Confidence bands in generalized linear models
نویسندگان
چکیده
منابع مشابه
Comparison Of Hyperbolic And Constant Width Simultaneous Confidence Bands in Multiple Linear Regression Under MVCS Criterion
A simultaneous confidence band gives useful information on the reasonable range of the unknown regression model. In this note, when the predictor variables are constrained to a special ellipsoidal region, hyperbolic and constant width confidence bonds for a multiple linear regression model are compared under the minimum volome confidence set (MVCS) criterion. The size of one speical an...
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In many applications it is necessary to know the stochastic fluctuation of the maximal deviations of the nonparametric quantile estimates, e.g. for various parametric models check. Uniform confidence bands are therefore constructed for nonparametric quantile estimates of regression functions. The first method is based on the strong approximations of the empirical process and extreme value theor...
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Construction of simultaneous confidence bands for a percentile line in linear regression has been considered by several authors. But only conservative symmetric bands, which use critical constants over the whole covariate range (−∞, ∞), are available in the literature. New methods allow the construction of exact symmetric bands for a percentile line over a finite interval of the covariate x. Th...
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In this paper uniform confidence bands are constructed for nonparametric quantile estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated empirical density function (edf) for residuals. It is known that the approximation error for the uniform confidence band by the asymptotic Gumbel distribution is logarithmically slow. It is p...
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We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f which is close to, but simpler than, f . The surrogate captures the significant features in f . We establish lower bounds on the width for any confidence band for f and construct a procedure tha...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2000
ISSN: 0090-5364
DOI: 10.1214/aos/1016218225