# Choice of Binary Matrices Under Inequality Restrictions on Row Totals and Column Totals.

December 1988

## Date of Award

Winter 12-12-1989

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

Computer Science

## Department

Applied Statistics Unit (ASU-Kolkata)

## Supervisor

Roy, Bimal Kumar (ASU-Kolkata; ISI)

## Abstract (Summary of the Work)

Let us consider a population with N = rc units represented by a r x c two-way array. Suppose each row represents a group with respect to some characteristic, and each column represents a group with respect to some other characteristic. Then a practical sampling problem may be n units, so that from any grou Samples including more than k non-preferred, following Sengu T33 < 1,, Â¥ 1,3 in order to ensure tne positiveness of the esti- mator of variance of the HTE, where n, and n are the first and second order inclusion probabilities respectively. Now if the inclusion probabilities are made constant, then the demand will be au tomatically satisfied as in the case of SRSWOR. Moreover, data analysis will be extremely simple. This is a problem of deep stratification. Sengupta [1) has posed and partly desolved this Â·problem with k = 2, In that paper he has shown the procedure of sampling in the following cases :(i) r = c = even ngr + 2(ii) r = c = odd, n s r +1(iii) r + c, min (r,c) odd, n s min (r,c) + 1(iv) r+ c, min (r,c) = even, n 3 min (r,c).In this paper the probl em has been solved when r c c for general k, and the sampling schemes along with their implementation as a software package has been shown for the following three cases :(a) r = c =0 (mod k), n s r(k-1) + k(b) r=c= 1 (mod k), n s (r-1)(k-1)+k r = c = j (mod k), 2 s3 s k-1, n (r-j)(k-1)+k(c) clearly (1) and (11) above are particular cases, putting k = 2, of (a) and (b) respectively. Case (c) is entirely new, since this case arises only if k 2 3.In section 1 sampling designs of cases (a) and (b) are described in details. In section 2 design of case (c) is discussed. Section 3 describes the algorithm to implement the design. Section 4 gives some results of the algorithm, as obtained from the compute output. Section 5 discuss about the possible scopes of improvement.

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