Hypothesis Testing For Functional Parameter In Functional Linear Model

With the development of advanced technologies, it is possible to collect and store data which is based on fine sampling records. In this paper, we mainly focus on the hypothesis testing issues about functional parameter in the functional linear model. The common point of functional data is that every observed sample is a curve, not a point or a scalar, namely. As to the statistical inference for functional data, the functional principal analysis is the main data processing tool, which could transform the functional data into scalar form.It should be noted that the errors in the linear model are no longer normally distributed as the truncation components are included in the residual. When there exists outliers in the residual, the least square theory will be adversely effected by the outliers. The Wilcoxon-type generalised likelihood ratio test is exactly apply to explore this kind of issues. We further theoretically prove that the test statistic is asymptotically ?2 distributed.Simulations are conducted to demonstrate that the null distribution of the Wilcoxon-type generalised likelihood ratio test statistic is asymptotically ?2 distributed. The power of the proposed test is also proved to perform better than that of least square test when there exists outliers in the residuals. In this case, the proposed test statistic owns good robustness.