Download Handbook of Statistics, Vol. 4. Nonparametric Methods by Krishnaiah P.R. PDF

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By Krishnaiah P.R.

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1957). Modified randomization tests for nonparametric hypotheses. Ann. Math. Statist. 28, 181-187. [29] Edgington, E. S. (1980). Randomization Tests. Marcel Dekker, New York. [30] Fisher, R. A. (1934). Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh. [31] Fraser, D. A. S. (1957). Nonparametric Methods in Statistics. Wiley, New York. [32] Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Amer. Statist. Assoc.

2) by the corresponding sample distribution functions. 5). 5) i=1 where E is a consistent estimate of the correlation matrix P ( F ) , with diagonal elements of E equal to one. 5). Univariate and multivariate multisample location and scale tests 47 As in Section 5, the T] and To criteria coincide when rl, ~- rl, which is often the case with linear rank statistics for the location problem. 13). °)= ' nln2''' nl nk Z " " tkg=1 ~)i(°)( X l t l nk ,1=1 ..... 9) 4~)(x,, X2, . . Xk ) = 4a ( r (~) i ) Here rl~) is the rank of xl~)in the k-tuplet (x{~), x~~).

K. 3), viz. , ' "~ p. i=1 Letting Si. (P) ],¢ we assume the regularity ill ' . . ~ ill " conditions ~ which are multivariate analogs of conditions M in Section 3. L J ' " " (i) S a m e as M(i). (ii) T h e Sill's are subject to the linear constraint k ~'~ ah,Si. 1) i=l w h e r e Ei a i . - - 1 and ~/. is a constant vector. It is a s s u m e d that ai. ,S~ . . . ), ~ be a class of nonsingular continuous L N1/2[S. (F)-* aq(F) u n d e r condition (i). (iv) For F in ~0 = {F E ~-: FI = F2 . . .

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