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Additional info for Sampling Algorithms (Springer Series in Statistics), 1st Edition
Example text
2, page 34, for SRSWOR; that is, the sample can be selected in one pass in the data file. The method was discussed in Fan et al. 3. The selection-rejection method is the best algorithm for selecting a sample according to SRSWOR; it is strictly sequential. 3. 3 Selection-rejection procedure for SRSWOR Definition k, j : Integer; j = 0; For k = 1, . . , N do n−j with probability then N − (k − 1) EndFor. select unit k; j = j + 1; This method was improved by Fan et al. (1962), Knuth (1981), Vitter (1987), Ahrens and Dieter (1985), Bissell (1986), and Pinkham (1987) in order to skip the nonselected units directly.
T ), of RN , such that • • • • µ(0) = µ = E(S), E [µ(t)|µ(t − 1), . . , µ(0)] = µ(t − 1), µ(t) is in the convex hull of the support, µ(T ) ∈ R. A martingale algorithm is thus a “random walk” in the convex hull of the support that begins at the inclusion probability vector and stops on a sample. Definition 34. In sampling without replacement, a sampling algorithm is said to be a martingale algorithm if it can be written as a finite sequence of random vectors π(0), π(1), π(2), . . , π(t), . .
3. The support Q(N − n) contains only one sample that is selected. 5 implements a standard eliminatory procedure for a fixed size sampling design without replacement. The eliminatory methods can be presented as the complementary procedures of the draw by draw methods. ). ). Finally, the sample 1−s is selected, where 1 is a vector of N ones. 8 Rejective Algorithms Definition 39. Let Q1 and Q2 be two supports such that Q1 ⊂ Q2 . ) be a sampling design on Q2 , such that p2 (s|Q1 ) = p1 (s), for all s ∈ Q1 .