On the stability of some replication variance estimators in the linear case

Krewski, Daniel

doi:10.1016/0378-3758(78)90021-6

Cited by 12 publications

(9 citation statements)

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“…This balanced orthogonal multi-array was used to apply the method and required only R = n = 240 replicates, which is the same as the jackknife. The randomly grouped balanced repeated replications method does as well in terms of relative bias, but, as is expected from the theoretical results of Krewski (1978), it is much less stable. Viewing Table 4, we see that for r, b and c the balanced orthogonal multi-array method and the jackknife method both perform well and similarly.…”

Section: R R S Irrermentioning

confidence: 52%

“…If one wished to use the method of Gurney & Jewett (1975) in this situation, it would require a much larger number of replicates. Krewski (1978, Table 4 shows the observed value for the simulation was 13 27. For Yst the balanced orthogonal multi-array and the jackknife variance estimates are algebraically equivalent.…”

Section: R R S Irrermentioning

confidence: 99%

“…Gurney & Jewett (1975) extend the balanced repeated replications method to p > 2 for p prime, but the extension requires a much larger number of replicates, and is thus seldom used in practice. Unfortunately, the resulting variance estimators can be very inefficient and have poor conditional properties (Krewski, 1978;Wu, 1991). What is often done is to group the units randomly within each stratum into two equal or nearly equal groups and apply the balanced repeated replications method to these groups.…”

Section: Introductionmentioning

confidence: 99%

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Balanced Repeated Replications Based on Orthogonal Multi-Arrays

Sitter¹

1993

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYTo obtain variance estimates in stratified sampling with possibly unequal numbers of primary sampling units per stratum, one can either randomly divide the units in each stratum into two groups and apply the balanced half-samples method to these groups, or use mixed orthogonal arrays to form a set of balanced subsamples. With the first technique, resulting variance estimates can be very inefficient, and with the second technique it can be difficult to construct orthogonal arrays with a small number of replicates for a given stratified design. The proposed extension of the orthogonal array method to orthogonal multi-arrays retains all of the orthogonal array method's desirable properties but allows greater flexibility in construction, and thus can handle more complex stratified designs using fewer replicates.

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Section: R R S Irrermentioning

confidence: 52%

Section: R R S Irrermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Balanced Repeated Replications Based on Orthogonal Multi-Arrays

Sitter¹

1993

Biometrika

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“…= W2/ (nh -1)-When nh = 2 for all h, a balanced half-samples variance estimator for ys, is (McCarthy, 1969) Vb(Yst) = R1 Er ( siSt i)9where yst is the mean of the rth half-sample Yh8(r,h)9 for r= 1,..., R, h = 1, . This unbiasedness result, which follows easily from (3) below, does not tell us the efficiency loss of VGB due to grouping Krewski (1978,. ., L,8(r, h) = 1, and respectively 2 if the (r, h)th entry of an R x L submatrix of a Hadamard matrix is 1 and respectively -1.…”

mentioning

confidence: 93%

Balanced Repeated Replications Based on Mixed Orthogonal Arrays

1991

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY For stratified samples with arbitrary numbers of primary sampling units per stratum, one can divide the units in the stratum into two groups and then apply the balanced half-samples method to the two groups thus formed. The efficiency loss of the grouped balanced half-samples variance estimator can be substantial. Use of a mixed orthogonal array, whose numbers of symbols correspond to the numbers of units per stratum, gives a set of balanced subsamples. Unlike that of Gupta & Nigam (1987), the proposed method of analysis gives a consistent variance estimator and bias reduction for nonlinear statistics. To further reduce the number of replicates, use of nearly orthogonal arrays is considered.

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“…[see Kreweski (1978)] where β 2h (y) = λ 40h = µ 40h µ 2 20h , λ rsh = µ rsh (µ r 20h µ s 02h ) 1/2 ,…”

Section: Introductionmentioning

confidence: 99%

Some Families of Estimators of Variance of Stratified Random Sample Mean Using Auxiliary Information

Singh

Vishwakarma

2008

Journal of Statistical Theory and Practice

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In this paper we have considered the problem of estimating the variance of the stratified random sample mean using information on a supplementary variate x. Various classes of estimators have been proposed and their properties are studied. It has been shown that the proposed classes of estimators are more efficient than usual unbiased estimator. An empirical study is carried out in support of the present study.

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On the stability of some replication variance estimators in the linear case

Cited by 12 publications

References 13 publications

Balanced Repeated Replications Based on Orthogonal Multi-Arrays

Balanced Repeated Replications Based on Orthogonal Multi-Arrays

Balanced Repeated Replications Based on Mixed Orthogonal Arrays

Some Families of Estimators of Variance of Stratified Random Sample Mean Using Auxiliary Information

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