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On the Maximum Likelihood estimation of a linear structural relationship when the intercept is known

Author

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  • Chan, Lai K.
  • Mak, Tak K.

Abstract

This paper considers the Maximum Likelihood (ML) estimation of the five parameters of a linear structural relationship y = [alpha] + [beta]x when [alpha] is known. The parameters are [beta], the two variances of observation errors on x and y, the mean and variance of x. When the ML estimates of the parameters cannot be obtained by solving a simple simultaneous system of five equations, they are found by maximizing the likelihood function directly. Some asymptotic properties of the estimates are also obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:2:p:304-313
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    Cited by:

    1. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno & Gasco, Loreta, 2002. "Measurement Error Models with Nonconstant Covariance Matrices," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 395-415, August.
    2. Sukhbir Singh & Kanchan Jain & Suresh Sharma, 2014. "Replicated measurement error model under exact linear restrictions," Statistical Papers, Springer, vol. 55(2), pages 253-274, May.
    3. Mengli Zhang & Yang Bai, 2021. "On the use of repeated measurement errors in linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 779-803, July.
    4. Singh, Sukhbir & Jain, Kanchan & Sharma, Suresh, 2012. "Using stochastic prior information in consistent estimation of regression coefficients in replicated measurement error model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 198-212.
    5. 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.
    6. Chunzheng Cao & Yahui Wang & Jian Qing Shi & Jinguan Lin, 2018. "Measurement Error Models for Replicated Data Under Asymmetric Heavy-Tailed Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 531-553, August.

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