Dimension reduction techniques for functional data: An illustration using a cancer screening medical device

Cervical cancer has been one of the most common cancers among women, especially in the developing countries. Our research group has built a new medical device which uses fluorescence spectroscopy for early detection of cervical cancer. The output of the device belongs to the functional data. My role in the project is to determine if the factor of room light is statistically significant using the data setting from the experiment. It is impossible to use traditional statistical method for large functional data because the number of dimensions is much larger than the number of observations. The thesis comes up with some ideas of dimension reduction techniques including PCA and EDA. Based upon the thoughts of Adaptively Truncated Hotelling T-Square Test, this thesis extends the method to more than two groups which we call it Adaptively Truncated MANOVA. Simulations are made on the three test statistics of Adaptively Truncated MANOVA. However, whether we can apply the Adaptively Truncated MANOVA to the real data still needs more work in the future.