seminars:stat:180503
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| + | <WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP> | ||
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| + | <WRAP 70% center> | ||
| + | ^ **DATE:**|Thursday, May 3, 2018 | | ||
| + | ^ **TIME:**|1:00pm -- 2:15pm | | ||
| + | ^ **LOCATION:**|WH 100E | | ||
| + | ^ **SPEAKER:**|Junyi Dong, Binghamton University | | ||
| + | ^ **TITLE:**|Marginal Distribution Method | | ||
| + | </WRAP> | ||
| + | \\ | ||
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| + | <WRAP center box 80%> | ||
| + | <WRAP centeralign>**Abstract**</WRAP> | ||
| + | Let Z be the covariate vector and Y | ||
| + | be the response variable with the joint cumulative distribution function | ||
| + | F. Given a random sample from F, | ||
| + | in order to analyze the data based on a certain | ||
| + | proportional hazards (PH) model, | ||
| + | one needs to test the null hypothesis Ho: | ||
| + | F belongs to the Ph model first. | ||
| + | The existing tests to achieve this task make use of the residuals and | ||
| + | are invalid in certain situations, such as | ||
| + | when | ||
| + | $F$ is not | ||
| + | from any PH model. To overcome this disadvantage, | ||
| + | we propose a valid model checking test of Ho. | ||
| + | It is based on the weighted average of the difference between | ||
| + | two estimators of the marginal distribution | ||
| + | of the response variable: its non-parametric maximum likelihood | ||
| + | estimator | ||
| + | and its estimator under the PH model. | ||
| + | This test is called the marginal distribution (MD) test. | ||
| + | We give the theoretical justification of the MD test. | ||
| + | The simulation study suggests that | ||
| + | the MD test is always consistent, | ||
| + | whereas | ||
| + | the existing tests may be invalid and they are often unlikely to reject the wrong PH model assumption | ||
| + | when they are not valid. | ||
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| + | </WRAP> | ||
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