IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v122y2013icp162-174.html
   My bibliography  Save this article

Bartlett-type adjustments for hypothesis testing in linear models with general error covariance matrices

Author

Listed:
  • Kojima, Masahiro
  • Kubokawa, Tatsuya

Abstract

Consider the problem of testing a linear hypothesis of regression coefficients in a general linear regression model with a covariance matrix involving several nuisance parameters. Then, the Bartlett-type adjustments of the Wald, Score, and modified Likelihood Ratio tests are derived for general consistent estimators of the unknown nuisance parameters. The adjusted test statistics have second-order corrections in type I errors. Simple parametric bootstrap methods are also suggested for estimating the Bartlett-type adjustments and it is shown that they have the second order accuracy.

Suggested Citation

  • Kojima, Masahiro & Kubokawa, Tatsuya, 2013. "Bartlett-type adjustments for hypothesis testing in linear models with general error covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 162-174.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:162-174
    DOI: 10.1016/j.jmva.2013.07.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13001486
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.07.016?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. Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2005. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 92(1), pages 183-196, March.
    2. Rayner, Robert K., 1990. "Bartlett's correction and the bootstrap in normal linear regression models," Economics Letters, Elsevier, vol. 33(3), pages 255-258, July.
    3. Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-842, July.
    Full references (including those not matched with items on IDEAS)

    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. Masahiro Kojima & Tatsuya Kubokawa, 2013. "Bartlett Adjustments for Hypothesis Testing in Linear Models with General Error Covariance Matrices," CIRJE F-Series CIRJE-F-884, CIRJE, Faculty of Economics, University of Tokyo.
    2. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Simulation based finite and large sample tests in multivariate regressions," Journal of Econometrics, Elsevier, vol. 111(2), pages 303-322, December.
    3. Malay Ghosh & Tatsuya Kubokawa & Yuki Kawakubo, 2014. "Benchmarked Empirical Bayes Methods in Multiplicative Area-level Models with Risk Evaluation," CIRJE F-Series CIRJE-F-918, CIRJE, Faculty of Economics, University of Tokyo.
    4. repec:csb:stintr:v:17:y:2016:i:1:p:9-24 is not listed on IDEAS
    5. Erciulescu Andreea L. & Fuller Wayne A., 2016. "Small Area Prediction Under Alternative Model Specifications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 9-24, March.
    6. Lixia Diao & David D. Smith & Gauri Sankar Datta & Tapabrata Maiti & Jean D. Opsomer, 2014. "Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 497-515, June.
    7. Md. Mizanur Rahman & Deluar J. Moloy & Md. Sifat Ar Salan, 2021. "Evaluating the Approaches of Small Area Estimation Using Poverty Mapping Data," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 10(2), pages 1-1.
    8. Linton, Oliver, 1995. "Second Order Approximation in the Partially Linear Regression Model," Econometrica, Econometric Society, vol. 63(5), pages 1079-1112, September.
    9. James G. MacKinnon & Russell Davidson, 1996. "The Size And Power Of Bootstrap Tests," Working Paper 932, Economics Department, Queen's University.
    10. Gauri Datta & Tatsuya Kubokawa & Isabel Molina & J. Rao, 2011. "Estimation of mean squared error of model-based small area estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 367-388, August.
    11. G. Datta & M. Ghosh & R. Steorts & J. Maples, 2011. "Bayesian benchmarking with applications to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 574-588, November.
    12. Stefano Marchetti & Caterina Giusti & Monica Pratesi, 2016. "The use of Twitter data to improve small area estimates of households’ share of food consumption expenditure in Italy [Die Nutzung von Twitter Daten um die Small Area Schätzungen vom Ausgabenanteil," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(2), pages 79-93, October.
    13. Hausman, Jerry & Kuersteiner, Guido, 2008. "Difference in difference meets generalized least squares: Higher order properties of hypotheses tests," Journal of Econometrics, Elsevier, vol. 144(2), pages 371-391, June.
    14. Banerjee, Anurag N. & Magnus, Jan R., 2000. "On the sensitivity of the usual t- and F-tests to covariance misspecification," Journal of Econometrics, Elsevier, vol. 95(1), pages 157-176, March.
    15. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    16. Gaia Bertarelli & Luigi Biggeri & Caterina Giusti & Stefano Marchetti & Monica Pratesi, 2020. "Intra-Country comparisons of Poverty Rate," Discussion Papers 2020/260, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    17. Torabi, Mahmoud & Rao, J.N.K., 2014. "On small area estimation under a sub-area level model," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 36-55.
    18. Tatsuya Kubokawa, 2010. "On Measuring Uncertainty of Small Area Estimators with Higher Order Accuracy," CIRJE F-Series CIRJE-F-754, CIRJE, Faculty of Economics, University of Tokyo.
    19. Szymkowiak Marcin & Młodak Andrzej & Wawrowski Łukasz, 2017. "Mapping Poverty at the Level of Subregions in Poland Using Indirect Estimation," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 609-635, December.
    20. Malay Ghosh, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.
    21. Schmid, Timo & Bruckschen, Fabian & Salvati, Nicola & Zbiranski, Till, 2016. "Constructing socio-demographic indicators for National Statistical Institutes using mobile phone data: Estimating literacy rates in Senegal," Discussion Papers 2016/9, Free University Berlin, School of Business & Economics.

    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:eee:jmvana:v:122:y:2013:i:c:p:162-174. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.