Approximate construction of a two-dimensional confidence region

Pavlík, Miloš

Applications of Mathematics, Tome 15 (1970) no. 5, pp. 305-309.

Résumé

If a sufficiently large random sample is taken from a population with known distribution, depending upon a couple $\zeta$ of parameters, so that Pearson $\chi^2$ criterion is applicable to test the agreement between the observed and the expected sample class frequencies, and if the $\chi^2$ statistic is considered to be a random function defined on the space of all admisible $\zeta$ values, then the region in on which $\chi^2$ is less than its $100\alpha$ per cent critical value, constitutes an approximately $100(1-\alpha)$ per cent level confidence region for the true population value $\zeta_0$ of $\zeta$. Under certain general conditions this region always exists and lies within a closed curve the graphic construction of which is not very difficult if the expected sample class frequencies in a sufficiently large area in , surrounding the maximum likelihood or the $\chi^2$ minimum estimate of $\zeta_0$, are known.

Détail

DOI : 10.21136/AM.1970.103301

Classification : 62F25