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Jack Carl Kiefer (January 25, 1924 – August 10, 1981) was an American statistician.

Biography

Jack Kiefer was born on January 25, 1924, in Cincinnati, Ohio, to Carl Jack Kiefer and Marguerite K. Rosenau. He began his undergraduate studies at the Massachusetts Institute of Technology in 1942, but left after one year, taking up a position as first lieutenant in the United States Air Force during World War II. In 1946, he returned to MIT, graduating with bachelor's and master's degrees in economics and engineering in 1948 under the supervision of Harold Freeman. He then began graduate studies at Columbia University, under the supervision of Abraham Wald and Jacob Wolfowitz, receiving his Ph.D. in mathematical statistics in 1952. While still a graduate student, he began teaching at Cornell University, remaining there until 1979, when he retired from Cornell and accepted a new position as Miller Research Professor in the Department of Statistics and Mathematics at the University of California, Berkeley. In 1957, he married Dooley Sciple, a former undergraduate student of his at Cornell, with whom he had two children. Kiefer died of a heart attack in Berkeley, California on August 10, 1981.

Awards and honors

Kiefer was a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics, a member of the American Academy of Arts and Sciences (elected 1972) and of the United States National Academy of Sciences (elected 1975). From 1969–1970 he was president of the Institute of Mathematical Statistics. In 1973, Kiefer and Michael Fisher were the first two Cornell faculty elected as Horace White Professors.

Contributions

Much of Kiefer's research was on the design of experiments; the American Statistician obituary calls him "undoubtedly the foremost worker in optimal experimental design". However, he also made significant contributions to other areas of statistics and optimization, including the introduction of golden section search (his master's thesis work) the Dvoretzky–Kiefer–Wolfowitz inequality and the Bahadur-Ghosh-Kiefer representation (with R. R. Bahadur and J. K. Ghosh)

Notes

^ Bechhofer 1982; O'Connor & Robertson 2004.
2 Professors Are Named To Horace White Chairs, Cornell Chronicle, vol. 4, no. 19, Feb. 22, 1973. Page 3. Retrieved May 30, 2011.
Wynn 1984.
Brown 1984
Lahiri, S. N (1992). "On the Bahadur—Ghosh—Kiefer representation of sample quantiles". Statistics & probability letters. 15 (2): 163–168. doi:10.1016/0167-7152(92)90130-w.

References

Bechhofer, R. (1982), "Jack Carl Kiefer 1924–1981", The American Statistician, 36 (4), American Statistical Association: 356–357, doi:10.1080/00031305.1982.10483047, JSTOR 2683084.
Brown, Lawrence D.; Olkin, Ingram; Sacks, J.; Wynn, H. P. (1985), Jack Carl Kiefer: Collected Papers, Vols. I, II, III, Springer-Verlag, ISBN 0-387-96003-1, ISBN 0-387-96004-X. Reviewed in Biometrics 43 (1): 257.
Brown, Lawrence D. (1984), "The research of Jack Kiefer outside the area of experimental design", Annals of Statistics, 12 (2): 406–415, doi:10.1214/aos/1176346495.
O'Connor, John J.; Robertson, Edmund F., "Jack Kiefer", MacTutor History of Mathematics Archive, University of St Andrews
Sacks, Jerome (1984), "Jack Carl Kiefer 1924–1981", Annals of Statistics, 12 (2): 403–405, doi:10.1214/aos/1176346494.
Wynn, Henry P. (1984), "Jack Kiefer's contributions to experimental design", Annals of Statistics, 12 (2): 416–423, doi:10.1214/aos/1176346496.
"The publications and writings of Jack Kiefer", Annals of Statistics, 12 (2): 424–430, 1984, doi:10.1214/aos/1176346497.

Statistics

Descriptive statistics

Continuous data

Center	Mean Arithmetic Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode
Dispersion	Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance
Shape	Central limit theorem Moments Kurtosis L-moments Skewness

Count data

Index of dispersion

Summary tables

Dependence

Graphics

Data collection

Study design	Effect size Missing data Optimal design Population Replication Sample size determination Statistic Statistical power
Survey methodology	Sampling Cluster Stratified Opinion poll Questionnaire Standard error
Controlled experiments	Blocking Factorial experiment Interaction Random assignment Randomized controlled trial Randomized experiment Scientific control
Adaptive designs	Adaptive clinical trial Stochastic approximation Up-and-down designs
Observational studies	Cohort study Cross-sectional study Natural experiment Quasi-experiment

Statistical inference

Statistical theory

Frequentist inference

Point estimation	Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao–Blackwellization Lehmann–Scheffé theorem Median unbiased Plug-in
Interval estimation	Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Testing hypotheses	1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons
Parametric tests	Likelihood-ratio Score/Lagrange multiplier Wald

Specific tests

Z-test (normal) Student's t-test F-test
Goodness of fit	Chi-squared G-test Kolmogorov–Smirnov Anderson–Darling Lilliefors Jarque–Bera Normality (Shapiro–Wilk) Likelihood-ratio test Model selection Cross validation AIC BIC
Rank statistics	Sign Sample median Signed rank (Wilcoxon) Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van der Waerden test

Bayesian inference

Correlation	Pearson product-moment Partial correlation Confounding variable Coefficient of determination
Regression analysis	Errors and residuals Regression validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS)
Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression
Non-standard predictors	Nonlinear regression Nonparametric Semiparametric Isotonic Robust Homoscedasticity and Heteroscedasticity
Generalized linear model	Exponential families Logistic (Bernoulli) / Binomial / Poisson regressions
Partition of variance	Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom

Categorical / Multivariate / Time-series / Survival analysis

Categorical

Multivariate

Time-series

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality
Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey
Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR)
Frequency domain	Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood

Survival

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time
Hazard function	Nelson–Aalen estimator
Test	Log-rank test

Applications

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics
Engineering statistics	Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification
Social statistics	Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National accounts Official statistics Population statistics Psychometrics
Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging

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