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Robust inference in a linear functional model with replications using the t distribution

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  • Galea, Manuel
  • de Castro, Mário

Abstract

In this paper, we investigate model assessment, estimation and hypothesis testing in a linear functional relationship for replicated data when the distribution of the measurement errors is a multivariate Student t distribution. For statistical inference, we adopt the unbiased estimating equations approach. The resulting estimator is consistent and asymptotically normal; a closed form expression is also given for its asymptotic covariance matrix. A simple graphical device for model checking is proposed. We also describe how to test some hypotheses of interest on the parameter vector using the Wald statistic. A simulation study is performed to gauge the performance of the estimators and of the Wald statistic. The methodology developed in the paper is illustrated with a real data set.

Suggested Citation

  • Galea, Manuel & de Castro, Mário, 2017. "Robust inference in a linear functional model with replications using the t distribution," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 134-145.
    • Handle: RePEc:eee:jmvana:v:160:y:2017:i:c:p:134-145
    DOI: 10.1016/j.jmva.2017.06.008
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    1. Alexandre Belloni & Victor Chernozhukov & Abhishek Kaul, 2017. "Confidence bands for coefficients in high dimensional linear models with error-in-variables," CeMMAP working papers 22/17, Institute for Fiscal Studies.
    2. Chan, Lai K. & Mak, Tak K., 1979. "On the Maximum Likelihood estimation of a linear structural relationship when the intercept is known," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 304-313, June.
    3. Sutradhar, B. C., 1993. "Score Test for the Covariance Matrix of the Elliptic t-Distribution," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 1-12, July.
    4. Alexandre Belloni & Mathieu Rosenbaum & Alexandre B. Tsybakov, 2017. "Linear and conic programming estimators in high dimensional errors-in-variables models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 939-956, June.
    5. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-546, October.
    6. Lloyd A. Mancl & Timothy A. DeRouen, 2001. "A Covariance Estimator for GEE with Improved Small‐Sample Properties," Biometrics, The International Biometric Society, vol. 57(1), pages 126-134, March.
    7. Patricia Giménez & María Patat, 2014. "Local influence for functional comparative calibration models with replicated data," Statistical Papers, Springer, vol. 55(2), pages 431-454, May.
    8. Vilca-Labra, F. & Arellano-Valle, R. B. & Bolfarine, H., 1998. "Elliptical Functional Models," Journal of Multivariate Analysis, Elsevier, vol. 65(1), pages 36-57, April.
    9. Michael P. Fay & Barry I. Graubard, 2001. "Small-Sample Adjustments for Wald-Type Tests Using Sandwich Estimators," Biometrics, The International Biometric Society, vol. 57(4), pages 1198-1206, December.
    10. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
    11. Aman Ullah & Shalabh & Debasri Mukherjee, 2001. "Consistent Estimation of Regression Coefficients in Replicated Data with Non-Normal Measurement Errors," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 249-264, May.
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