IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v55y2014i2p543-561.html
   My bibliography  Save this article

Equalities between OLSE, BLUE and BLUP in the linear model

Author

Listed:
  • Stephen Haslett
  • Jarkko Isotalo
  • Yonghui Liu
  • Simo Puntanen

Abstract

We consider equalities between the ordinary least squares estimator ( $$\mathrm {OLSE} $$ ), the best linear unbiased estimator ( $$\mathrm {BLUE} $$ ) and the best linear unbiased predictor ( $$\mathrm {BLUP} $$ ) in the general linear model $$\{ \mathbf y , \mathbf X \varvec{\beta }, \mathbf V \}$$ extended with the new unobservable future value $$ \mathbf y _{*}$$ of the response whose expectation is $$ \mathbf X _{*}\varvec{\beta }$$ . Our aim is to provide some new insight and new proofs for the equalities under consideration. We also collect together various expressions, without rank assumptions, for the $$\mathrm {BLUP} $$ and provide new results giving upper bounds for the Euclidean norm of the difference between the $$\mathrm {BLUP} ( \mathbf y _{*})$$ and $$\mathrm {BLUE} ( \mathbf X _{*}\varvec{\beta })$$ and between the $$\mathrm {BLUP} ( \mathbf y _{*})$$ and $$\mathrm {OLSE} ( \mathbf X _{*}\varvec{\beta })$$ . A remark is made on the application to small area estimation. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Stephen Haslett & Jarkko Isotalo & Yonghui Liu & Simo Puntanen, 2014. "Equalities between OLSE, BLUE and BLUP in the linear model," Statistical Papers, Springer, vol. 55(2), pages 543-561, May.
  • Handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:543-561
    DOI: 10.1007/s00362-013-0500-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-013-0500-7
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00362-013-0500-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Farrow, Andrew & Larrea, Carlos & Hyman, Glenn & Lema, German, 2005. "Exploring the spatial variation of food poverty in Ecuador," Food Policy, Elsevier, vol. 30(5-6), pages 510-531.
    2. Harold Alderman & Miriam Babita & Gabriel Demombynes & Nthabiseng Makhatha & Berk Özler, 2002. "How Low Can You Go? Combining Census and Survey Data for Mapping Poverty in South Africa," Journal of African Economies, Centre for the Study of African Economies, vol. 11(2), pages 169-200, June.
    3. Stephen Haslett & Simo Puntanen, 2011. "On the equality of the BLUPs under two linear mixed models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(3), pages 381-395, November.
    4. Kam, Suan-Pheng & Hossain, Mahabub & Bose, Manik Lal & Villano, Lorena S., 2005. "Spatial patterns of rural poverty and their relationship with welfare-influencing factors in Bangladesh," Food Policy, Elsevier, vol. 30(5-6), pages 551-567.
    5. Pawel Pordzik, 2012. "A bound for the Euclidean distance between restricted and unrestricted estimators of parametric functions in the general linear model," Statistical Papers, Springer, vol. 53(2), pages 299-304, May.
    6. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    7. Minot, Nicholas & Baulch, Bob, 2005. "Spatial patterns of poverty in Vietnam and their implications for policy," Food Policy, Elsevier, vol. 30(5-6), pages 461-475.
    8. Jürgen Groß, 2004. "The general Gauss-Markov model with possibly singular dispersion matrix," Statistical Papers, Springer, vol. 45(3), pages 311-336, July.
    9. Oskar Baksalary & Götz Trenkler, 2009. "A projector oriented approach to the best linear unbiased estimator," Statistical Papers, Springer, vol. 50(4), pages 721-733, August.
    10. Kristjanson, Patricia & Radeny, Maren & Baltenweck, Isabelle & Ogutu, Joseph & Notenbaert, An, 2005. "Livelihood mapping and poverty correlates at a meso-level in Kenya," Food Policy, Elsevier, vol. 30(5-6), pages 568-583.
    11. Amarasinghe, Upali & Samad, Madar & Anputhas, Markandu, 2005. "Spatial clustering of rural poverty and food insecurity in Sri Lanka," Food Policy, Elsevier, vol. 30(5-6), pages 493-509.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nesrin Güler & Melek Eriş Büyükkaya & Melike Yiğit, 2022. "Comparison of Covariance Matrices of Predictors in Seemingly Unrelated Regression Models," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(3), pages 801-809, September.
    2. Changli Lu & Yuqin Sun & Yongge Tian, 2018. "Two competing linear random-effects models and their connections," Statistical Papers, Springer, vol. 59(3), pages 1101-1115, September.
    3. Yongge Tian & Wenxing Guo, 2016. "On comparison of dispersion matrices of estimators under a constrained linear model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 623-649, November.
    4. Tian, Yongge & Zhang, Xuan, 2016. "On connections among OLSEs and BLUEs of whole and partial parameters under a general linear model," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 105-112.
    5. S. J. Haslett & X. Q. Liu & A. Markiewicz & S. Puntanen, 2020. "Some properties of linear sufficiency and the BLUPs in the linear mixed model," Statistical Papers, Springer, vol. 61(1), pages 385-401, February.
    6. Bo Jiang & Yuqin Sun, 2019. "On the equality of estimators under a general partitioned linear model with parameter restrictions," Statistical Papers, Springer, vol. 60(1), pages 273-292, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kiran, Rubina & Jabbar, Abdul, 2022. "Policy-oriented food insecurity estimation and mapping at district level in Pakistan," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 8(4), December.
    2. Kifayat Ullah & M. Tariq Majeed & Ghulam Mustafa, 2020. "Exploring Spatial Patterns and Determinants of Poverty: New Evidence from Pakistan," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 59(3), pages 439-459.
    3. Graw, Valerie & Husmann, Christine Ladenburger, 2012. "Mapping Marginality Hotspots – Geographical Targeting for Poverty Reduction," Working Papers 147917, University of Bonn, Center for Development Research (ZEF).
    4. Mohamed Ayadi & Mohamed Amara, 2009. "Spatial Patterns and Geographic Determinants of Welfare and Poverty in Tunisia," Working Papers 478, Economic Research Forum, revised Mar 2009.
    5. Jad Chaaban & Hala Ghattas & Alexandra Irani & Alban Thomas, 2018. "Targeting mechanisms for cash transfers using regional aggregates," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 10(2), pages 457-472, April.
    6. Mohamed Amara & Hatem Jemmali, 2018. "Household and Contextual Indicators of Poverty in Tunisia: A Multilevel Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 137(1), pages 113-138, May.
    7. Barbier, Edward B., 2012. "Natural capital, ecological scarcity and rural poverty," Policy Research Working Paper Series 6232, The World Bank.
    8. Simler, Kenneth R., 2006. "Nutrition mapping in Tanzania: an exploratory analysis," FCND discussion papers 204, International Food Policy Research Institute (IFPRI).
    9. Andi Syah Putra & Guangji Tong & Didit Okta Pribadi, 2020. "Spatial Analysis of Socio-Economic Driving Factors of Food Expenditure Variation between Provinces in Indonesia," Sustainability, MDPI, vol. 12(4), pages 1-18, February.
    10. Enamorado, Ted & López-Calva, Luis F. & Rodríguez-Castelán, Carlos & Winkler, Hernán, 2016. "Income inequality and violent crime: Evidence from Mexico's drug war," Journal of Development Economics, Elsevier, vol. 120(C), pages 128-143.
    11. Azzarri, Carlo & Signorelli, Sara, 2020. "Climate and poverty in Africa South of the Sahara," World Development, Elsevier, vol. 125(C).
    12. Simler, Kenneth R. & Nhate, Virgulino, 2005. "Poverty, inequality, and geographic targeting: Evidence from Small-Area Estimates in Mozambique," FCND discussion papers 192, International Food Policy Research Institute (IFPRI).
    13. Enamorado, Ted & López-Calva, Luis F. & Rodríguez-Castelán, Carlos, 2014. "Crime and growth convergence: Evidence from Mexico," Economics Letters, Elsevier, vol. 125(1), pages 9-13.
    14. Healy, Andrew J. & Jitsuchon, Somchai, 2007. "Finding the poor in Thailand," Journal of Asian Economics, Elsevier, vol. 18(5), pages 739-759, October.
    15. Mónica Navarrete & Patricio Aroca & Jorge Bernal, 2017. "Matching espacial para georreferenciar datos de encuestas de hogar," Estudios de Economia, University of Chile, Department of Economics, vol. 44(1 Year 20), pages 53-80, June.
    16. Gabriel Demombynes & Chris Elbers & Jean O. Lanjouw & Peter Lanjouw & Johan A. Mistiaen & Berk Özler, 2002. "Producing an Improved Geographic Profile of Poverty: Methodology and Evidence from Three Developing Countries," WIDER Working Paper Series DP2002-39, World Institute for Development Economic Research (UNU-WIDER).
    17. Deon Filmer & Kinnon Scott, 2012. "Assessing Asset Indices," Demography, Springer;Population Association of America (PAA), vol. 49(1), pages 359-392, February.
    18. Tomoki Fujii, 2004. "Commune-Level Estimation of Poverty Measures and its Application in Cambodia," WIDER Working Paper Series RP2004-48, World Institute for Development Economic Research (UNU-WIDER).
    19. Marcel Fafchamps & Forhad Shilpi & The World Bank, 2004. "Isolation and Subjective Welfare," Economics Series Working Papers 216, University of Oxford, Department of Economics.
    20. Permanyer, Iñaki, 2013. "Using Census Data to Explore the Spatial Distribution of Human Development," World Development, Elsevier, vol. 46(C), pages 1-13.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:543-561. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.