Adaptive Control and Inference. (1988) (0)
Review: S. M. Ulam, Adventures of a mathematician (1978) (0)
Optimal sequential sampling from two populations ( two-armed bandit / adaptive allocation ) (0)
Reducing theNumberofInferior Treatments inClinical Trials (1972) (0)
" M Cox * Two-stage Procedures for Estimating the Difference Be'lween Mfans * Two-stage Procedures for Estimating the Difference between Means Introduction and Summarl. given Two Populations Pi (i = 1, 2) with Unknown (2008) (0)
Volume I: Joseph Berkson, Estimation by Least Squares and by Maximum Likeli- (1957) (0)
Topics in Statistical Estimation and Control. (1996) (0)
Wither Mathematical Statistics (1975) (0)
ON OPTIMAL STOPPING IN A CLASS OF UNIFORM GAMES. (1965) (0)

This paper list is powered by the following services:

Other Resources About Herbert Robbins

en.wikipedia.org

What Schools Are Affiliated With Herbert Robbins?

Herbert Robbins is affiliated with the following schools:

Herbert Robbins's Academic­Influence.com Rankings