- Thesis:
- Bachelor in Mathematics
- Author:
- Lars Kutschinski
- Title:
- Testen von Hypothesen im funktionalen linearen Modell
- Supervisor:
- Jan JOHANNES
- Abstract:
- This thesis studies the problem of how to perform a hypothesis test for the parameter function in a functional linear model with scalar response. Given a random function X and a scalar response variable Y, the model is given by Y = int ψ(t)X(t)dt + ε, where ψ is a function in L2([0,1]) and the noise ε is independent of X. We will define two different test statistics for the problem of testing H0 : ψ = 0 against H1 : ψ ̸= 0. Testing for the nullity of ψ is often used to check for a relationship between X and Y. The test statistics rely on the asymptotic distribution of the empirical covariance operator of X and Y. While the first statistic is based on a chi-squared distribution, the second statistics follows a standard gaussian distribution. Further Simulations show that the test statistics perform quite well in estimating the level and power of the test.
References:- H. Cardot, F. Ferraty, A. Mas et P. Sarda. Testing hypotheses in the functional linear model, Scandinavian Journal of Statistics, 30(1):241–255, 2003.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |