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1.
针对部分线性模型提出了一种新的估计方法-Profile局部最小二乘估计,方法结合了非参数部分的参数信息.另外对于部分线性模型中非参数部分是否为某一参数函数的检验问题,基于比较原假设与备择假设下模型拟合的残差平方和的思想构造了检验统计量,并给出了计算检验p-值的精确方法和三阶矩χ2逼近方法. 相似文献
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关于Smarandache函数的一个新的下界估计 总被引:2,自引:1,他引:1
利用初等方法研究Smarandache函数在某些特殊值上的下界估计,给出了Smarandache函数在某些特殊值上的一个较强的下界估计,证明了估计式S(2p+1)≥6p+1,其中P≥7为任意素数. 相似文献
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陈乃辉 《纯粹数学与应用数学》2010,26(2):220-230
在函数逼近论的观点下研究了半参数变系数非线性回归函数的估计问题.采用总体之下L2多项式最佳逼近的方法与样本之下矩估计的方法,独立地分别作出非参数部分与变系数参数部分的解析函数形式的估计,最终得到回归函数的L2与强相合之联合收敛意义下的估计. 相似文献
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讨论了拟线性对流占优扩散问题的数值模拟.对对流部分采用特征线格式进行离散,以消除流动锋线前沿的数值弥散现象,保证格式的稳定性;而对扩散部分采用扩展混合有限元方法,同时逼近未知函数,未知函数的梯度及伴随向量函数.理论分析和数值算例表明,此方法是稳定的,具有最优L2逼近精度. 相似文献
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总体服从二项分布B(n,p),p为未知参数,应用麦克劳林公式,得出了只有当f(p)=a1p a2p2 ... anpn时,函数f(p)才存在无偏估计,并给出了无偏估计量. 相似文献
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探讨超收敛猜想中p=4的情形.为此目的我们推导了离散格林函数的权模估计. 相似文献
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增长曲线模型回归系数线性估计的可容许性 总被引:26,自引:1,他引:25
其中 x、ε为 p 阶随机向量,A:p×q,q≤p 及 p×p 阶阵 G>0已知,β∈R~q 及σ~2>0是未知参数;若 Kβ可估(即 K 是满足μ(K)(?)μ(A′)的已知常数阵),C.R.Rao在二次损失函数: 相似文献
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IP Waicheung 《中国科学A辑(英文版)》2006,49(9):1211-1222
In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test. 相似文献
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Testing for additivity with B-splines 总被引:1,自引:0,他引:1
Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance. 相似文献
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Gang Li 《Journal of multivariate analysis》2003,86(1):166-182
Berk and Jones (Z. Wahrsch. Verw. Gebiete 47 (1979) 47) described a nonparametric likelihood test of uniformity that is more efficient, in Bahadur's sense, than any weighted Kolmogorov-Smirnov test at any alternative. This article shows how to obtain a nonparametric likelihood test of a general parametric family for incomplete survival data. A nonparametric likelihood ratio test process is employed to measure the discrepancy between a parametric family and the observed data. Large sample properties of the likelihood ratio test process are studied under both the null and alternative hypotheses. A Monte Carlo simulation method is proposed to estimate its null distribution. We show how to produce a likelihood ratio graphical check as well as a formal test of a parametric family based on the developed theory. Our method is developed for the right-censorship model, but can be easily extended to some other survival models. Illustrations are given using both real and simulated data. 相似文献
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Stephan Derbort Holger Dette Axel Munk 《Annals of the Institute of Statistical Mathematics》2002,54(1):60-82
A simple consistent test of additivity in a multiple nonparametric regression model is proposed, where data are observed on a lattice. The new test is based on an estimator of the L
2-distance between the (unknown) nonparametric regression function and its best approximation by an additive nonparametric regression model. The corresponding test-statistic is the difference of a classical ANOVA style statistic in a two-way layout with one observation per cell and a variance estimator in a homoscedastic nonparametric regression model. Under the null hypothesis of additivity asymptotic normality is established with a limiting variance which involves only the variance of the error of measurements. The results are extended to models with an approximate lattice structure, a heteroscedastic error structure and the finite sample behaviour of the proposed procedure is investigated by means of a simulation study. 相似文献
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Marilena Furno 《Computational Statistics》2010,25(4):707-723
The test of misspecification presented compares parametric and nonparametric regressions. The latter is estimated using order
statistics, which provide robust and distribution free estimators. The former is estimated using, in turn, least squares and
least absolute deviation (LAD). When implementing LAD, robust and distribution free estimators are considered in both parametric
and nonparametric regressions. This defines a very homogeneous test which can discriminate misspecification from the impact
of outliers and/or skewness. These two effects are instead mixed together in the tests comparing OLS with nonparametric estimators,
potentially driving to erroneous conclusions. An example and a Monte Carlo experiment analyze the behavior of the proposed
test. 相似文献
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Eugenia Stoimenova 《Annals of the Institute of Statistical Mathematics》2000,52(2):255-266
Rank tests based on the maximum number of exceeding observations for several standard nonparametric hypotheses are proposed. An approach to constructing nonparametric rank tests via metrics on the permutation group is used. The test statistics are based on a metric induced by Chebyshev's norm. 相似文献
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含估计参数的加权经验过程 总被引:1,自引:0,他引:1
在讨论(广义)非参数似然比拟合优度检验时,加权经验过程理论是一个非常重要的基础.但对含估计参数的加权经验过程理论,目前文献中很少讨论.对含估计参数的加权经验过程的上界型和积分型两种统计量的近似分布进行了讨论,给出了较一般的结果.所得结论叮以为进一步讨论复合零假设下(广义)非参似然比拟合优度检验提供理论基础. 相似文献
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Heteroscedasticity checks for regression models 总被引:1,自引:0,他引:1
For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in
parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the
choice of smoothing parameters which are involved in estimation of the nonparametric regression function. The limiting null
distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional,
the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap
approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap
is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed.
A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the
literature. The approach may readily be extended to handle partial linear, and linear autoregressive models. 相似文献
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广义非参数似然比检验统计量是一类很广的统计量,包含了众多重要的检验统计量,如Anderson-Darling(AD)等.利用Rubin的随机经验分布函数替代经验分布函数的方法,得到了广义非参数似然比检验统计量的新版本,构造了新的检验统计量.由于新的检验统计量在给定样本下仍然是随机变量,选择了它的分位点和期望作为检验统计量,分别称之为分位点型检验统计量和期望型检验统计量.在简单假设情况下,证明了分位点型检验统计量和期望型检验统计量在固定备择下的相合性.模拟结果显示,在某些备择下,新的检验的功效明显高于原有的基于经验分布函数的检验的功效. 相似文献
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LU WenBin 《中国科学A辑(英文版)》2009,(6)
Recurrent event time data are common in biomedical follow-up studies, in which a study subject may experience repeated occurrences of an event of interest. In this paper, we evaluate two popular nonparametric tests for recurrent event time data in terms of their relative effciency. One is the log-rank test for classical survival data and the other a more recently developed nonparametric test based on comparing mean recurrent rates. We show analytically that, somewhat surprisingly, the log-rank test that onl... 相似文献