论文信息 - The Use of the Concept of a Future Observation in Goodness‐Of‐Fit Problems

The Use of the Concept of a Future Observation in Goodness‐Of‐Fit Problems

An attack on the problem of goodness of fit is made by combining a Bayesian and sampling argument; the Bayesian part is effected by using the distribution of a future observation, while the sampling argument concerns itself with the distribution of a "chi-squared like" statistic, which measures discrepancies of observed frequencies from those predicted by the distribution of the future observation. Examples are given for the case of sampling from the binomial, Poisson and normal distributions. An interesting application arising from the above approach is a procedure for estimating the degree of a polynomial response function.

I. Guttman

[1] J. Wishart. THE CUMULANTS OF THE zAND OF THE LOGARITHMIC x2 AND t DISTRIBUTIONS , 1947 .

[2] H. Chernoff,et al. The Use of Maximum Likelihood Estimates in {\chi^2} Tests for Goodness of Fit , 1954 .

[3] J. Hammersley. A Million Random Digits with 100,000 Normal Deviates. , 1955 .

[4] G. S. Watson,et al. THE X2 GOODNESS-OF-FIT TEST FOR NORMAL DISTRIBUTIONS , 1957 .

[5] I. Guttman. A note on a series solution of a problem in estimation , 1958 .

[6] Geoffrey Stuart Watson,et al. Some Recent Results in Chi-Square Goodness-of-Fit Tests , 1959 .

[7] G. C. Tiao,et al. A Further Look at Robustness via Bayes's Theorem , 1962 .

[8] F. J. Anscombe. Tests of Goodness of Fitt , 1963 .

[9] A. R. Thatcher,et al. Relationships between Bayesian and Confidence Limits for Predictions , 1964 .

[10] Irwin Guttman,et al. A Bayesian Approach to Some Best Population Problems , 1964 .

[11] J Aitchison,et al. Some problems of statistical prediction. , 1965, Biometrika.

[12] N. Draper,et al. Unequal group variances in the fixed-effects one-way analysis of variance: a Bayesian sidelight. , 1966, Biometrika.