Fast integer-valued algorithms for optimal allocations under constraints in stratified sampling

Friedrich, Ulf; Münnich, Ralf; Vries, Sven de; Wagner, Matthias

doi:10.1016/j.csda.2015.06.003

Cited by 15 publications

(25 citation statements)

References 26 publications

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“…The associated RMSEs are also different. This shows the advantage of the integer optimal allocation -especially when considering that the computing times of the continuous and integer solver are of the same magnitude (Friedrich et al 2015).…”

Section: Comparison Of Continuous and Integer Solutionmentioning

confidence: 96%

“…Nevertheless, it is possible to solve these more general problems with the help of a reformulation as linear integer problems (Hochbaum 1995). A reformulation of this type has been solved with the commercial software FICO Xpress Optimization Suite in Friedrich et al (2015) with the result that computation times worsen significantly (many hours instead of seconds). Therefore, we do not solve the integer version of the non-separable problems in Section 4.…”

Section: Solution As Integer Optimization Problemmentioning

confidence: 99%

“…The problem reduces to a single-objective optimization problem and algorithms developed for the univariate allocation problem can be applied directly. Friedrich et al (2015) present three algorithms for the problem that use the fact that the minimization of a separable and convex function is polynomially solvable in integer variables if the feasible set is a so-called polymatroid, which is a convex polytope with strong combinatorial properties. An exhaustive discussion of the mathematical background is given in Friedrich (2016).…”

Section: Solution As Integer Optimization Problemmentioning

confidence: 99%

“…Friedrich, Münnich, de Vries, and Wagner (2015) provide a further extension that ensures integrality of the solution of the optimal allocation. Using Gabler et al (2012) and by separating different sub-regions, the method can be rewritten to a simultaneous optimal allocation for multiple areas.…”

Section: Introductionmentioning

confidence: 99%

“…Because stratumspecific sample sizes are integer values, we also provide an alternative algorithm to derive a multivariate optimal allocation in which all stratum-specific samples are integer-valued. This strategy avoids rounding and is based on the integer optimal allocation techniques published in Friedrich et al (2015).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Multivariate optimal allocation with box-constraints

Friedrich¹,

Münnich²,

Rupp³

2018

AJS

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Modern surveys aim at fostering accurate information on demographic and other variables. The necessity for providing figures on regional levels and on a variety of subclasses leads to fine stratifications of the population. Optimizing the accuracy of stratified random samples requires incorporating a vast amount of strata on various levels of aggregation. Accounting for several variables of interest for the optimization yields a multivariate optimal allocation problem in which practical issues such as cost restrictions or control of sampling fractions have to be considered. Taking advantage of the special structure of the variance functions and applying Pareto optimization, efficient algorithms are developed which allow solving large-scale problems. Additionally, integrality-and box-constraints on the sample sizes are considered. The performance of the algorithms is presented comparatively using an open household dataset illustrating their advantages and relevance for modern surveys.

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Section: Comparison Of Continuous and Integer Solutionmentioning

confidence: 96%

Section: Solution As Integer Optimization Problemmentioning

confidence: 99%

Section: Solution As Integer Optimization Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Multivariate optimal allocation with box-constraints

Friedrich¹,

Münnich²,

Rupp³

2018

AJS

Self Cite

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An index tracking model with stratified sampling and optimal allocation

Wang

Dai

2017

Appl Stoch Models Bus & Ind

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This paper investigates the portfolio strategy problem for passive fund management. We propose a novel portfolio strategy that combines the existing stratified strategy and optimized sampling strategy. The proposed method enables one to include adequate practical information in portfolio decision making, and promotes better out-of-sample performance. A mixed-integer program model is built that captures the stratification information, the cardinality requirement, and other practical constraints. The corresponding model is able to forecast and generate optimal tracking portfolios with high performance, especially in out-of-sample time period. As mixed-integer program is a well-known NP-hard problem, to tackle the computational challenge, we propose a stratified hybrid genetic algorithm, in which a novel crossover operator is introduced. To evaluate the proposed strategy and algorithm, we conduct numerical tests on real data sets collected from China Stock Exchange Markets. The experimental resultsshow that the algorithm runs efficiently and the portfolio strategy performs significantly better than other existing strategies.KEYWORDS index tracking, out-of-sample performance, stratified sampling, stratified hybrid genetic algorithm, s-rar crossover

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Neyman-type sample allocation for domains-efficient estimation in multistage sampling

Khan

Wesołowski

2018

AStA Adv Stat Anal

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We consider a problem of allocation of a sample in two-and three-stage sampling. We seek allocation which is both multi-domain and population efficient. Choudhry et al. (Survey Methods 38(1):23-29, 2012) recently considered such problem for one-stage stratified simple random sampling without replacement in domains. Their approach was through minimization of the sample size under constraints on relative variances in all domains and on the overall relative variance. To attain this goal, they used nonlinear programming. Alternatively, we minimize here the relative variances in all domains (controlling them through given priority weights) as well as the overall relative variance under constraints imposed on total (expected) cost. We consider several two-and three-stage sampling schemes. Our aim is to shed some light on the analytic structure of solutions rather than in deriving a purely numerical tool for sample allocation. To this end, we develop the eigenproblem methodology introduced in optimal allocation problems in Niemiro and Wesołowski (Appl Math 28:73-82, 2001) and recently updated in Wesołowski and Wieczorkowski (Commun Stat Theory Methods 46(5):2212-2231, 2017) by taking under account several new sampling schemes and, more importantly, by the (single) total expected variable cost constraint. Such approach allows for solutions which are direct generalization of the Neyman-type allocation. The structure of the solution is deciphered from the explicit allocation formulas given in terms of an eigenvector v * of a population-based matrix D. The solution we provide can be viewed as a multi-domain version of the Neyman-type allocation in multistage stratified SRSWOR schemes.

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Fast integer-valued algorithms for optimal allocations under constraints in stratified sampling

Cited by 15 publications

References 26 publications

Multivariate optimal allocation with box-constraints

Multivariate optimal allocation with box-constraints

An index tracking model with stratified sampling and optimal allocation

Neyman-type sample allocation for domains-efficient estimation in multistage sampling

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