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--- seminars:stat:180503 [2018/05/06 12:24] – created qyu
+++ seminars:stat:180503 [2018/05/06 12:47] (current) – qyu
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+<WRAP centeralign>##Statistics Seminar##\\ Department of Mathematical Sciences</WRAP>
+<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>
+\\
+<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.
+</WRAP>