Counting, sampling and integrating: algorithms and by Mark Jerrum

By Mark Jerrum

Textual content made out of notes originating in a postgraduate lecture sequence given by way of the writer on the ETH in Zurich within the Spring of 2000. Covers the counting of combinatorial constructions and similar issues, considered from a computational viewpoint. Softcover.

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Can. J. Stat. : Small area estimation for spatial correlation in watershed erosion assessment. J. Agric. Biol. Environ. Stat. : Small area estimation: the EBLUP estimator based on spatially correlated random area effects. Stat. Methods Appl. : Small area estimation in the presence of correlated random area effects. J. Off. Stat. : Semiparametric M-quantile regression using penalized splines. J. Nonparametr. Stat. : Semiparametric M-quantile regression for estimating the proportion of acidic lakes in 8-digit HUCs of the North-eastern US.

The z-variables of course include the y-variables of interest as well as the domain indicator variables. B/;HT D nB X zkB wkB ; (14) kD1 where the two estimators of the overlap domain are obtained by using each sample separately and the HT-weights wkA and wkB are defined as usual. Clearly, there could be a number of new zero functions and this grows as the number of overlap domains with multiple frames grows. B/;HT , and tyab(A) tyab(B),HT . domain counts and domain y-totals are N Most of the estimators proposed in the literature deal with only these two types of zero functions.

The initial estimators now becomes SMHQ HT where HQ signifies Hájek-ratio adjustment to random controls. In the second step, ty;SMHQ HT is regressed on t x C ; HQ HT T x C without including NA and NB as components of T x C as these controls continue to be satisfied after performing regression estimation to be termed GROUM(s*) where s* denotes that the initial estimator is SMHQ HT and not SMHT. AB/ in place of the original fixed controls NA and NB (in fact, original fixed controls are automatically implied by the new random domain control counts) and where indicator vectors for the three domain samples are now used as x-variables in place of the indicators for units in the full samples sA and sB .

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