Resumen
This pager presents a classification of statistical models using a simple and logical framework. Some remarks are made about 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.
Similar content being viewed by others
References
ANSCOMBE, F. J., and TUKEY, J. W. (1963): «The examination and analysis of residuals»,Technometrics, 5, 141–160.
BARNETT, V., and LEWIS, T. (1978):Outliers in Statistical Data, Wiley.
BELSELY, D. A.; KUH, E., and WELSCH, R. E. (1980):Regression Diagnostics, Wiley.
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.
BOX, G. E. P.; HUNTER, W. G., and HUNTER, J. S. (1978):Statistics for Experimenters, Wiley.
BOX, G. E. P., and JENKINS, G. M. (1970):Time Series Analysis, Holden Day.
BOX, G. E. P., and TIAO, G. C. (1973):Bayesian Inference in Statistical Analysis, Addison-Wesley.
BOX, G. E. P., and COX, D. R. (1964): «An analysis of transformations»,JRSS, B, 26, 211–243.
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.
BOX, J. F. (1978):Fisher, The Life of a Scientist, New York, Wiley.
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.
COOK, R. D., and WEISBERG, S. (1982):Residuals and Influence in Regression, Chapman and Hall.
DE FINETTI, B. (1975):Theory of Probability. Wiley.
DRAPER, N. R., and SMITH H. (1966):Applied Regression Analysis, Wiley (2nd edition, 1980).
EPHREMIDES, A., and THOMAS, J. B. (1973) (editor):Random Processes (Vol I), Dowden Hutchingon and Ross Inc.
EPHREMIDES, A. (1975) (editor)Random Processes (Vol. II), Halted Press.
KENDALL, D. G. (1966): «Branching processes since 1873»,J. London Math. Society, 41, 385–406.
HANNAN, E. J. (1970):Multiple Time Series, New York, Wiley.
HARRIS, T. E. (1963):The Theory of Branching Processes, Berlin.
JEFFREYS, H. (1932): «An alternative to the rejection of observations»,Proc. Roy. Soc. A., CXXXVII, 78–87.
KARLIN, S., and TAYLOR, H. M. (1975):A First Course in Stochastic Processes, Academic Press.
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.
MAISTROV, I. E. (1974):Probability Theory. A Historical Sketch, Academic Press.
PEÑA, D. (1978): «Modelos con parámetros variables en el análisis de series temporales»,Questiio, 4, 2, 75–87.
PEÑA, D., and BOX, G. E. P. (1987): «Identifying a Simplifying Structure in time series»,JASA, 82, 399, pp. 836–843.
SEAL, H. L. (1967): «The historical development of the Gauss linear model»,Biometrika, 54, 1–24.
STIGLER, S. M. (1975): «Napoleonic Statistics: The Work of Laplace»,Biometrika, 62, 3, 503–517.
THATCHER, A. R. (1957): «A note on the early solutions of the problem of the duration of the play»,Biometrika, 44, 515–518.
TODHUNTER, I. (1865):History of the Mathematical Theory of Probability, Cambridge Univ. Press (Reprinted by Chelsea, N. Y., 1949, 1961).
TUKEY, J. M. (1960): «A survey of sampling from contaminated distributions» inContributions to Probability and Statistics, Olkin, I. (edit.), University Press.
TIAO, G. C., and BOX, G. E. P. (1981): «Modeling Multiple Time Series with Applications»,JASA, 76, 376, 802–816.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Daniel, P. On the logical development of statistical models. TDE 3, 195–213 (1988). https://doi.org/10.1007/BF02884334
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02884334