Simultaneous inference for linear mixed model parameters with an application to small area estimation
Summary Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed paramet...
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| Published in | International statistical review Vol. 91; no. 2; pp. 193 - 217 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken
John Wiley & Sons, Inc
01.08.2023
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0306-7734 1751-5823 |
| DOI | 10.1111/insr.12519 |
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| Abstract | Summary
Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed parameters are rare. This is surprising because one often faces inferential problems beyond the pointwise examination of fixed or mixed parameters. For example, there is an interest in a comparative analysis of cluster‐level parameters or subject‐specific estimates in studies with repeated measurements. We discuss methods for simultaneous inference assuming a linear mixed model. Specifically, we develop simultaneous prediction intervals as well as multiple testing procedures for mixed parameters. They are useful for joint considerations or comparisons of cluster‐level parameters. We employ a consistent bootstrap approximation of the distribution of max‐type statistic to construct our tools. The numerical performance of the developed methodology is studied in simulation experiments and illustrated in a data example on household incomes in small areas. |
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| AbstractList | Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed parameters are rare. This is surprising because one often faces inferential problems beyond the pointwise examination of fixed or mixed parameters. For example, there is an interest in a comparative analysis of cluster‐level parameters or subject‐specific estimates in studies with repeated measurements. We discuss methods for simultaneous inference assuming a linear mixed model. Specifically, we develop simultaneous prediction intervals as well as multiple testing procedures for mixed parameters. They are useful for joint considerations or comparisons of cluster‐level parameters. We employ a consistent bootstrap approximation of the distribution of max‐type statistic to construct our tools. The numerical performance of the developed methodology is studied in simulation experiments and illustrated in a data example on household incomes in small areas. Summary Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical tools for valid simultaneous inference for mixed parameters are rare. This is surprising because one often faces inferential problems beyond the pointwise examination of fixed or mixed parameters. For example, there is an interest in a comparative analysis of cluster‐level parameters or subject‐specific estimates in studies with repeated measurements. We discuss methods for simultaneous inference assuming a linear mixed model. Specifically, we develop simultaneous prediction intervals as well as multiple testing procedures for mixed parameters. They are useful for joint considerations or comparisons of cluster‐level parameters. We employ a consistent bootstrap approximation of the distribution of max‐type statistic to construct our tools. The numerical performance of the developed methodology is studied in simulation experiments and illustrated in a data example on household incomes in small areas. |
| Author | Reluga, Katarzyna Sperlich, Stefan Lombardía, María‐José |
| Author_xml | – sequence: 1 givenname: Katarzyna orcidid: 0000-0001-9651-5030 surname: Reluga fullname: Reluga, Katarzyna email: katarzyna.reluga@berkeley.edu organization: University of California – sequence: 2 givenname: María‐José orcidid: 0000-0001-9452-9818 surname: Lombardía fullname: Lombardía, María‐José email: maria.jose.lombardia@udc.es organization: University of A Coruña – sequence: 3 givenname: Stefan orcidid: 0000-0001-5366-2612 surname: Sperlich fullname: Sperlich, Stefan email: stefan.sperlich@unige.ch organization: University of Geneva |
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Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever... Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered,... |
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| SubjectTerms | Applied statistics Clusters Mathematical models Max‐type statistic mixed parameter multiple testing Parameters simultaneous confidence interval small area estimation Statistical analysis Statistical inference |
| Title | Simultaneous inference for linear mixed model parameters with an application to small area estimation |
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