By Agnes Chao Hsiung, Zhiliang Ying, Cun-Hui Zhang

This quantity is a suite of papers in social gathering of the eightieth birthday of Yuan-Shih Chow, whose influential paintings in likelihood and mathematical information has contributed tremendously to arithmetic schooling and the advance of facts study and alertness in Taiwan and mainland China. The twenty-two papers disguise a variety of difficulties reflecting either the huge scope of components the place Professor Chow has made significant contributions and up to date advances in chance thought and facts.

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Kou and Z. Ying 171 A New Test of Symmetry about an Unknown Median W. R. L. Gastwirth 199 The Cox Proportional Hazards Model with a Partially Known Baseline 215 M. M. H. P. -S. A. -C. -J. -T. Fang, J. J. Hickernell and R. -D. Fuh and I. Hu 269 The Li-Norm Kernel Estimator of Conditional Median for Stationary Processes Z. Lin and D. Li 281 Statistical Applications 297 From Microstructures to Properties: Statistical Aspects of Computational Materials Science C. Ji 299 The Impact of Population Stratification on Commonly Used Statistical Procedures in Population-Based QTL Association Studies H.

It is well understood that the procedure of interim treatment arm selection would alter the rejection region and therefore the type I error rate would be inflated due to the nature of multiplicity and the interim adaptability if no correction is made. One may consider there is a certain "% of multiplicity" depending upon the time of interim selection is performed. If 29 the interim selection is performed at early stage of the study, there will be less multiplicity issue compared to the situation where the interim selection is performed in a later time of the study.

Thus by (14) a ^1/a fn{y) « ( — j - + y Let f(y) = [^-l+y)1/a- (2i) Note that by (5) and (21) a Urn /(») = (~^-\ j/->0 = lim n-VV*. „ = 1/Ba to obtain ^ = ( ^ l + = ) 1 / a ' (23) and W = h((3a). Now substituting into (19) f " h(u)du - f i + /3a J h(0a) = 0 which explains the theorem. 3. Some Lemmas In this section we determine the limiting behavior of the sequence of functions / „ , n = 1,2,... d. sequence with distribution (10), a representative of F € V{GJj). 1. Let fn(y) and f(y) be given in (1\) and (21), respectively.

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