Abstract
We propose the concept of unification of statistical methods in order to develop a general philosophy of statistical data analysis. We propose that ways of thinking about statistical ends (goals) and means (procedures) are needed that provide a framework for implementing and comparing several different approaches to a data analysis problem. We believe that unification has benefits which include: existing (often parametric) methods will be better understood; many new (often nonparametric) methods will be developed. The new methods are usually computer intensive; consequently unification of statistical methods can be considered to be closely related to computational statistics. We define computational statistical methods as characterized by being graphics intensive and number crunching intensive.
Keywords
- Quantile Function
- Quadratic Detector
- Comparison Density
- Linear Rank Statistic
- Parametric Probability Model
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alexander, William (1989) “Boundary kernel estimation of the two-sample comparison density function” Texas A&M Department of Statistics Ph.D. thesis.
Aly, E. A. A., M. Csorgo, and L. Horvath (1987) “P-P plots, rank processes, and Chernoff-Savage theorems” in New Perspectives in Theoretical and Applied Statistics (ed. M. L. Puri, J. P. Vilaplann, W. Wertz) New York: Wiley 135–156.
Boos, Dennis D. (1986) “Comparing k populations with linear rank statistics”, Journal of the American Statistican Association, 81, 1018–1025.
Cheng, R. C. H. and Stephens, M. A. (1989) “A goodness of fit test using Moran’s statistic with estimated parameters”, Biometrika, 76, 385–392.
Chui, C. K., Deutsch, F., Ward, J. D. (1990) “Constrained best approximation in Hilbert space,” Constructive Approximation, 6, 35–64.
Eubank, R. L., V. N. LaRiccia, R. B. Rosenstein (1987) “Test statistics derived as components of Pearson’s Phi-squared distance measure”, Journal of the American Statistical Association, 82, 816–825.
Freedman, D., Pisani, R., Purves, R. (1978) Statistics, New York: Norton.
Parzen, E. (1979) “Nonparametric statistical data modelling”, Journal of the American Statistical Association, 74, 105–131.
Parzen, E. (1989) “Multi-sample functional statistical data analysis,” in Statistical Data Analysis and Inference, (ed. Y. Dodge). Amsterdam: North Holland, pp. 71–84.
Rayner, J. C. W. and Best, D. J. (1989). Smooth Tests of Goodness of Fit, Oxford University Press, New York.
Read, T. R. C. and Cressie, N. A. C. (1988). Goodness of Fit Statistics for Discrete Multivariate Data, Springer Verlag, New York.
Renyi, A. (1961). “On measures of entropy and information.” Proc. 4th Berkeley Symp. Math. Statist. Probability, 1960, 1, 547–561. University of California Press: Berkeley.
Shorack, Galen and John Wellner (1986) Empirical Processes With Applications to Statistics, New York: Wiley.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Parzen, E. (1992). Unification of Statistical Methods for Continuous and Discrete Data. In: Page, C., LePage, R. (eds) Computing Science and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2856-1_30
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2856-1_30
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97719-5
Online ISBN: 978-1-4612-2856-1
eBook Packages: Springer Book Archive