SEMIPARAMETRIC EFFICIENCY BOUND IN TIME-SERIES MODELS FOR CONDITIONAL QUANTILES

We derive the semi parametric efficiency bound in dynamic models of conditional quantiles under a sole strong mixing assumption. We also provide an expression of Stein's (1956) least favorable parametric submodel. Our approach is as follows: First, we construct a fully parametric submodel of the semiparametric model defined by the conditional quantile restriction that contains the data generating process. We then compare the asymptotic covariance matrix of the MILE obtained in this submodel with those of the M-estimators for the conditional quantile parameter that are consistent and asymptotically normal. Finally, we show that the minimum asymptotic covariance matrix of this class of M-estimators equals the asymptotic covariance matrix of the parametric submodel MILE. Thus, (i) this parametric submodel is a least favorable one, and (ii) the expression of the semiparametric efficiency bound for the conditional quantile parameter follows.