Estimates of least squares and least squares trimmed for linear regression with natural twisted errors

Abstract

The twisted normal distribution of the ESN torsion parameter (ESN, μ, σ, ε) represents a
parameter class of probability distributions that provide a more flexible model given the
potential of this parameter to continuously change from normal to abnormal. In theory,
the process of estimating the parameters of a linear regression model with an average
error of value, not zero, is a major challenge because of the difficulties involved in this
process. These estimates are evaluated only through numerical methods. In this paper, the
parameters of the SNGLM in LS and LTS and MSE as a criterion for comparing the
preference of these two methods were estimated by using the simulation study by
generating relevant data. A normal twist to the right and left, with different sample sizes,
shows that the LS method gives more accurate values for SNGLM parameters than the
LTS method.