  Traditional methods for linear regression generally assume that the
underlying error distribution, equivalently the distribution of the responses,
is normal. Yet, sometimes real life response data may exhibit a skewed pattern,
and assuming normality would not give reliable results in such cases. This is
often observed in cases of some biomedical, behavioral, socio-economic and
other variables. In this paper, we propose to use the class of skew normal (SN)
distributions, which also includes the ordinary normal distribution as its
special case, as the model for the errors in a linear regression setup and
perform subsequent statistical inference using the popular and robust minimum
density power divergence approach to get stable insights in the presence of
possible data contamination (e.g., outliers). We provide the asymptotic
distribution of the proposed estimator of the regression parameters and also
propose robust Wald-type tests of significance for these parameters. We provide
an influence function analysis of these estimators and test statistics, and
also provide level and power influence functions. Numerical verification
including simulation studies and real data analysis is provided to substantiate
the theory developed.
