Least Absolute Deviations
|Author:||Bc. Daniel Pacák|
|Year:||2017 - summer|
|Leaders:|| prof. RNDr. Jan Ámos Víšek CSc.
|Work type:|| Bachelors
|Awards and prizes:|
|Abstract:||This is a theoretical study of the Least Absolute Deviations (LAD) fits. In
the first part, fundamental mathematical properties of LAD fits are established.
Computational aspects of LAD fits are shown and the Barrodale-Roberts Algorithm
for finding LAD fits is presented. In the second part, the statistical
properties of LAD estimator are discussed in the concept of linear regression.
It is shown that LAD estimator is a maximum likelihood estimator if the error
variables follow Laplace distribution. We state theorems establishing strong
consistency and asymptotic normality of LAD estimator and we discuss the bias
of LAD estimator. In the last section, we present the results of numerical experiments
where we numerically showed consistency of LAD estimator, discussed its
behaviour under different distributions of error variables with comparison to the
Ordinary Least Squares (OLS) estimator. Lastly, we looked at the behaviour of
LAD and OLS estimators in the presence of corrupted observations.