Peña, Daniel On the logical development of statistical models. (English) Zbl 0731.62008 Trab. Estad. 3, No. 2, 195-213 (1988). Summary: This paper presents a classification of statistical models using a simple and logical framework. Some remarks are made on the historical appearance of each type of model and the practical problems that motivated them. It is argued that the current stages of the statistical methodology for model building have arisen in response to the needs of more sophisticated procedures for building dynamic-explicative types of models. Some potentially important topics for future research are included. MSC: 62A01 Foundations and philosophical topics in statistics 62-03 History of statistics 01A99 History of mathematics and mathematicians Keywords:history of statistics; robustness; classification of statistical models; methodology for model building PDFBibTeX XMLCite \textit{D. Peña}, Trab. Estad. 3, No. 2, 195--213 (1988; Zbl 0731.62008) Full Text: DOI EuDML References: [1] ANSCOMBE, F. J., and TUKEY, J. W. (1963): “The examination and analysis of residuals{”,Technometrics, 5, 141–160.} · Zbl 0118.13903 [2] BARNETT, V., and LEWIS, T. (1978):Outliers in Statistical Data, Wiley. · Zbl 0377.62001 [3] BELSELY, D. A.; KUH, E., and WELSCH, R. E. (1980):Regression Diagnostics, Wiley. [4] BERNOULLI, D. (1777): “The most probable choice between several discrepant observations and the formation therefrom of the most likely induction{”, Reprinted inBiometrika, 48, 1–18, 1961.} [5] BOX, G. E. P.; HUNTER, W. G., and HUNTER, J. S. (1978):Statistics for Experimenters, Wiley. · Zbl 0394.62003 [6] BOX, G. E. P., and JENKINS, G. M. (1970):Time Series Analysis, Holden Day. · Zbl 0249.62009 [7] BOX, G. E. P., and TIAO, G. C. (1973):Bayesian Inference in Statistical Analysis, Addison-Wesley. · Zbl 0271.62044 [8] BOX, G. E. P., and COX, D. R. (1964): “An analysis of transformations{”,JRSS, B, 26, 211–243.} · Zbl 0156.40104 [9] BOX, G. E. P. (1983): “The importance of practice in the development of statistics{”,Technical Report No. 2471, Mathematics Research Center, University of Wisconsin-Madison.} · Zbl 0563.62001 [10] BOX, J. F. (1978):Fisher, The Life of a Scientist, New York, Wiley. [11] BRUSH, S. G. (1968): “A history of random processes. I. Brownian movement from Brown to Perrin{”,Archive for the History of Exact Sciences, 5, 1–36.} · Zbl 0177.29803 [12] COOK, R. D., and WEISBERG, S. (1982):Residuals and Influence in Regression, Chapman and Hall. · Zbl 0564.62054 [13] DE FINETTI, B. (1975):Theory of Probability. Wiley. [14] DRAPER, N. R., and SMITH H. (1966):Applied Regression Analysis, Wiley (2nd edition, 1980). [15] EPHREMIDES, A., and THOMAS, J. B. (1973) (editor):Random Processes (Vol I), Dowden Hutchingon and Ross Inc. · Zbl 0364.60005 [16] EPHREMIDES, A. (1975) (editor)Random Processes (Vol. II), Halted Press. · Zbl 0367.60036 [17] KENDALL, D. G. (1966): “Branching processes since 1873{”,J. London Math. Society, 41, 385–406.} · Zbl 0154.42505 [18] HANNAN, E. J. (1970):Multiple Time Series, New York, Wiley. · Zbl 0211.49804 [19] HARRIS, T. E. (1963):The Theory of Branching Processes, Berlin. · Zbl 0117.13002 [20] JEFFREYS, H. (1932): “An alternative to the rejection of observations{”,Proc. Roy. Soc. A., CXXXVII, 78–87.} · JFM 58.0569.02 [21] KARLIN, S., and TAYLOR, H. M. (1975):A First Course in Stochastic Processes, Academic Press. · Zbl 0315.60016 [22] LANCASTER, H. O. (1977): “Development of the notion of statistical dependence{”, instudies in the History of Statistics (Vol. II), M. Kendall and R. L. Placket (editores), Mac Millan Publishing Co., Inc.} [23] MAISTROV, I. E. (1974):Probability Theory. A Historical Sketch, Academic Press. · Zbl 0308.01001 [24] PEÑA, D. (1978): “Modelos con parámetros variables en el análisis de series temporales{”,Questiio, 4, 2, 75–87.} [25] PEÑA, D., and BOX, G. E. P. (1987): “Identifying a Simplifying Structure in time series{”,JASA, 82, 399, pp. 836–843.} · Zbl 0623.62081 [26] SEAL, H. L. (1967): “The historical development of the Gauss linear model{”,Biometrika, 54, 1–24.} · Zbl 0154.25103 [27] STIGLER, S. M. (1975): “Napoleonic Statistics: The Work of Laplace{”,Biometrika, 62, 3, 503–517.} · Zbl 0315.01004 [28] THATCHER, A. R. (1957): “A note on the early solutions of the problem of the duration of the play{”,Biometrika, 44, 515–518.} · Zbl 0078.32703 [29] TODHUNTER, I. (1865):History of the Mathematical Theory of Probability, Cambridge Univ. Press (Reprinted by Chelsea, N. Y., 1949, 1961). [30] TUKEY, J. M. (1960): “A survey of sampling from contaminated distributions{” inContributions to Probability and Statistics, Olkin, I. (edit.), University Press.} [31] TIAO, G. C., and BOX, G. E. P. (1981): “Modeling Multiple Time Series with Applications{”,JASA, 76, 376, 802–816.} · Zbl 0483.62074 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.