English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 93932/124380 (76%)
Visitors : 28990357      Online Users : 394
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/96300
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/96300

    Title: The Construction and E-optimality of Linear Trend-Free Block Designs
    Authors: 高建國
    Contributors: 丁兆平

    Keywords: BIB design
    Linear trend-free design
    Nearly trend-free design
    Date: 2002
    Issue Date: 2016-05-10 18:56:14 (UTC+8)
    Abstract:   Suppose there is a systematic effect or trend that influences the observations in addition to the block and treatment effects. The problem of experimental designs in the presence of trends was first studied by Cox (1951,1952). Bradley and Yeh (1980) define the concept of trend-free block designs, i.e., the designs in which the analysis of treatment effects are essentially the same whether the trend effects are present or not. If the trend effect within each blocks are the same and linear, Yeh and Bradley (1983) derive a simple necessary condition for designs to be linear trend-free,
      r<sub>i</sub>(k+1)≡0 (mod 2), 1≦i≦v,     (1)
      where r<sub>i</sub> is the replication of treatment i, for 1≦i≦v, and k is block size.
      In case where a trend-free version does not exist Yeh et al. (1985) suggest the use of “ nearly trend-free version”. Chai (1995) pays attention to situations where (1) does not hold. He also shows that often, under these circumstances, a nearly linear trend-free design could be constructed.
      Designs that are derived by extending or deleting m disjoint and binary blocks from BIBD (v,b,k,r,λ)'s are considered. If the resulting designs have linear trend-free versions, by Constantine (1981), they are E-optimal designs with the corresponding classes. When k is even, however, it is impossible to have linear trend-free versions since not all the r<sub>i</sub>'s are even in such type of designs and (1) is violated. In this paper, we shall convert the designs to be nearly linear trend-free versions of them by permuting the treatment symbols within blocks, and investigate that the resulting designs remain to be E-optimal.
    Reference: Agrawal, H. (1966). Some generalizations of distinct representatives with applications to statistical designs. Ann. Math. Statist. 37, 526-527.
    Agrawal, H. and Prasad, J. (1981). On the structure of incomplete block designs. Calcutta Statistical Association Bulletin 30, 65-76.
    Bradley, R.A. and Yeh, C.M. (1980). Trend-free block designs: theory. Ann. Statist. 8, 883-893.
    Chai, F.S. and D.Majumdar (1993). On the Yeh-Bradley conjecture on linear trend-free block design. Ann. Statist. 21, 2087-2097.
    Chai, F.S. (1995). Construction and optimality of nearly linear trend-free designs. J. Statist. Plann. Inference 48, 113-129.
    Chai, F.S. (1998). A note on generalization of distinct representatives. Statistics & Probability Letters 39, 173-177.
    Cochran, W.G. and Cox, G.M. (1957). Experimental Designs. 2nd edition. Wiley, New York.
    Connor, W.S., Jr. (1952). On the structure of balanced incomplete block designs. Ann. Math. Statist. 23, 57-71.
    Constantine, G.M. (1981). Some E-optimal block designs. Ann. Statist. 9, 886-892.
    Cox, D.R. (1951). Some systematic experimental designs. Biometrika 39, 312-323.
    Cox, D.R (1952). Some recent work on systematic experimental designs. J. Roy. Statist. Soc. Ser. B. 14, 211-219.
    Graybill, F.A. (1971). Introduction to Matrices with Applications in Statistics. Wadsworth Publishing, Belmont, CA.
    Hall, M. Jr. (1986). Combinatorial Theory. 2nd edition. Wiley, New York.
    Jacroux, M., Majumdar, D. and Shah, K.R. (1995). Efficiency block designs in the presence of trends. Statist. Sinica 5, 605-615.
    Jacroux, M., Majumdar, D. and Shah, K.R. (1997). On the determination and construction of optimal block designs in the presence of linear trends. J. Amer. Satist. Ass. 92, 375-383
    Jacroux, M. (1998). On the determination and construction of E-optimal block designs in the presence of linear trends. J. Statist. Plann. Inference 67, 331-342.
    König, D. (1950). Theorie der Endlichen and Unendlichen Graphen 170-178. Chelsea, New York.
    Lin, M. and Dean, A.M. (1991). Trend-free block designs for varietal and factorial experiments. Ann. Statist. 19, 1582-1596.
    Raghavarao, D. (1971). Construction and Combinatorial Problems of Design of Experiments. Wiley, New York.
    Stufken, J. (1988). On the existence of linear trend-free block designs. Comm. Statist. Theory Methods 17, 3857-3863.
    Yeh, C.M. and Bradley, R.A. (1983). Trend-free block design; existence and construction results. Comm. Statist. Theory Methods 12, 1-24.
    Yeh, C.M., Bradley, R.A. and Notz, W.I. (1985). Nearly trend-free block designs. J. Amer. Statist. Assoc. 80, 985-992.
    Description: 博士
    Source URI: http://thesis.lib.nccu.edu.tw/record/#A2010000074
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

    Files in This Item:

    File SizeFormat

    All items in 政大典藏 are protected by copyright, with all rights reserved.

    社群 sharing

    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback