Regression quantiles were developed by Koenker and Bassett (Econometrica 46 (1978), 33–50); they provide natural and extremely useful counterparts of the sample quantiles in general linear models. The regression rank scores were introduced by Gutenbrunner and Jurečková (Ann. Statist. 8 (1992), 305–329) as dual variables to regression quantiles. Koul and Saleh (Ann. Statist. 23 (1995), 670–689) developed the procedures based on the regression quantiles of Koenker and Bassett (Econometrica 46 (1978), 33–50) and the regression rank scores of Gutenbrunner and Jurečková Ann. Statist. 8 (1992), 305–329 in linear regression to the pth-order autoregression models. In this paper, we further develop and investigate the analogs of these procedures to a larger class of processes and derive a test for a bilinear model without estimating the bilinear coefficient and the autoregression constants.
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