Testing of homogeneity for correlation and variance in nonlinear regression models with DBL(p, 0, 1) random errors

It is a standard assumption for regression models that all the random errors are mutually independent and have equal variances. However, in some situations, the assumption is untenable. Tsai (Tsai, C. L. (1986). Score test for the first-order autoregreesive model with heteroscedasticity. Biometrika 73:455-460) introduced a composite test for heteroscedasticity and autocorrelation in linear regression models with AR(l) errors. In this article, we extend Tsai's (Tsai, C. L. (1986). Score test for the first-order autoregreesive model with heteroscedasticity. Biometrika 73:455-460) results to more general case. For the underlying model, we consider nonlinear regression rather than the linear one. For the random error, we extend it from AR(1) process to AR(p) process. Moreover, since the random error may behave nonlinearity sometime, we put a bilinear term in it, which is a simple way to indicate the nonlinearity. So we discuss the test of heteroscedasticity, autocorrelation and bilinearity for nonlinear regression with DBL (p, 0, 1) random errors. Several test statistics based on the score test are obtained, and expressed in simple matrix formulas. The simulation study is performed to investigate the powers of the test statistics.