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Dominique Fourdrinier William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2003,55(4):803-816
We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In
3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988,
On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual
estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized
Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly,
that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax
estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes
estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator
of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss.
Research supported by NSF Grant DMS-97-04524. 相似文献
3.
Marianna Pensky 《Annals of the Institute of Statistical Mathematics》2002,54(1):83-99
The traditional empirical Bayes (EB) model is considered with the parameter being a location parameter, in the situation when the Bayes estimator has a finite degree of smoothness and, possibly, jump discontinuities at several points. A nonlinear wavelet EB estimator based on wavelets with bounded supports is constructed, and it is shown that a finite number of jump discontinuities in the Bayes estimator do not affect the rate of convergence of the prior risk of the EB estimator to zero. It is also demonstrated that the estimator adjusts to the degree of smoothness of the Bayes estimator, locally, so that outside the neighborhoods of the points of discontinuities, the posterior risk has a high rate of convergence to zero. Hence, the technique suggested in the paper provides estimators which are significantly superior in several respects to those constructed earlier. 相似文献
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运用一种新的动力学突变检测方法——排列熵(permutation entropy,PE)算法,计算并分析了中国华北地区52个站点1960年—2000年逐日平均气温资料的排列熵演化情况,发现中国华北地区气温在20世纪70年代中期、80年代初均发生了较大突变;进一步用经验模态分解(empirical mode decomposition,EMD)方法对排列熵序列进行逐级平稳化处理,结果发现这一地区的气温突变与准10年这一年代际时间尺度的周期变率密切相关,其原因与太阳黑子活动有着密切联系.
关键词:
华北
突变
排列熵算法
经验模态分解 相似文献
8.
对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差.最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计. 相似文献
9.
Automatic detection and identification of shocks in Gaussian state‐space models: a Bayesian approach
An automatic monitoring and intervention algorithm that permits the supervision of very general aspects in an univariate linear Gaussian state–space model is proposed. The algorithm makes use of a model comparison and selection approach within a Bayesian framework. In addition, this algorithm incorporates the possibility of eliminating earlier interventions when subsequent evidence against them comes to light. Finally, the procedure is illustrated with two empirical examples taken from the literature. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
10.
This paper introduces a profile empirical likelihood and a profile conditionally empirical likelihood to estimate the parameter
of interest in the presence of nuisance parameters respectively for the parametric and semiparametric models. It is proven
that these methods propose some efficient estimators of parameters of interest in the sense of least-favorable efficiency.
Particularly, for the decomposable semiparametric models, an explicit representation for the estimator of parameter of interest
is derived from the proposed nonparametric method. These new estimations are different from and more efficient than the existing
estimations. Some examples and simulation studies are given to illustrate the theoretical results.
The first author is supported by NNSF projects (10371059 and 10171051) of China. The second author is supported by a grant
from The Research Grants Council of the Hong Kong Special Administrative Region, China (#HKU7060/04P). The third author is
supported by the University Research Committee of the University of Hong Kong and a grant from the Research Grants Council
of the Hong Kong Special Administrative Region, China (Project No. HKU7323/01M). 相似文献