Paper detail

On existence of a change in mean of functional data

Functional data often arise as sequential temporal observations over a continuous state-space. A set of functional data with a possible change in its structure may lead to a wrong conclusion if it is not taken in to account. So, sometimes, it is crucial to know about the existence of change point in a given sequence of functional data before doing any further statistical inference. We develop a new methodology to provide a test for detecting a change in the mean function of the corresponding data. To obtain the test statistic we provide an alternative estimator of the covariance kernel. The proposed estimator is asymptotically unbiased under the null hypothesis and, at the same time, has smaller amount of bias than that of the existing estimator. We show here that under the null hypothesis the proposed test statistic is pivotal asymptotically. Moreover, it is shown that under alternative hypothesis the test is consistent for large enough sample size. It is also found that the proposed test is more powerful than the available test procedure in the literature. From the extensive simulation studies we observe that the proposed test outperforms the existing one with a wide margin in power for moderate sample size. The developed methodology performs satisfactorily for the average daily temperature of central England and monthly global average anomaly of temperatures.