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

Summary 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.