Abstract
At Harvard professors get to choose their titles. Bill Cochran was Professor of Statistics; Art Dempster is Professor of Theoretical Statistics. Since the start of Harvard’s department, Frederick Mosteller has been Professor of Mathematical Statistics.
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References
Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H., and Tukey, J.W. (1972). Robust Estimates of Location. Princeton, NJ: Princeton University Press.
Atkinson, R.C., Bower, G.H., and Crothers, E.J. (1965). An Introduction to Mathematical Learning Theory. New York: Wiley.
Bahadur, R.R. (1950). On a problem in the theory of k populations. Annals of Mathematical Statistics, 21, 362–375.
Balmer, D.W., Boulton, M., and Sack, R.A. (1974). Optimal solutions in parameter estimation problems for the Cauchy distribution. Journal of the American Statistical Association, 69, 238–242.
Barnett, V. and Lewis, T. (1984). Outliers in Statistical Data. 2nd Ed. New York: Wiley.
Barnsley, M.F., Ervin, V., Hardin, D.P., and Lancaster, J. (1986). Solution of an inverse problem for fractals and other sets. Proceedings of the National Academy of Sciences, 83, 1975–1977.
Bechhofer, R.E. (1954). A single-sample multiple decision procedure for ranking means of normal populations with known variances. Annals of Mathematical Statistics, 25, 16–39.
Benson, F. (1949). A note on the estimation of mean and standard deviation from quantiles. Journal of the Royal Statistical Society, Series B, 11, 91–100.
Billingsley, P. (1974). The probability theory of additive arithmetic functions. Annals of Probability, 2, 749–791.
Bloch, D. (1966). A note on the estimation of the location parameter of the Cauchy distribution. Journal of the American Statistical Association, 61, 852–855.
Bofinger, V.J. (1965). The k-sample slippage problem. Australian Journal of Statistics, 7, 20–31.
Bougerol, P. and Lacroix, J. (1985). Products of Random Matrices with Applications to Schrödinger Operators. Boston: Birkhäuser.
Bower, G.H. and Hilgard, E.R. (1981). Theories of Learning. 5th Ed. Englewood Cliffs, NJ: Prentice-Hall.
Brown, B.M. (1981). Symmetric quantile averages and related estimators. Biometrika, 68, 235–242.
Butler, R.W. (1981). The admissible Bayes character of subset selection techniques involved in variable selection, outlier detection, and slippage problems. Annals of Statistics, 9, 960–973.
Cadwell, J.H. (1953). The distribution of quasi-ranges in samples from a normal population. Annals of Mathematical Statistics, 24, 603–613.
Chan, L.K. and Chan, N.N. (1973). On the optimum best linear unbiased estimates of the parameters of the normal distribution based on selected order statistics. Skandinavisk Aktuarietidskrift, 1973, 120–128.
Chan, L.K. and Rhodin, L. (1980). Robust estimation of location using optimally chosen sample quantiles. Technometrics, 22, 225–237.
Conover, W.J. (1968). Two k-sample slippage tests. Journal of the American Statistical Association, 63, 614–626.
Crow, E.L. and Siddiqui, M.M. (1967). Robust estimation of location. Journal of the American Statistical Association, 62, 353–389.
David, H.A. (1981). Order Statistics. 2nd Ed. New York: Wiley.
Demko, S., Hodges, L., and Naylor, B. (1985). Construction of fractal objects with iterated function systems. Computer Graphics, 19, No. 3, 271–278. (SIGGRAPH’85 Proceedings).
Diaconis, P. (1976). Asymptotic expansions for the mean and variance of the number of prime factors of a number n. Technical Report No. 96, Department of Statistics, Stanford University.
Diaconis, P. (1980). Average running time of the fast Fourier transform. Journal of Algorithms, 1, 187–208.
Diaconis, P. and Shahshahani, M. Products of random matrices and computer image generation. In Random Matrices and Their Applications (Contemporary Mathematics, Vol. 50), edited by J.E. Cohen, H. Kesten, and CM. Newman. Providence, RI: American Mathematical Society, 1986. pp. 173–182.
Dixon, W.J. (1957). Estimates of the mean and standard deviation of a normal population. Annals of Mathematical Statistics, 28, 806–809.
Doornbos, R. (1966). Slippage tests. Mathematical Centre Tracts, No. 15, Mathematisch Centrum, Amsterdam.
Doornbos, R. and Prins, H.J. (1956). Slippage tests for a set of gammavariates. Indagationes Mathematicae, 18, 329–337.
Doornbos, R. and Prins, H.J. (1958). On slippage tests. Indagationes Mathematicae, 20, 38–55
Doornbos, R. and Prins, H.J. (1958). On slippage tests. Indagationes Mathematicae, 20 438–447.
Dubey, S.D. (1967). Some percentile estimators for Weibull parameters. Technometrics, 9, 119–129.
Dubins, L.E. and Freedman, D. (1966). Invariant probabilities for certain Markov processes. Annals of Mathematical Statistics, 37, 837–848.
Dunnett, C.W. (1960). On selecting the largest of k normal population means (with discussion). Journal of the Royal Statistical Society, Series B, 22, 1–40.
Elliott, P.D.T.A. (1979). Probabilistic Number Theory I: Mean-Value Theorems. New York: Springer-Verlag.
Elliott, P.D.T.A. (1980). Probabilistic Number Theory II: Central Limit Theorems. New York: Springer-Verlag.
Estes, W. (1950). Toward a statistical theory of learning. Psychological Review, 57, 94–107.
Eubank, R.L. (1981). Estimation of the parameters and quantiles of the logistic distribution by linear functions of sample quantiles. Scandinavian Actuarial Journal, 1981, 229–236.
Ferguson, T.S. (1961). On the rejection of outliers. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, edited by J. Neyman. Berkeley and Los Angeles: University of California Press, 1961. pp. 253–287.
Ferguson, T.S. (1989). Who solved the secretary problem? Statistical Science, 4, 282–296.
Gallagher, P.X. (1976). On the distribution of primes in short intervals. Mathematika, 23, 4–9.
Garsia, A. (1962). Arithmetic properties of Bernoulli convolutions. Transactions of the American Mathematical Society, 102, 469–482.
Gastwirth, J.L. (1966). On robust procedures. Journal of the American Statistical Association, 61, 929–948.
Gibbons, J.D., Olkin, I., and Sobel, M. (1977). Selecting and Ordering Populations. New York: Wiley.
Govindarajulu, Z. (1963). On moments of order statistics and quasi-ranges from normal populations. Annals of Mathematical Statistics, 34, 633–651.
Grundy, P.M., Healy, M.J.R., and Rees, D.H. (1956). Economic choice of the amount of experimentation. Journal of the Royal Statistical Society, Series B, 18, 32–49.
Gupta, S.S. (1956). On a decision rule for a problem in ranking means. Ph.D. Thesis (Mimeo. Ser. No. 150). Inst, of Statist., Univ. of North Carolina, Chapel Hill.
Gupta, S.S. (1965). On some multiple decision (selection and ranking) rules. Technometrics, 7, 225–245.
Gupta, S.S. and Huang, D.-Y. (1981). Multiple Statistical Decision Theory: Recent Developments. New York: Springer-Verlag.
Gupta, S.S. and Panchapakesan, S. (1979). Multiple Decision Procedures: Theory and Methodology of Selecting and Ranking Populations. New York: Wiley.
Guttman, I. and Tiao, G.C. (1964). A Bayesian approach to some best population problems. Annals of Mathematical Statistics, 35, 825–835.
Hall, I.J. and Kudo, A. (1968). On slippage tests. I. Annals of Mathematical Statistics, 39, 1693–1699.
Hall, I.J. Kudo, A., and Yeh, N.C. (1968). On slippage tests. II. Annals of Mathematical Statistics, 39, 2029–2037.
Hall, R.R. (1982). On the distribution of square free numbers in short intervals. Mathematika, 29, 57–68.
Harter, H.L. (1959). The use of sample quasi-ranges in estimating population standard deviation. Annals of Mathematical Statistics, 30, 980–999. Correction: 31, 228.
Hashemi-Parast, S.M. and Young, D.H. (1979). Distribution free slippage tests following a Lehmann model. Journal of Statistical Computation and Simulation, 8, 237–251.
Hawkins, D.M. (1980). Identification of Outliers. London and New York: Chapman and Hall.
Herkenrath, U., Kalin, D., and Vogel, W. (Eds.) (1983). Mathematical Learning Models—Theory and Algorithms. New York: Springer-Verlag.
Hull, C.L. (1952). A Behavior System. New Haven: Yale University Press.
Iosifescu, M. and Theodorescu, R. (1969). Random Processes and Learning. New York: Springer-Verlag.
Joshi, S. and Sathe, Y.S. (1981). A k-sample slippage test for location parameter. Journal of Statistical Planning and Inference, 5, 93–98.
Kac, M. (1959). Statistical Independence in Probability, Analysis and Number Theory. (Carus Mathematical Monograph 12, Mathematical Association of America). New York: Wiley.
Kahneman, D., Slovic, P., and Tversky, A. (Eds.) (1982). Judgment under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press.
Kaijser, T. (1978). A limit theorem for Markov chains in compact metric spaces with application to products of random matrices. Duke Mathematical Journal, 45, 311–349.
Kakiuchi, I. and Kimura, M. (1975). On slippage rank tests. I. Bulletin of Mathematical Statistics, 16, 55–71.
Kakiuchi, I., Kimura, M., and Yanagawa, T. (1977). On slippage rank tests. II. Bulletin of Mathematical Statistics, 17, 1–13.
Kapur, M.N. (1957). A property of the optimum solution suggested by Paulson for the k-sample slippage problem for the normal distribution. Indian Society of Agricultural Statistics, 9, 179–190.
Karlin, S. (1953). Some random walks arising in learning models I. Pacific Journal of Mathematics, 3, 725–756.
Karlin, S. and Truax, D. (1960). Slippage problems. Annals of Mathematical Statistics, 31, 296–324.
Kimura, M. (1984). The asymptotic efficiency of conditional slippage tests for exponential families. Statistics and Decisions, 2, 225–245.
Kudo, A. (1956). On the invariant multiple decision procedures. Bulletin of Mathematical Statistics, 6, 57–68.
Lakshmivarahan, S. (1981). Learning Algorithms: Theory and Applications. New York: Springer-Verlag.
Lee, K.R., Kapadia, C.H., and Hutcherson, D. (1982). Statistical properties of quasi-range in small samples from a gamma density. Communications in Statistics Part B—Simulation and Computation, 11, 175–195.
Miller, G.A. (1964). Mathematics and Psychology. New York: Wiley.
Miller, R.G., Jr. (1981). Simultaneous Statistical Inference. 2nd Ed. New York: Springer-Verlag.
Mosteller, F. (1971). Fifty Challenging Problems in Probability with Solutions. Russian translation, pp. 23, [See B21 in Bibliography.]
Mosteller, F. (1971). Fifty Challenging Problems in Probability with Solutions Russian translation, 98–101. [See B21 in Bibliography.]
Neave, H.R. (1975). A quick and simple technique for general slippage problems. Journal of the American Statistical Association, 70, 721–726.
Norman, M.F. (1972). Markov Processes and Learning Models. New York: Academic Press.
Norman, M.F. and Yellott, J.I., Jr. (1966). Probability matching. Psychometrika, 31, 43–60.
Ogawa, J. (1951). Contributions to the theory of systematic statistics, I. Osaka Journal of Mathematics, 3, 175–213.
Paulson, E. (1952a). On the comparison of several experimental categories with a control. Annals of Mathematical Statistics, 23, 239–246.
Paulson, E. (1952b). An optimum solution to the k-sample slippage problem for the normal distribution. Annals of Mathematical Statistics, 23, 610–616.
Paulson, E. A non-parametric solution for the k-sample slippage problem. In Studies in Item Analysis and Prediction, edited by H. Solomon. Stanford, CA: Stanford University Press, 1961. pp. 233–238.
Paulson, E. (1962). A sequential procedure for comparing several experimental categories with a standard or control. Annals of Mathematical Statistics, 33, 438–443.
Pfanzagl, J. (1959). Ein kombiniertes test und klassifikations-problem. Metrika, 2, 11–45.
Ramachandran, K.V. and Khatri, C.G. (1957). On a decision procedure based on the Tukey statistic. Annals of Mathematical Statistics, 28, 802–806.
Rejali, A. (1978). On the asymptotic expansions for the moments and the limiting distributions of some additive arithmetic functions. Ph.D. dissertation, Department of Statistics, Stanford University.
Roberts, C.D. (1963). An asymptotically optimal sequential design for comparing several experimental categories with a control. Annals of Mathematical Statistics, 34, 1486–1493.
Roberts, C.D. (1964). An asymptotically optimal fixed sample size procedure for comparing several experimental categories with a control. Annals of Mathematical Statistics, 35, 1571–1575.
Sarhan, A.E. and Greenberg, B.G. (Eds.). (1962). Contributions to Order Statistics. New York: Wiley.
Schwager, S.J. Mean slippage problems. In Encyclopedia of Statistical Sciences, Vol. 5, edited by S. Kotz and N.L. Johnson. New York: Wiley, 1985. pp. 372–375.
Somerville, P.N. (1954). Some problems of optimum sampling. Biometrika, 41, 420–429.
Somerville, P.N. (1970). Optimum sample size for a problem in choosing the population with the largest mean. Journal of the American. Statistical Association, 65, 763–775.
Srivastava, M.S. (1973). The performance of a sequential procedure for a slippage problem. Journal of the Royal Statistical Society, Series B, 35, 97–103.
Stein, C (1981). The variance of the number of square-free numbers in a random interval. Technical Report, Department of Statistics, Stanford University.
Thurstone, L.L. (1919). The learning curve equation. Psychological Monographs, 26, No. 3.
Truax, D.R. (1953). An optimum slippage test for the variances of k normal distributions. Annals of Mathematical Statistics, 24, 669–674.
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Diaconis, P., Lehmann, E. (1990). Contributions to Mathematical Statistics. In: Fienberg, S.E., Hoaglin, D.C., Kruskal, W.H., Tanur, J.M. (eds) A Statistical Model. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3384-8_4
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