caa a22 4500 475826876 CHVBK 20180406123831.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1023/A:1017521225616 doi (NATIONALLICENCE)springer-10.1023/A:1017521225616 Asymptotically Optimal Tests and Optimal Designs for Testing the Mean in Regression Models with Applications to Change-Point Problems [Elektronische Daten] [Wolfgang Bischoff, Frank Miller] Let a linear regression model be given with an experimental region [a, b] → R and regression functions f 1, ..., f d+1 : [a, b] → R. In practice it is an important question whether a certain regression function f d+1, say, does or does not belong to the model. Therefore, we investigate the test problem H 0 : "f d+1 does not belong to the model" against K : "f d+1 belong to the model" based on the least-squares residuals of the observations made at design points of the experimental region [a, b]. By a new functional central limit theorem given in Bischoff (1998, Ann. Statist. 26, 1398-1410), we are able to determine optimal tests in an asymptotic way. Moreover, we introduce the problem of experimental design for the optimal test statistics. Further, we compare the asymptotically optimal test with the likelihood ratio test (F-test) under the assumption that the error is normally distributed. Finally, we consider real change-point problems as examples and investigate by simulations the behavior of the asymptotic test for finite sample sizes. We determine optimal designs for these examples. The Institute of Statistical Mathematics, 2000 Asymptotically optimal tests nationallicence linear regression nationallicence F-test nationallicence likelihood ratio test nationallicence Gaussian processes nationallicence optimal designs nationallicence change-point problem nationallicence quality control nationallicence Bischoff Wolfgang Institute of Mathematical Stochastics, Department of Mathematics, University of Karlsruhe, D-76128, Karlsruhe, Germany aut Miller Frank Institute of Mathematical Stochastics, Department of Mathematics, University of Karlsruhe, D-76128, Karlsruhe, Germany aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/4(2000-12-01), 658-679 0020-3157 52:4<658 2000 52 10463 https://doi.org/10.1023/A:1017521225616 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1017521225616 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bischoff Wolfgang Institute of Mathematical Stochastics, Department of Mathematics, University of Karlsruhe, D-76128, Karlsruhe, Germany aut NATIONALLICENCE 700 1- Miller Frank Institute of Mathematical Stochastics, Department of Mathematics, University of Karlsruhe, D-76128, Karlsruhe, Germany aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/4(2000-12-01), 658-679 0020-3157 52:4<658 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer