Some extensions in measurement error models
Abstract
In this dissertation, we approach three different contributions in measurement error model
(MEM). Initially, we carry out maximum penalized likelihood inference in MEM’s under the
normality assumption. The methodology is based on the method proposed by Firth (1993),
which can be used to improve some asymptotic properties of the maximum likelihood estimators.
In the second contribution, we develop two new estimation methods based on generalized
fiducial inference for the precision parameters and the variability product under the Grubbs
model considering the two-instrument case. One method is based on a fiducial generalized
pivotal quantity and the other one is built on the method of the generalized fiducial distribution.
Comparisons with two existing approaches are reported. Finally, we propose to study inference
in a heteroscedastic MEM with known error variances. Instead of the normal distribution for
the random components, we develop a model that assumes a skew-t distribution for the true
covariate and a centered Student’s t distribution for the error terms. The proposed model enables
to accommodate skewness and heavy-tailedness in the data, while the degrees of freedom of the
distributions can be different. We use the maximum likelihood method to estimate the model
parameters and compute them via an EM-type algorithm. All proposed methodologies are
assessed numerically through simulation studies and illustrated with real datasets extracted from
the literature.