  In real life we often deal with independent but not identically distributed
observations (i.n.i.d.o), for which the most well-known statistical model is
the multiple linear regression model (MLRM) without random covariates. While
the classical methods are based on the maximum likelihood estimator (MLE), it
is well known its lack of robustness to small deviations from the assumed
conditions. In this paper, and based on the R\'enyi's pseudodistance (RP), we
introduce a new family of estimators in case our information about the unknown
parameter is given for i.n.i.d.o.. This family of estimators, let say minimum
RP estimators (as they are obtained by minimizing the RP between the assumed
distribution and the empirical distribution of the data), contains the MLE as a
particular case and can be applied, among others, to the MLRM without random
covariates. Based on these estimators, we introduce Wald-type tests for testing
simple and composite null hypotheses, as an extension of the classical
MLE-based Wald test. Influence functions for the estimators and Wald-type tests
are also obtained and analysed. Finally, a simulation study is developed in
order to asses the performance of the proposed methods and some real-life data
are analysed for illustrative purpose.
