ASYMPTOTICS FOR ESTIMATION OF TRUNCATED INFINITE-DIMENSIONAL QUANTILE REGRESSIONS

Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, only results for finite-order processes are available at a level of generality that accommodates time series processes. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. As an example, many time series processes may be represented as an AR(?) or an MA(?); here we use a simulation to illustrate the degree of conformity of finite sample results with the asymptotics, in case of a truncated AR representation of a moving average.