Shayle R. Searle

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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.



  • 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




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

Selected journal articles[edit]

  • Searle, SR (1999). "Comments from thirty years of teaching matrix algebra to applied statisticians" (PDF). The Bulletin of the International Linear Algebra Society (22): 3–5. 
  • Searle, S. R. (1998). "Winning Probabilities of Lotto in the United States". Chance. American Statistical Association. 11: 20–25. doi:10.1080/09332480.1998.10542073. 
  • Searle, S. R. (1997). "Built-In Restrictions on Best Linear Unbiased Predictors (BLUP) of Random Effects in Mixed Models". The American Statistician. 51 (1): 19–21. doi:10.2307/2684686. JSTOR 2684686. 
  • Searle, SR (1997). "Selecting high-producing farm animals – With help from statistics". Chance, New Directions for Statistics and Computers. 10 (2): 15–18. 
  • Searle, S. R. (1997). "The matrix Handling of BLUE and BLUP in the mixed linear model". Linear Algebra and its Applications. 264: 291–201. doi:10.1016/S0024-3795(96)00400-4. 
  • McCulloch, C. E.; Searle, S. R. (1995). "On an Identity Derived from Unbiasedness in Linear Models". The American Statistician. 49 (1): 39–42. doi:10.2307/2684809. 
  • Searle, S. R. (1995). "An overview of variance component estimation". Metrika. 42: 215. doi:10.1007/BF01894301. 
  • Searle, S. R. (1994). "Extending some results and proofs for the singular linear model". Linear Algebra and its Applications. 210: 139–201. doi:10.1016/0024-3795(94)90469-3. 
  • Searle, S. R. (1994). "Analysis of Variance Computing Package Output for Unbalanced Data from Fixed-Effects Models with Nested Factors". The American Statistician. 48 (2): 148–153. doi:10.2307/2684275. JSTOR 2684275. 
  • Yu, H.; Searle, S. R.; McCulloch, C. E. (1994). "Properties of maximum likelihood estimators of variance components in the one-way classification, balanced data". Communications in Statistics - Simulation and Computation. 23 (4): 897. doi:10.1080/03610919408813207. 
  • Searle, S. R. (1991). "C. R. Henderson, the Statistician; and His Contributions to Variance Components Estimation". Journal of Dairy Science. 74 (11): 4035–4044. doi:10.3168/jds.S0022-0302(91)78599-8. PMID 1757641. 
  • Henderson, H. V.; Searle, S. R. (1990). "Generalized dispersion matrices for covariance structural analysis". Linear Algebra and its Applications. 127: 543. doi:10.1016/0024-3795(90)90361-F. 
  • Searle, S. R. (1989). "Obituary: Charles Roy Henderson 1911-1989". Biometrics. 45 (4): 1333–1335. JSTOR 2531789. 
  • Searle, SR (1989). "Obituary: Charles Roy Henderson, 1911–1989". Bulletin of the Institute of Mathematical Statistics. 18: 338–338. 
  • Searle, S. R. (1989). "\The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator]: Comment". The American Statistician. 43 (3): 162–163. doi:10.2307/2685064. JSTOR 2685064. 
  • Searle, S. R. (1988). "Annotated Computer Output, Second Edition: ACO2". The American Statistician. 42 (4): 272. doi:10.2307/2685138. JSTOR 2685138. 
  • Searle, S. R. (1988). "Mixed models and unbalanced data: Wherefrom, whereat and whereto?". Communications in Statistics - Theory and Methods. 17 (4): 935–968. doi:10.1080/03610928808829667. 
  • Searle, S. R. (1988). "Parallel Lines in Residual Plots". The American Statistician. 42 (3): 211. doi:10.2307/2685008. JSTOR 2685008. 
  • Searle, SR (1988). J. Srivastava, ed. "Probability and Statistics Essays in Honor of Franklin A. Graybill". Amsterdam: North-Holland.  |chapter= ignored (help)
  • Mcculloch, C.E., Schwager, S.J., Casella,G. and Searle, SR, eds. (1986). Statistical Design: Theory and Practice: Proc. of a Conference in Honor of Walter T. Federer. Ithaca, NY: Cornell University. 
  • Searle, S. R.; Pukelsheim, F. (1986). "Effects of Intraclass Correlation on Weighted Averages". The American Statistician. 40 (2): 103–105. doi:10.2307/2684865. 
  • Searle, S. R.; Pukelsheim, F. (1985). "Establishing χ2 Properties of Sums of Squares Using Induction". The American Statistician. 39 (4): 301–303. doi:10.2307/2683710. 
  • Anderson, R. D., Henderson, HV, Pukelsheim, F., Searle, SR (1984). "Best estimation of variance components from balanced data, with arbitrary kurtosis". Mathematische Operationsforschung und Statistik, Series Statistics. 15: 163–176. doi:10.1080/02331888408801755. 
  • Manfredi, E. J.; Everett, R. W.; Searle, S. R. (1984). "Phenotypic and Genetic Statistics of Components of Milk and Two Measures of Somatic Cell Concentration". Journal of Dairy Science. 67 (9): 2028–2033. doi:10.3168/jds.S0022-0302(84)81539-8. PMID 6541666. 
  • Searle, S. R. (1984). "Restrictions and Generalized Inverses in Linear Models". The American Statistician. 38 (1): 53–54. doi:10.2307/2683560. JSTOR 2683560. 
  • Searle, S. R.; Swallow, W. H.; McCulloch, C. E. (1984). "Nontestable Hypotheses in Linear Models". SIAM. J. on Algebraic and Discrete Methods. 5 (4): 486–496. doi:10.1137/0605047. 
  • Searle, S. R.; Henderson, H. V. (1983). "Faults in a computing algorithm for reparameterizing linear models". Communications in Statistics - Simulation and Computation. 12: 67. doi:10.1080/03610918308812300. 
  • Searle, S. R.; Hudson, G. F. S.; Federer, W. T. (1983). "Annotated Computer Output for Analysis of Covariance". The American Statistician. 37 (2): 172–173. doi:10.2307/2685886. 
  • Searle, S. R. (1983). "The Recurrence Formulae for Means and Variances". Teaching Statistics. 5: 7. doi:10.1111/j.1467-9639.1983.tb00481.x. 
  • Searle, S. R.; Hudson, G. F. S. (1982). "Some Distinctive Features of Output from Statistical Computing Packages for Analysis of Covariance". Biometrics. 38 (3): 737–745. doi:10.2307/2530053. 
  • Henderson, H. V.; Searle, S. R. (1981). "On Deriving the Inverse of a Sum of Matrices". SIAM Review. 23 (1): 53–60. doi:10.1137/1023004. 
  • Henderson, H. V.; Searle, S. R. (1981). "The vec-permutation matrix, the vec operator and Kronecker products: A review". Linear and Multilinear Algebra. 9 (4): 271. doi:10.1080/03081088108817379. 
  • Searle, S. R. (1981). "Annotated Computer Output for Variance Components". The American Statistician. 35 (2): 111–112. doi:10.2307/2683158. JSTOR 2683158. 
  • Searle, S. R.; Speed, F. M.; Henderson, H. V. (1981). "Some Computational and Model Equivalences in Analyses of Variance of Unequal-Subclass-Numbers Data". The American Statistician. 35 (1): 16–33. doi:10.2307/2683578. 
  • Searle, SR (1981). "Quirks in linear model calculations with unbalanced data" (PDF). Proceedings of the Sixth Annual SAS Users Group International Conference: 38–45. 
  • Searle, S. R. (1980). "Arbitrary hypotheses in linear mod fi.S with unbalanced data". Communications in Statistics - Theory and Methods. 9 (2): 181–200. doi:10.1080/03610928008827870. 
  • Searle, S. R.; Firey, P. A. (1980). "Computer Generation of Data Sets for Homework Exercises in Simple Regression". The American Statistician. 34 (1): 51–54. doi:10.2307/2682999. 
  • Searle, S. R.; Speed, F. M.; Milliken, G. A. (1980). "Population Marginal Means in the Linear Model: An Alternative to Least Squares Means". The American Statistician. 34 (4): 216–221. doi:10.2307/2684063. 
  • Henderson, H. V.; Searle, S. R. (1979). "Vec and Vech Operators for Matrices, with Some Uses in Jacobians and Multivariate Statistics". The Canadian Journal of Statistics. 7 (1): 65–81. doi:10.2307/3315017. 
  • Searle, S. R. (1979). "Alternative covariance models for the 2-way crossed classification". Communications in Statistics - Theory and Methods. 8 (8): 799–818. doi:10.1080/03610927908827800. 
  • Searle, S. R. (1979). "Annotated Computer Output for Analysis of Variance of Unequal-Subclass- Numbers Data". The American Statistician. 33 (4): 222–223. doi:10.2307/2683742. JSTOR 2683742. 
  • Searle, SR (1979). "Discussion of H. Ahrens' '`An invariance property for first and second order moments of stimated variance-covariance components (19th Session on Stochastics)". Biometrical Journal. Journal of Mathematical Methods in Biosciences. [Continues: iometrische Zeitschrift. Zeitschrift für mathematische Methoden in den Biowissenschaften]. 21: 389–398. 
  • Searle, S. R.; Henderson, H. V. (1979). "Dispersion Matrices for Variance Components Models". Journal of the American Statistical Association. 74 (366): 465–470. doi:10.2307/2286357. 
  • Swallow, W. H.; Searle, S. R. (1978). "Minimum Variance Quadratic Unbiased Estimation (MIVQUE) of Variance Components". Technometrics. 20 (3): 265–272. doi:10.2307/1268135. 
  • Searle, S. R. (1977). "Proof". International Journal of Mathematical Education in Science and Technology. 8 (2): 185–192. doi:10.1080/0020739770080207. 
  • Corbeil, R. R.; Searle, S. R. (1976). "A Comparison of Variance Component Estimators". Biometrics. 32 (4): 779–791. doi:10.2307/2529264. 
  • Corbeil, R. R.; Searle, S. R. (1976). "Restricted Maximum Likelihood (REML) Estimation of Variance Components in the Mixed Model". Technometrics. 18 (1): 31–38. doi:10.2307/1267913. 
  • Henderson, C. R.; Searle, S. R.; Schaeffer, L. R. (1974). "The Invariance and Calculation of Method 2 for Estimating Variance Components". Biometrics. 30 (4): 583–588. doi:10.2307/2529223. 
  • Searle, S. R.; Rounsaville, T. R. (1974). "A Note on Estimating Covariance Components". The American Statistician. 28 (2): 67–68. doi:10.2307/2683606. 
  • Searle, S. R. (1973). "On Publishing Extended Abstracts, and Reviews". The American Statistician. 27 (4): 155–157. doi:10.2307/2684045. JSTOR 2684045. 
  • Rudan, J. W.; Searle, S. R. (1971). "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. doi:10.2307/2528844. 
  • Searle, S. R. (1971). "A Biometrics Invited Paper. Topics in Variance Component Estimation". Biometrics. 27 (1): 1–76. doi:10.2307/2528928. JSTOR 2528928. 
  • Townsend, E. C.; Searle, S. R. (1971). "Best Quadratic Unbiased Estimation of Variance Components from Unbalanced Data in the 1-Way Classification". Biometrics. 27 (3): 643–657. doi:10.2307/2528602. 
  • Searle, S. R. (1970). "Large Sample Variances of Maximum Likelihood Estimators of Variance Components Using Unbalanced Data". Biometrics. 26 (3): 505–524. doi:10.2307/2529105. JSTOR 2529105. 
  • Searle, S. R.; Fawcett, R. F. (1970). "Expected Mean Squares in Variance Components Models Having Finite Populations". Biometrics. 26 (2): 243–254. doi:10.2307/2529072. 
  • Hartley, H. O.; Searle, S. R. (1969). "A Discontinuity in Mixed Model Analyses". Biometrics. 25 (3): 573–576. doi:10.2307/2528909. 
  • Searle, S. R. (1969). "Correlation Between Means of Parts and Wholes". The American Statistician. 23 (2): 23–24. doi:10.2307/2681294. JSTOR 2681294. 
  • Searle, SR (1968). "A remark on solving equations in sums of powers". Journal of the Royal Statistical Society, Series B. 30: 567–569. 
  • Searle, S. R. (1968). "Another Look at Henderson's Methods of Estimating Variance Components". Biometrics. 24 (4): 749–787. doi:10.2307/2528870. JSTOR 2528870. 
  • Searle, S. R. (1965). "The Value of Indirect Selection: I. Mass Selection". Biometrics. 21 (3): 682–707. doi:10.2307/2528550. JSTOR 2528550. PMID 5858099. 
  • Searle, SR (1965). "Additional results concerning estimable functions and generalized inverse matrices". Journal of the Royal Statistical Society, Series B. 27: 486–490. 
  • Searle, S. R. (1963). "The efficiency of ancestor records in animal selection". Heredity. 18 (3): 351–821. doi:10.1038/hdy.1963.35. 
  • Searle, S. R. (1961). "Variance Components in the Unbalanced 2-Way Nested Classification". The Annals of Mathematical Statistics. 32 (4): 1161. doi:10.1214/aoms/1177704854. 
  • Searle, S. R.; Henderson, C. R. (1961). "Computing Procedures for Estimating Components of Variance in the Two-Way Classification, Mixed Model". Biometrics. 17 (4): 607–616. doi:10.2307/2527859. 
  • Searle, S. R.; Henderson, C. R. (1960). "Judging the Effectiveness of Age-Correction Factors". Journal of Dairy Science. 43 (7): 966. doi:10.3168/jds.S0022-0302(60)90260-5. 
  • VanVleck, LD and Searle, SR and Henderson, CR (1960). "The Number of Daughter-Dam Pairs Needed for Estimating Heritability". Journal of Animal Science. 19 (3): 916. 
  • Henderson, C. R.; Kempthorne, O.; Searle, S. R.; Von Krosigk, C. M. (1959). "The Estimation of Environmental and Genetic Trends from Records Subject to Culling". Biometrics. 15 (2): 192–218. doi:10.2307/2527669. 
  • Searle, S. R. (1959). "Use of the Selection Index Method to Account for the Number of Daughters and Records in Progeny-Testing a Dairy Bull". Journal of Dairy Science. 42 (10): 1666–1674. doi:10.3168/jds.S0022-0302(59)90785-4. 
  • Searle, S. R.; Henderson, C. R. (1959). "Establishing Age-Correction Factors Related to the Level of Herd Production". Journal of Dairy Science. 42 (5): 824. doi:10.3168/jds.S0022-0302(59)90659-9. 
  • Searle, S. R. (1958). "Sampling Variances of Estimates of Components of Variance". The Annals of Mathematical Statistics. 29: 167. doi:10.1214/aoms/1177706713. 
  • Castle, O. M.; Searle, S. R. (1957). "Repeatability of Dairy Cow Butterfat Records in New Zealand". Journal of Dairy Science. 40 (10): 1277. doi:10.3168/jds.S0022-0302(57)94626-X. 
  • Callow, E. H.; Searle, S. R. (1956). "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. doi:10.1017/S002185960003032X. 
  • Searle, S. R. (1956). "Matrix Methods in Components of Variance and Covariance Analysis". The Annals of Mathematical Statistics. 27 (3): 737. doi:10.1214/aoms/1177728180. 
  • Searle, SR (1951). "Probability: difficulties of definition.". Journal of Institute of Actuaries Students' Society: 204–212. 


External links[edit]