Consider an ordinary errors-in-variables model. The true level an(θ) of a test at nominal level a and sample size n is called to be pointwise robust if an (θ)→ α as n → ∞ for each parameter θ. Define an = sUPθEnan(θ), where n is the parameter space of θ. The test is said to be uniformly robust over Ω if an → α as n → ∞.
It is known that all existing large-sample tests for the key parameters are pointwise robust but not uniformly robust, even for a narrow subset of parameter space. In this talk, we construct uniformly robust tests for some primary parameters in both functional and structural errors-in-variables models. These results can be used to establish the related confidence sets with certain desirable property in the same models. A small simulation showing that the proposed tests are superior to the ordi!1ary large-sample ones in the finite sample is also provided.
2000年國際數學與統計研討會暨第34屆中華民國數學會年會：慶祝淡江大學創校五十週年校慶 ( 2000 international conference on mathematics and statistics and 34th annual meeting of mathematical society of R.O.C. : commemorating the 50th anniversary of Tamkang University), pp.32