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Abstract. We apply recent results on local U‐statistics to obtain uniform in bandwidth consistency and central limit theorems for some commonly used estimators of integral functionals of density functions. 相似文献
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Jan G. De Gooijer 《Journal of applied statistics》2007,34(4):371-381
We compare and investigate Neyman's smooth test, its components, and the Kolmogorov-Smirnov (KS) goodness-of-fit test for testing the uniformity of multivariate forecast densities. Simulations indicate that the KS test lacks power when the forecast distributions are misspecified, especially for correlated sequences of random variables. Neyman's smooth test and its components work well in samples of size typically available, although there sometimes are size distortions. The components provide directed diagnosis regarding the kind of departure from the null. For illustration, the tests are applied to forecast densities obtained from a bivariate threshold model fitted to high-frequency financial data. 相似文献
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将实变量函数的一致可微性推广到复变量函数中,所得结果与实变量情形既有类似又有差别,并进一步研究了复函数一致可微与其导函数一致连续的关系、有界闭域上解析函数的无穷一致可微性以及函数一致可微可推出其本身一致连续的条件等. 相似文献
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白国仲 《佛山科学技术学院学报(社会科学版)》1995,(4)
给出了Banach空间的很极光滑性、一致极光滑性和平均一致凸Banach空间之间的关系. 相似文献
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Joseph P. Romano 《Revue canadienne de statistique》1989,17(1):75-80
An important statistical problem is to construct a confidence set for some functional T(P) of some unknown probability distribution P. Typically, this involves approximating the sampling distribution Jn(P) of some pivot based on a sample of size n from P. A bootstrap procedure is to estimate Jn(P) by Jn(&Pcirc;n), where P?n is the empirical measure based on a sample of size n from P. Typically, one has that Jn(P) and Jn(P?n) are close in an appropriate sense. Two questions are addressed in this note. Are Jn(P) and Jn(P?n) uniformly close as P varies as well? If so, do confidence statements about T(P) possess a corresponding uniformity property? In the case T(P) = P, the answer to the first questions is yes; the answer to the second is no. However, bootstrap confidence statements about T(P) can be made uniform over a restricted, though large, class of P. Similar results apply to other functional T(P). 相似文献
29.
白国仲 《佛山科学技术学院学报(社会科学版)》1995,(2)
给出平均一致凸Banach空间的定义,证明了一致凸Banach空间是平均一致凸Banach空间,平均一致凸Banach空间是自反和弱局部一致凸Banach空间,并且平均一致凸Banach空间X中任意元在X的闭凸子集中存在唯一的最佳逼近元. 相似文献
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Abstract. In this paper, we consider a semiparametric time-varying coefficients regression model where the influences of some covariates vary non-parametrically with time while the effects of the remaining covariates follow certain parametric functions of time. The weighted least squares type estimators for the unknown parameters of the parametric coefficient functions as well as the estimators for the non-parametric coefficient functions are developed. We show that the kernel smoothing that avoids modelling of the sampling times is asymptotically more efficient than a single nearest neighbour smoothing that depends on the estimation of the sampling model. The asymptotic optimal bandwidth is also derived. A hypothesis testing procedure is proposed to test whether some covariate effects follow certain parametric forms. Simulation studies are conducted to compare the finite sample performances of the kernel neighbourhood smoothing and the single nearest neighbour smoothing and to check the empirical sizes and powers of the proposed testing procedures. An application to a data set from an AIDS clinical trial study is provided for illustration. 相似文献