An analytic comparison of permutation methods for tests of partial regression coefficients in the linear model

Ali Shadrokh (1) , Gérard Aubigny (d') (2)

1 Department of Statistics
2 MS3 - Méthodologie Statistique et Sciences Sociales

Several method of perturbation tests have been proposed for testing nullity of a partial regression coefficient in a linera model. These methods were compared in terms of empirical type 1 error and power by statisticians. One striking result of the simulation based comparison is that the two emerging methods, while previously identified as equivalent formulations of the permutation strategy under the reduced model, did actiually produce quite different results. And one of this methods have almost the best result. Some theoretical justification to the empirical findings is given here. We compared estimators and variances of these two methods analytically in the double regression linear model. Our results give mathematical support to the observation obtained by simulation. Furthermore, for the first time we obtained the expected value of the estimators of the variance by the permutational distribution and we found that one of these estimators is unbias.

Mots clés: permutation test; permutational p-value; partial regression

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Ali Shadrokh, Gérard Aubigny (d'). An analytic comparison of permutation methods for tests of partial regression coefficients in the linear model. Applied Mathematical Sciences, 2010, 4 (18), pp.857-878. ⟨hal-00851657⟩