Shayle R. Searle Explained

Shayle Robert Searle PhD (26 April 1928 – 18 February 2013) was a New Zealand mathematician who was professor emeritus of biological statistics at Cornell University.^[1] He was a leader in the field of linear and mixed models in statistics, and published widely on the topics of linear models, mixed models, and variance component estimation.^[2]

Searle was one of the first statisticians to use matrix algebra in statistical methodology, and was an early proponent of the use of applied statistical techniques in animal breeding.

He died at his home in Ithaca, New York.

Education

• BA – Victoria University of Wellington – 1949
• MSc – Victoria University of Wellington – 1950
• PhD – Cornell University – 1958
• DSc (h.c.) – Victoria University of Wellington – 2005

Employment

• Research statistician – New Zealand Dairy Board – 1953 to 1955, 1959 to 1962
• Statistician – University Computing Center, Cornell University – 1962 to 1965
• Professor of biological statistics – Cornell University – 1965 to 1996

Honours

• Winner, Humboldt Research Award of the Alexander von Humboldt Foundation
• Fellow, American Statistical Association
• Fellow, Royal Statistical Society
• Honorary Fellow, Royal Society of New Zealand^[3]

Bibliography

Books

• Book: Shayle R. Searle . The Collected Works of Shayle R. Searle . Wiley . New York . 2009 . 978-0-470-55606-1.
• Book: Neuhaus, John William . McCulloch, Charles E. . Shayle R. Searle . Generalized, Linear, and Mixed Models (Wiley Series in Probability and Statistics) . Wiley-Interscience . New York . 2008 . 978-0-470-07371-1 . 2nd.
• Book: Shayle R. Searle . Linear Models for Unbalanced Data (Wiley Series in Probability and Statistics) . Wiley-Interscience . New York . 2006 . 0-470-04004-1.
• Book: McCulloch, Charles E. . Shayle R. Searle . George Casella . Casella, George . Variance Components (Wiley Series in Probability and Statistics) . Wiley-Interscience . New York . 2006 . 0-470-00959-4.
• Book: Shayle R. Searle . Matrix Algebra Useful for Statistics (Wiley Series in Probability and Statistics) . Wiley-Interscience . New York . 2006 . 0-470-00961-6.
• Book: Shayle R. . Searle . McCulloch . Charles E. . Generalized, Linear, and Mixed Models . John Wiley & Sons . Chichester . 2001 . 0-471-19364-X . 1st.
• Book: Willett, Lois Schertz . Searle, S. R. . Matrix algebra for applied economics . John Wiley & Sons . Chichester . 2001 . 0-471-32207-5.
• Book: Searle, S. R. . Linear models . registration . Wiley . New York . 1971 . 0-471-18499-3.
• Book: Hausman, Warren H. . Searle, S. R. . Matrix algebra for business and economics . Wiley-Interscience . New York . 1970 . 0-471-76941-X . registration .
• Book: Shayle R. Searle . Matrix Algebra for the Biological Sciences (Series on Quantitative Methods for Biologists & Medical Scientists) . John Wiley & Sons Inc . 1966 . 0-471-76930-4.

Selected journal articles

2000s

• Cowpertwait . P.. Wake . G.. Anderson . R. D.. Edwards . H.. Searle . S.. Statistics and applied probability: a tribute to Jeffrey J. Hunter. Journal of Applied Mathematics and Decision Sciences. 2007. 1–4. 2007. 10.1155/2007/57619. free.
• 2005 . Searle, SR . Recollections from a 50-year random walk midst matrices, statistics and computing . Research Letters in the Information and Mathematical Sciences . 1175-2777 . 8 . 45–52 . dead . https://web.archive.org/web/20081014072829/http://www-ub.massey.ac.nz/%7Ewwiims/research/letters/volume8/index.html . 14 October 2008 . dmy-all .
• Costa . C. N. . Blake . R. W. . Pollak . E. J. . Oltenacu . P. A. . Quaas . R. L. . Searle . S. R. . 10.3168/jds.S0022-0302(00)75196-4 . Genetic Analysis of Holstein Cattle Populations in Brazil and the United States . Journal of Dairy Science . 83 . 12 . 2963–2974 . 2000 . 11132868. free .
• 2000 . Searle, SR . The infusion of matrices into statistics . The Bulletin of the International Linear Algebra Society . 24 . 25–32 .

1990s

• 1999 . Searle, SR . Comments from thirty years of teaching matrix algebra to applied statisticians . The Bulletin of the International Linear Algebra Society . 3–5. 22 .
• Winning Probabilities of Lotto in the United States. Searle . S. R.. Chance. 1998. 11. 20–25. American Statistical Association. 10.1080/09332480.1998.10542073.
• Searle . S. R. . Built-In Restrictions on Best Linear Unbiased Predictors (BLUP) of Random Effects in Mixed Models . The American Statistician . 51 . 1 . 19–21 . 10.2307/2684686 . 1997 . 2684686 . 1813/31824 . free .
• 1997 . Searle, SR . Selecting high-producing farm animals – With help from statistics . Chance, New Directions for Statistics and Computers . 10 . 15–18 . 2.
• Searle . S. R. . 10.1016/S0024-3795(96)00400-4 . The matrix Handling of BLUE and BLUP in the mixed linear model . Linear Algebra and Its Applications . 264 . 291–311. 1997 . 1813/31864 . free .
• McCulloch . C. E. . Searle . S. R. . On an Identity Derived from Unbiasedness in Linear Models . The American Statistician . 49 . 1 . 39–42 . 10.2307/2684809 . 1995 . 2684809 . 1813/31745 . free .
• Searle . S. R. . 10.1007/BF01894301 . An overview of variance component estimation . Metrika . 42 . 215–230 . 1995 . 1813/31816 . 122756737 . free .
• Searle . Shayle . 1995 . Comments on J. A. Nelder. 'The statistics of linear models: back to basics' . Statistics and Computing . 5 . 2 . 103–107 . 10.1007/BF00143939. 119967856 .
• Searle . S. R. . 10.1016/0024-3795(94)90469-3 . Extending some results and proofs for the singular linear model . Linear Algebra and Its Applications . 210 . 139–201 . 1994 . 1813/31746 . free .
• Searle . S. R. . Analysis of Variance Computing Package Output for Unbalanced Data from Fixed-Effects Models with Nested Factors . The American Statistician . 48 . 2 . 148–153 . 10.2307/2684275 . 1994 . 2684275 . 1813/31786 . free .
• Yu . H. . Searle . S. R. . McCulloch . C. E. . 10.1080/03610919408813207 . Properties of maximum likelihood estimators of variance components in the one-way classification, balanced data . Communications in Statistics - Simulation and Computation . 23 . 4 . 897 . 1994 . 1813/31711 . free .
• Loynes . R . Searle . S . Casella . G . McCulloch . Charles . 1994 . Variance Components . Biometrics . 50 . 1224 . 10.2307/2533462 . 2533462 .
• Searle . Shayle . Casella . George . MacCulloch . Charles . 1994 . Variance Components . Journal of the American Statistical Association . 89 . 10.2307/2291239 . 2291239 .
• Westfall . Peter . Searle . S . Casella . G . McCulloch . Charles . 1993 . Variance Components . Journal of Marketing Research . 30 . 258 . 10.2307/3172833. 3172833 .
• Searle . S. R. . 1993 . Analysis of variance computing then and now, with reference to unbalanced data . 18th SAS Users’ Group Conference . 1077–1087 . New York .
• Searle . S. R. . C. R. Henderson, the Statistician; and His Contributions to Variance Components Estimation . 10.3168/jds.S0022-0302(91)78599-8 . Journal of Dairy Science . 74 . 11 . 4035–4044 . 1991 . 1757641. 1813/31657 . free .
• Henderson . H. V. . Searle . S. R. . 10.1016/0024-3795(90)90361-F . Generalized dispersion matrices for covariance structural analysis . Linear Algebra and Its Applications . 127 . 543–565 . 1990 . 1813/32786 . free .

1980s

• Searle . Shayle . 1989 . Variance components – some history and summary account of estimation methods . Journal of Animal Breeding and Genetics . 106 . 1–6 . 1–29 . 10.1111/j.1439-0388.1989.tb00209.x . 1813/33072 . free .
• Searle . S. R. . Obituary: Charles Roy Henderson 1911–1989 . Biometrics . 45 . 4 . 1333–1335 . 1989 . 2531789.
• 1989 . Searle, SR . Obituary: Charles Roy Henderson, 1911–1989 . Bulletin of the Institute of Mathematical Statistics . 18 . 338.
• Searle . S. R. . The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator: Comment . The American Statistician . 43 . 3 . 162–163 . 10.2307/2685064 . 1989 . 2685064 .
• Searle . Shayle . 1989 . Statistical Computing Packages: Some Words of Caution . American Statistician . 43 . 4 . 189–190 . 10.1080/00031305.1989.10475656.
• Searle . S. R. . Annotated Computer Output, Second Edition: ACO₂ . The American Statistician . 42 . 4 . 272 . 10.2307/2685138 . 1988 . 2685138 .
• Searle . S. R. . Mixed models and unbalanced data: Wherefrom, whereat and whereto? . 10.1080/03610928808829667 . Communications in Statistics - Theory and Methods . 17 . 4 . 935–968 . 1988 . 1813/33040 . free .
• Searle . S. R. . Parallel Lines in Residual Plots . The American Statistician . 42 . 3 . 211 . 10.2307/2685008 . 1988 . 2685008 . 1813/33060 . free .
• Book: 1988 . Searle, SR . Best linear unbiased estimation in mixed models of the analysis of variance . Probability and Statistics Essays in Honor of Franklin A. Graybill . J. Srivastava . Amsterdam . North-Holland.
• Ziegel . Eric . McCulloch . Charles . Schwager . Steven . Casella . George . Searle . Shayle . 1988 . Statistical Design: Theory and Practice . Technometrics . 30 . 10.2307/1270187. 1270187 .
• Book: 1986 . Mcculloch, C.E. . Schwager, S.J. . Casella, G. . Searle, SR . Statistical Design: Theory and Practice: Proc. of a Conference in Honor of Walter T. Federer. . Cornell University . Ithaca, NY.
• Searle . S. R. . Pukelsheim . F. . Effects of Intraclass Correlation on Weighted Averages . The American Statistician . 40 . 2 . 103–105 . 10.2307/2684865 . 1986 . 2684865 . 1813/32989 . free .
• Searle . S. R. . Pukelsheim . F. . Establishing χ² Properties of Sums of Squares Using Induction . The American Statistician . 39 . 4 . 301–303 . 10.2307/2683710 . 1985 . 2683710 .
• 1984 . Anderson, R. D., Henderson, HV, Pukelsheim, F., Searle, SR . Best estimation of variance components from balanced data, with arbitrary kurtosis . Mathematische Operationsforschung und Statistik, Series Statistics . 15 . 2 . 163–176 . 10.1080/02331888408801755. 1813/32795 . free .
• Manfredi . E. J. . Everett . R. W. . Searle . S. R. . 10.3168/jds.S0022-0302(84)81539-8 . Phenotypic and Genetic Statistics of Components of Milk and Two Measures of Somatic Cell Concentration . Journal of Dairy Science . 67 . 9 . 2028–2033 . 1984 . 6541666. free .
• Searle . S. R. . Restrictions and Generalized Inverses in Linear Models . The American Statistician . 38 . 1 . 53–54 . 10.2307/2683560 . 1984 . 2683560 . 1813/32898 . free .
• Searle . S. R. . Swallow . W. H. . McCulloch . C. E. . 10.1137/0605047 . Nontestable Hypotheses in Linear Models . . 5 . 4 . 486–496 . 1984 . 1813/32926 . free .
• 1983 . Henderson . H.V. . Pukelsheim . F. . Searle . S.R. . On the history of the Kronecker product . Linear and Multilinear Algebra . 14 . 2 . 113–120 . 10.1080/03081088308817548 . 1813/32834 . free .
• Searle . S. R. . Henderson . H. V. . 10.1080/03610918308812300 . Faults in a computing algorithm for reparameterizing linear models . Communications in Statistics - Simulation and Computation . 12 . 67–76 . 1983 .
• Searle . S. R. . Hudson . G. F. S. . Federer . W. T. . Annotated Computer Output for Analysis of Covariance . The American Statistician . 37 . 2 . 172–173 . 10.2307/2685886 . 1983 . 2685886 .
• Searle . S. R. . 10.1111/j.1467-9639.1983.tb00481.x . The Recurrence Formulae for Means and Variances . Teaching Statistics . 5 . 7–10 . 1983 . 1813/32866 . free .
• Hypothesis Testing with Type IV Sums of Squares of the Computer Routine SAS GLM . Hudson . G. F. S. . Searle . S. R. . SUGI 1982 . 1982 .
• Searle . S. R. . Hudson . G. F. S. . Some Distinctive Features of Output from Statistical Computing Packages for Analysis of Covariance . Biometrics . 38 . 3 . 737–745 . 10.2307/2530053 . 1982 . 2530053 . 1813/32863 . free .
• Henderson . H. V. . Searle . S. R. . Shayle R. Searle . 10.1137/1023004 . On Deriving the Inverse of a Sum of Matrices . SIAM Review . 23 . 1 . 53–60 . 1981 . 1813/32750 . free .
• Henderson . H. V. . Searle . S. R. . 10.1080/03081088108817379 . The vec-permutation matrix, the vec operator and Kronecker products: A review . Linear and Multilinear Algebra . 9 . 4 . 271 . 1981 . 1813/32747 . free .
• Searle . S. R. . Annotated Computer Output for Variance Components . The American Statistician . 35 . 2 . 111–112 . 10.2307/2683158 . 1981 . 2683158 .
• Searle . S. R. . Speed . F. M. . Henderson . H. V. . Some Computational and Model Equivalences in Analyses of Variance of Unequal-Subclass-Numbers Data . The American Statistician . 35 . 1 . 16–33 . 10.2307/2683578 . 1981 . 2683578 . 1813/32769 . free .
• 1981 . Searle, SR . Quirks in linear model calculations with unbalanced data . Proceedings of the Sixth Annual SAS Users Group International Conference . 38–45 .
• Searle . S. R. . Arbitrary hypotheses in linear mod fi.S with unbalanced data . 10.1080/03610928008827870 . Communications in Statistics - Theory and Methods . 9 . 2 . 181–200 . 1980 .
• Searle . S. R. . Firey . P. A. . Computer Generation of Data Sets for Homework Exercises in Simple Regression . The American Statistician . 34 . 1 . 51–54 . 10.2307/2682999 . 1980 . 2682999 . 1813/32759 . free .
• Searle . S. R. . Speed . F. M. . Milliken . G. A. . Population Marginal Means in the Linear Model: An Alternative to Least Squares Means . The American Statistician . 34 . 4 . 216–221 . 10.2307/2684063 . 1980 . 2684063 .

1970s

• 1979 . Searle . S.R. . On inverting circulant matrices . Linear Algebra and Its Applications . 25 . 77–89 . 10.1016/0024-3795(79)90007-7 . 1813/32683 . free .
• Henderson . H. V. . Searle . S. R. . Vec and Vech Operators for Matrices, with Some Uses in Jacobians and Multivariate Statistics . The Canadian Journal of Statistics . 7 . 1 . 65–81 . 10.2307/3315017 . 1979 . 3315017 .
• Searle . S. R. . Alternative covariance models for the 2-way crossed classification . 10.1080/03610927908827800 . Communications in Statistics - Theory and Methods . 8 . 8 . 799–818 . 1979 .
• Searle . S. R. . Annotated Computer Output for Analysis of Variance of Unequal-Subclass- Numbers Data . The American Statistician . 33 . 4 . 222–223 . 10.2307/2683742 . 1979 . 2683742 .
• 1979 . Searle, SR . Discussion of H. Ahrens' An invariance property for first and second order moments of estimated variance-covariance components (19th Session on Stochastics) . Biometrical Journal . 21 . 389–398. 10.1002/bimj.4710210407 . 1813/32735 . free .
• Searle . S. R. . Henderson . H. V. . Dispersion Matrices for Variance Components Models . Journal of the American Statistical Association . 74 . 366 . 465–470 . 10.2307/2286357 . 1979 . 2286357 .
• Book: Searle, S.R. . 1978 . A univariate formulation of the multivariate linear model . Contributions to Survey Sampling and Applied Statistics, Papers in Honor of H.O. Hartley . H.A. . David . Academic Press . New York . 181–189 . 978-0122047503.
• Swallow . W. H. . Searle . S. R. . Minimum Variance Quadratic Unbiased Estimation (MIVQUE) of Variance Components . Technometrics . 20 . 3 . 265–272 . 10.2307/1268135 . 1978 . 1268135 .
• Searle . S. R. . Proof . 10.1080/0020739770080207 . International Journal of Mathematical Education in Science and Technology . 8 . 2 . 185–192 . 1977 .
• Corbeil . R. R. . Searle . S. R. . A Comparison of Variance Component Estimators . Biometrics . 32 . 4 . 779–791 . 10.2307/2529264 . 1976 . 2529264 . 1813/32662 . free .
• Corbeil . R. R. . Searle . S. R. . Restricted Maximum Likelihood (REML) Estimation of Variance Components in the Mixed Model . Technometrics . 18 . 1 . 31–38 . 10.2307/1267913 . 1976 . 1267913 .
• Henderson . C. R. . Searle . S. R. . Schaeffer . L. R. . The Invariance and Calculation of Method 2 for Estimating Variance Components . Biometrics . 30 . 4 . 583–588 . 10.2307/2529223 . 1974 . 2529223 .
• Searle . S. R. . Rounsaville . T. R. . A Note on Estimating Covariance Components . The American Statistician . 28 . 2 . 67–68 . 10.2307/2683606 . 1974 . 2683606 .
• Searle . S. R. . On Publishing Extended Abstracts, and Reviews . The American Statistician . 27 . 4 . 155–157 . 10.2307/2684045 . 1973 . 2684045 .
• Rudan . J. W. . Searle . S. R. . 323. Note: Large Sample Variances of Maximum Likelihood Estimators of Variance Components in the 3-Way Nested Classification, Random Model, with Unbalanced Data . Biometrics . 27 . 4 . 1087–1091 . 10.2307/2528844 . 1971 . 2528844 .
• Searle . S. R. . A Biometrics Invited Paper. Topics in Variance Component Estimation . Biometrics . 27 . 1 . 1–76 . 10.2307/2528928 . 1971 . 2528928 .
• Townsend . E. C. . Searle . S. R. . Best Quadratic Unbiased Estimation of Variance Components from Unbalanced Data in the 1-Way Classification . Biometrics . 27 . 3 . 643–657 . 10.2307/2528602 . 1971 . 2528602 . 1813/32414 . free .
• Searle . S. R. . Large Sample Variances of Maximum Likelihood Estimators of Variance Components Using Unbalanced Data . Biometrics . 26 . 3 . 505–524 . 10.2307/2529105 . 1970 . 2529105 .
• Searle . S. R. . Fawcett . R. F. . Expected Mean Squares in Variance Components Models Having Finite Populations . Biometrics . 26 . 2 . 243–254 . 10.2307/2529072 . 1970 . 2529072 .

1960s

• Hartley . H. O. . Searle . S. R. . A Discontinuity in Mixed Model Analyses . Biometrics . 25 . 3 . 573–576 . 10.2307/2528909 . 1969 . 2528909 .
• Searle . S. R. . Correlation Between Means of Parts and Wholes . The American Statistician . 23 . 2 . 23–24 . 10.2307/2681294 . 1969 . 2681294 .
• 1968 . Searle, SR . A remark on solving equations in sums of powers . Journal of the Royal Statistical Society, Series B . 30 . 3 . 567–569. 10.1111/j.2517-6161.1968.tb00756.x .
• Searle . S. R. . Another Look at Henderson's Methods of Estimating Variance Components . Biometrics . 24 . 4 . 749–787 . 10.2307/2528870 . 1968 . 2528870 .
• Searle . S. R. . The Value of Indirect Selection: I. Mass Selection . Biometrics . 21 . 3 . 682–707 . 10.2307/2528550 . 1965 . 5858099. 2528550 .
• 1965 . Searle, SR . Additional results concerning estimable functions and generalized inverse matrices . Journal of the Royal Statistical Society, Series B . 27 . 3 . 486–490. 10.1111/j.2517-6161.1965.tb00608.x .
• Searle . S. R. . The efficiency of ancestor records in animal selection . 10.1038/hdy.1963.35 . Heredity . 18 . 3 . 351–821 . 1963 . 14058937. free .
• Searle . S. R. . Variance Components in the Unbalanced 2-Way Nested Classification . 10.1214/aoms/1177704854 . The Annals of Mathematical Statistics . 32 . 4 . 1161–1166 . 1961 . free .
• Searle . S. R. . Henderson . C. R. . Computing Procedures for Estimating Components of Variance in the Two-Way Classification, Mixed Model . Biometrics . 17 . 4 . 607–616 . 10.2307/2527859 . 1961 . 2527859 .
• Searle . S. R. . Henderson . C. R. . 10.3168/jds.S0022-0302(60)90260-5 . Judging the Effectiveness of Age-Correction Factors . Journal of Dairy Science . 43 . 7 . 966 . 1960 . free .
• 1960 . VanVleck, LD and Searle, SR and Henderson, CR . The Number of Daughter-Dam Pairs Needed for Estimating Heritability . Journal of Animal Science . 19 . 916 . 3. 10.2527/jas1960.193916x . 82532852 .

1950s

• Henderson . C. R. . Kempthorne . O. . Searle . S. R. . Von Krosigk . C. M. . The Estimation of Environmental and Genetic Trends from Records Subject to Culling . Biometrics . 15 . 2 . 10.2307/2527669 . 192–218 . 1959 . 2527669 .
• Searle . S. R. . Use of the Selection Index Method to Account for the Number of Daughters and Records in Progeny-Testing a Dairy Bull . 10.3168/jds.S0022-0302(59)90785-4 . Journal of Dairy Science . 42 . 10 . 1666–1674 . 1959 . free .
• Searle . S. R. . Henderson . C. R. . 10.3168/jds.S0022-0302(59)90659-9 . Establishing Age-Correction Factors Related to the Level of Herd Production . Journal of Dairy Science . 42 . 5 . 824 . 1959 . free .
• Searle . S. R. . 10.1214/aoms/1177706713 . Sampling Variances of Estimates of Components of Variance . The Annals of Mathematical Statistics . 29 . 167–178 . 1958 . free .
• Castle . O. M. . Searle . S. R. . 10.3168/jds.S0022-0302(57)94626-X . Repeatability of Dairy Cow Butterfat Records in New Zealand . Journal of Dairy Science . 40 . 10 . 1277 . 1957 . free .
• Callow . E. H. . Searle . S. R. . 10.1017/S002185960003032X . Comparative studies of meat V. Factors affecting the iodine number of the fat from the fatty and muscular tissues of cattle . The Journal of Agricultural Science . 48 . 61–73 . 1956. 85188693 .
• Searle . S. R. . Matrix Methods in Components of Variance and Covariance Analysis . 10.1214/aoms/1177728180 . The Annals of Mathematical Statistics . 27 . 3 . 737–748 . 1956 . free .
• 1951 . Searle, SR . Probability: difficulties of definition. . Journal of Institute of Actuaries Students' Society . 204–212.

Further reading

• Web site: Oral and Personal Histories of Computing at Cornell . Shayle Searle . Office of Information Technologies, Cornell University . 1968.
• 2005 . Searle, Shayle R. . Recollections from a 50-year random walk midst matrices, statistics and computing . Research Letters in the Information and Mathematical Sciences . 1175-2777 . 8 . 45–52 . dead . https://web.archive.org/web/20081014072829/http://www-ub.massey.ac.nz/%7Ewwiims/research/letters/volume8/index.html . 14 October 2008 . dmy-all .
• 10.1214/08-STS259 . 2009 . Martin T. Wells . A Conversation with Shayle R. Searle . Statistical Science . 24 . 2 . 244–254 . 1001.3272 . 62162161 .
• Hunter . Jeffrey . 2015 . Shayle R. Searle: Pioneer in Linear Modelling . 57 . Australian & New Zealand Journal of Statistics . 1–14 . 10.1111/anzs.12107. free .

Notes and References

1. http://stats.org.nz/Newsletter74/Obituaries.htm Professor Shayle Robert Searle (April 26, 1928 – February 18, 2013)
2. Hunter . Jeffrey J. . Shayle R. Searle: Pioneer in Linear Modelling . Australian & New Zealand Journal of Statistics . 57 . 1–14 . 2015 . 10.1111/anzs.12107 . free .
3. Web site: Royal Society of New Zealand elects Shayle Searle, Cornell statistics professor, honorary fellow . Cornell Chronicle . January 28, 2000.