An Algorithm for Estimating Measurement Error Models Employing Spline Approximation
DOI:
https://doi.org/10.60923/issn.1973-2201/21497Keywords:
B-spline basis, Expectation-Maximization, Maximum likelihood, Measurement errorAbstract
An algorithm has been derived for finding maximum likelihood estimates of a measurement error model when the B-spline basis function of degree one is used to model the true regression function. In a measurement error model, the true variable is not observed. Hence the likelihood function is not completely known. This in turn induces difficulty in the maximization of the likelihood function. To address this problem, the Expectation-Maximization algorithm has been used to derive the results. We also illustrate the algorithm using simulation and a real life application.
References
K. AYUB, W. SONG, J. SHI (2022). Extrapolation estimation in parametric regression models with measurement error. Computational Statistics and Data Analysis, 172, p. 107478.
A. BHADRA (2017). An expectation–maximization scheme for measurement error models. Statistics & Probability Letters, 120, pp. 61–68.
A. BHADRA, R. J. CARROLL (2016). Exact sampling of the unobserved covariates in Bayesian spline models for measurement error problems. Statistics and Computing, 26, no. 4, pp. 827–840.
C. BUTUCEA, C. MATIAS (2005). Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model. Bernoulli, 11, no. 2, pp. 309–340.
R. J. CARROLL, J. D. MACA, D. RUPPERT (1999). Nonparametric regression in the presence of measurement error. Biometrika, 86, no. 3, pp. 541–554.
R. J. CARROLL, D. RUPPERT, L. A. STEFANSKI, C. M. CRAINICEANU (2006). Measurement error in nonlinear models: a modern perspective. Chapman and Hall/CRC, Boca Raton, 2nd ed.
J. COOK, L. STEFANSKI (1994). Simulation-extrapolation estimation in parametric measurement error models. Journal of the American Statistical Association, 89, no. 428, pp. 1314–1328.
A. P. DEMPSTER, N. M. LAIRD, D. B. RUBIN (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39, no. 1, pp. 1–22.
P. H. C. EILERS, B. D. MARX (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, no. 2, pp. 89 – 121.
T. LI, Q.VUONG (1998). Nonparametric estimation of the measurement error model using multiple indicators. Journal of Multivariate Analysis, 65, no. 2, pp. 139–165.
T. LYCHE, C. MANNI, H. SPELEERS (2018). Foundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement. Springer, Cham.
A. MEISTER (2006). Density estimation with normal measurement error with unknown variance. Statistica Sinica, 16, no. 1, pp. 195–211.
C. F. J. WU (1983). On the convergence properties of the EM algorithm. The Annals of Statistics, 11, no. 1, pp. 95–103.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Statistica
This work is licensed under a Creative Commons Attribution 4.0 International License.
