Estimation and Testing on Independent Not Identically Distributed Observations Based on Rényi’s Pseudodistances

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 multiple linear regression (MLRM) non-random covariates. While classical methods are based on maximum likelihood estimator (MLE), it well known its lack of robustness to small deviations from assumed conditions. this paper, and Rényi’s pseudodistance (RP), introduce a new family estimators in case our information about unknown parameter given i.n.i.d.o.. This estimators, let us say minimum RP (as they obtained by minimizing between distribution empirical data), contains MLE as particular can be applied, among others, MLRM Based these Wald-type tests testing simple composite null hypotheses, an extension MLE-based Wald test. Influence functions also analysed. Finally, simulation study developed order asses performance proposed some real-life data analysed illustrative purpose.