Asymptotic consistency of fixed-width sequential confidence intervals for a multiple regression function
Copyright policy )Asymptotic consistency of fixed-width sequential confidence intervals for a multiple regression function
Let \(m_ n(x)\) be the recursive kernel estimator of the multiple regression function \(m(x)=E[Y| X=x]\). For given \(\alpha\) \((00\) we define a certain class of stopping times \(N=N(\alpha,d,x)\) and take \(I_{N,d}(x)=[m_ N(x)-d\), \(m_ N(x)+d]\) as a 2d-width confidence interval for m(x) at a given point x. In this paper it is shown that the probability \(P\{m(x)\in I_{N,d}(x)\}\) converges to \(\alpha\) as d tends to zero.
- Niigata University Japan
Nonparametric tolerance and confidence regions, Sequential estimation, recursive kernel estimator, sequential confidence intervals, Nonparametric estimation, asymptotic consistency, multiple regression function, stopping times
Nonparametric tolerance and confidence regions, Sequential estimation, recursive kernel estimator, sequential confidence intervals, Nonparametric estimation, asymptotic consistency, multiple regression function, stopping times
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