| Title:
|
Approximate construction of a two-dimensional confidence region (English) |
| Author:
|
Pavlík, Miloš |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
15 |
| Issue:
|
5 |
| Year:
|
1970 |
| Pages:
|
305-309 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. () |
| MSC:
|
62F25 |
| idZBL:
|
Zbl 0212.50701 |
| idMR:
|
MR0266362 |
| DOI:
|
10.21136/AM.1970.103301 |
| . |
| Date available:
|
2008-05-20T17:48:35Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103301 |
| . |
| Reference:
|
[1] Bateman H. A. Erdélyi: Higher transcendental functions.vol. 1. McGraw-Hill, New York- Toronto-London, 1953. |
| Reference:
|
[2] : Таблицы логарифмической производной гамма-функции и ее производных в комплексной области.Вычислительный центр AHCCCP, Москва, 1965. Zbl 1099.01519 |
| Reference:
|
[3] Wilks S. S.: Shortest average confidence intervals for large samples.Ann. Math. Stat. 9, 166-175, 1938. 10.1214/aoms/1177732308 |
| Reference:
|
[4] Wilks S. S.: Optimum fiducial regions for simultaneous estimation of several population parameters from large samples.(Abstract.) Ann. Math. Stat. 10, 85-86, 1939. |
| Reference:
|
[5] Wilks S. S. J. F. Daly: An optimum property of confidence regions associated with the likelihood function.Ann. Math. Stat. 10, 225 - 235, 1939. MR 0000386, 10.1214/aoms/1177732181 |
| . |
