On two-dimensional optimal controlled selection

On two-dimensional optimal controlled nearest proportional to size sampling designs

“…While all other two-dimensional optimal controlled selection plans discussed by earlier authors attempt to minimize the selection probabilities of the non-preferred samples, the proposed strategy completely eliminates the non-preferred samples by assigning zero probabilities to them. The plan obtained through the proposed strategy is superior to the plans suggested by Sitter and Skinner [24] and Tiwari and Nigam [28] in the sense that it ensures zero probability to non-preferred samples. The proposed plan also incorporates the possibility of 'controls beyond stratification' by introducing further controls in addition to the marginal requirements of the two-dimensional array, which was not considered by Sitter and Skinner [24].…”

“…In Section 3, we suggest an alternative strategy for estimation of population total and variance in two-dimensional controlled selection problems using the method of random groups. The proposed estimator appears to perform better than the 'split sample' method of Jessen [15] and the 'half sample' method of Tiwari and Nigam [28].…”

“…Rao and Nigam [22,23] used the simplex method in linear programming to solve the one-dimensional controlled selection problem. Sitter and Skinner [26] and Tiwari and Nigam [28] extended the linear programming approach to multi-way stratification, with the difference that [28] also considered the problem of 'controls beyond stratification'. The plan of Tiwari and Nigam [28] is best suited to problems with integer marginals, whereas the method of Sitter and Skinner [26] is best suited for non-integer marginals.…”

“…Sitter and Skinner [26] and Tiwari and Nigam [28] extended the linear programming approach to multi-way stratification, with the difference that [28] also considered the problem of 'controls beyond stratification'. The plan of Tiwari and Nigam [28] is best suited to problems with integer marginals, whereas the method of Sitter and Skinner [26] is best suited for non-integer marginals. Extending the linear programming approach of Sitter and Skinner [26], Lu and Sitter [17] developed some methods to reduce the amount of computation so that very large problems became feasible using the linear programming approach.…”

“…A practical difficulty while dealing with the multi-dimensional controlled selection problems is that they generally do not satisfy the non-negativity condition of the Yates-Grundy [31] form of the Horvitz-Thompson [12] variance estimator. To overcome this difficulty, Jessen [15] suggested the use of 'split sample' method, whereas Tiwari and Nigam [28] suggested a variance estimator using 'half sample' method. In Section 3, we suggest an alternative strategy for estimation of population total and variance in two-dimensional controlled selection problems using the method of random groups.…”