Thin Plate Spline Method Of The Semi-parametric Regression

Semi-parametric regression has the special advantage in resolving the problem of systematic errors, and the theory has been fully developed .But these developed theory only resolve systematic errors connecting with only one factor. In fact, many systematic errors are correlative with the multi-factors, For example, in the GPS surveying, the delay of the satellite signal among the aerosphere and ionosphere correlate with the satellitic altitudinal angle and observation time, So in the thesis , it is put forward the method that solving the systematic errors connection with the multi-dimension variables. In the theory of semi-parametric regression, we must pose a hypothesis to the non-parameter that has the characteristic of continuity, smoothness, periodicity and so on. In this condition, it is suitable for adopting the TPS to match non-parameter part. In the thesis, I first introduce the TPS into the theory of Semi-parametric regression, deduced the regular matrix R, discussed smoothing parameter α selection, and analyzed the statistical nature of the TPS method of Semi-parametric regression. At the end, a stimulant example and gravity abnormity example are adopted and mainly analyzed the second. The application of the theory shows that it is feasible and has wide prospect in dealing with systematic errors connection with the multi-dimension variables.