Abstract
In the goodness-of-fit test of parameters of the multinomial distribution we show that the exact multinomial test is asymptotically equivalent to the likelihood ratio test by using Stirling's formula. In an r×c contingency table, we show that the extended Fisher's exact test conditional on row and column margins for the test of independence is also asymptotically equivalent to the likelihood ratio test. From the Bahadur asymptotic optimality of the likelihood ratio test in both unconditional and conditional cases, we prove that the two exact tests are asymptotically optimal in the sense of Bahadur efficiency.
| Original language | English |
|---|---|
| Pages (from-to) | 201-207 |
| Number of pages | 7 |
| Journal | Statistics and Probability Letters |
| Volume | 44 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1999 Aug 15 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
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An optimal property of the exact multinomial test and the extended Fisher's exact test. / Kang, Seung Ho.
In: Statistics and Probability Letters, Vol. 44, No. 2, 15.08.1999, p. 201-207.Research output: Contribution to journal › Article
TY - JOUR
T1 - An optimal property of the exact multinomial test and the extended Fisher's exact test
AU - Kang, Seung Ho
PY - 1999/8/15
Y1 - 1999/8/15
N2 - In the goodness-of-fit test of parameters of the multinomial distribution we show that the exact multinomial test is asymptotically equivalent to the likelihood ratio test by using Stirling's formula. In an r×c contingency table, we show that the extended Fisher's exact test conditional on row and column margins for the test of independence is also asymptotically equivalent to the likelihood ratio test. From the Bahadur asymptotic optimality of the likelihood ratio test in both unconditional and conditional cases, we prove that the two exact tests are asymptotically optimal in the sense of Bahadur efficiency.
AB - In the goodness-of-fit test of parameters of the multinomial distribution we show that the exact multinomial test is asymptotically equivalent to the likelihood ratio test by using Stirling's formula. In an r×c contingency table, we show that the extended Fisher's exact test conditional on row and column margins for the test of independence is also asymptotically equivalent to the likelihood ratio test. From the Bahadur asymptotic optimality of the likelihood ratio test in both unconditional and conditional cases, we prove that the two exact tests are asymptotically optimal in the sense of Bahadur efficiency.
UR - http://www.scopus.com/inward/record.url?scp=0043098353&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0043098353&partnerID=8YFLogxK
U2 - 10.1016/S0167-7152(99)00010-3
DO - 10.1016/S0167-7152(99)00010-3
M3 - Article
AN - SCOPUS:0043098353
VL - 44
SP - 201
EP - 207
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
IS - 2
ER -