Small sample inference for the structural and functional simple linear measurement error models /
Small sample inference for both structural and functional simple linear measurement error models is investigated. We assume that measurement errors for both the dependent and independent variables are independent identically distributed normal random variables with known variance ratio. Likelihood...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1996.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=743266511&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Small sample inference for both structural and functional simple linear measurement error models is investigated. We assume that measurement errors for both the dependent and independent variables are independent identically distributed normal random variables with known variance ratio. Likelihood ratio and adjusted likelihood ratio test statistics for joint hypothesis about the slope and intercept parameters are derived. An important finding of our research is that the structural model likelihood ratio-based test statistic, T, has aw exact chi-square distribution with two degrees of freedom at the null hypothesis under either the structural or functional model. In principal, T, can be used to perform exact tests under either the structural or functional models. Under the structural model, power of the test statistic T, was compared to that of a Wald-type test statistic Tw. Because T. exhibited an empirical bias in nominal level for small sample sizes, an empirically adjusted T. was used in the power comparison with Ts. Power appears to be greater for T, than for the adjusted Waldtype test statistic in regions of the parameter space which are of particular interest, based on our simulation comparisons. An interesting anomaly in the power curve for T, occurs in the alternative hypothesis region corresponding to the line which is perpendicular to the true regression line and which intersects the true regression line at the point (A., Oo + Oil-L.). At this point, the test statistic T, has power equal to the level of the test. In spite of this anomaly, we argue that application of the test statistic T, is preferred to use of the (adjusted) Wald test statistic in the structural model setting. Under the functional model, we recommend use of a Bartlett-adjusted likelihood ratio test statistic, Tb. The distribution of Tb at the null hypothesis under the functional model is closely approximated by a chi-square distribution with two degrees of freedom. The power of Tb appears to be substantially greater than the power of T,, even in those regions of particular importance near the null hypothesis. |
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| Item Description: | Vita. "Major Subject: Statistics". |
| Physical Description: | xiii, 93 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references. |