SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL
研究了一类一阶非线性时间序列模型中的线性性检验问题，提出了上确界检验方法，并推导了其渐近分布，通过模拟研究了有限样本性质。
We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite-sample properties of the sup-tests are studied by simulations.