Multivariate optimal allocation with box-constraints
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Austrian Statistical Society
2018-02-01
|
| Series: | Austrian Journal of Statistics |
| Online Access: | http://www.ajs.or.at/index.php/ajs/article/view/764 |
| _version_ | 1818942075947712512 |
|---|---|
| author | Ulf Friedrich Ralf Münnich Martin Rupp |
| author_facet | Ulf Friedrich Ralf Münnich Martin Rupp |
| author_sort | Ulf Friedrich |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T07:05:40Z |
| format | Article |
| id | doaj.art-5017fdf942a943a1a6f4616e8642289b |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-12-20T07:05:40Z |
| publishDate | 2018-02-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-5017fdf942a943a1a6f4616e8642289b2022-12-21T19:49:03ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2018-02-0147210.17713/ajs.v47i2.764Multivariate optimal allocation with box-constraintsUlf FriedrichRalf MünnichMartin RuppModern 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.http://www.ajs.or.at/index.php/ajs/article/view/764 |
| spellingShingle | Ulf Friedrich Ralf Münnich Martin Rupp Multivariate optimal allocation with box-constraints Austrian Journal of Statistics |
| title | Multivariate optimal allocation with box-constraints |
| title_full | Multivariate optimal allocation with box-constraints |
| title_fullStr | Multivariate optimal allocation with box-constraints |
| title_full_unstemmed | Multivariate optimal allocation with box-constraints |
| title_short | Multivariate optimal allocation with box-constraints |
| title_sort | multivariate optimal allocation with box constraints |
| url | http://www.ajs.or.at/index.php/ajs/article/view/764 |
| work_keys_str_mv | AT ulffriedrich multivariateoptimalallocationwithboxconstraints AT ralfmunnich multivariateoptimalallocationwithboxconstraints AT martinrupp multivariateoptimalallocationwithboxconstraints |