2006 Fiscal Year Final Research Report Summary
Asymptotic properties of likelihood ratio statistics on non-inferiority hypothesis testing
| Project/Area Number |
16500178
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
TAKAGI Yoshiji Osaka Prefecture University, Graduate School of Science, Associate Professor, 理学系研究科, 助教授 (00231390)
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| Project Period (FY) |
2004 – 2006
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| Keywords | non-inferiority hypothesis / exponential distribution / type I censored data / likelihood ratio statistic / k-sample problem / normal distribution / non-differentiable point |
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| Research Abstract |
We have the following two research results.
1.The non-inferiority testing problem between some treatments is discussed in survival model where the underlying distribution is exponential and data are subject to type I censoring. The asymptotic distribution of the likelihood ratio statistic is derived in two-sample and k-sample cases. One testing procedure for the non-inferiority testing hypotheses is proposed based on the likelihood ratio statistic.
2.The non-inferiority testing problem between two treatments is discussed based on the likelihood ratio statistic. Let the underlying distribution for the two treatments be normally distributed with mean θ and μ, respectively, and common unknown variance. We consider the following general hypotheses including the non-inferiority hypotheses : H_0:θ≧h(μ) v.s. H_1:θ<h(μ), where h(μ)is any continuous and strictly increasing function. In this situation, the asymptotic distribution of the log-likelihood ratio statistic is obtained under the true value on the boundary of the hypotheses. When the true value is any differentiable point, the asymptotic distribution becomes 1/2+(1/2)x^2_1 irrespective to the function h(μ), where x^2_1 is the chi-squared random variable with one degree of freedom. On the other hand, if the true point is any non-differentiable point for the function h(,μ), the asymptotic distribution is expressed in the form depending on right and left differential coefficients of the function h(μ).
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