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151.
Yanjiao Meng 《统计学通讯:理论与方法》2019,48(9):2206-2217
For negatively associated (NA) random variables, we obtain two general strong laws of large numbers (SLLN) in which the coefficient of sum and the weight are both general functions. As corollaries, we obtain Marcinkiewicz-type SLLN, the logarithmic SLLN and Marcinkiewicz SLLN for NA random variables. 相似文献
152.
We provide a comprehensive and critical review of Yates’ continuity correction for the normal approximation to the binomial distribution, in particular emphasizing its poor ability to approximate extreme tail probabilities. As an alternative method, we also review Cressie's finely tuned continuity correction. In addition, we demonstrate how Yates’ continuity correction is used to improve the coverage probability of binomial confidence limits, and propose new confidence limits by applying Cressie's continuity correction. These continuity correction methods are numerically compared and illustrated by data examples arising from industry and medicine. 相似文献
153.
The Craig-Sakamoto theorem establishes a sufficient and necessary condition for the independence of two quadratic forms in normal variates, fascinating many statisticians and mathematicians, who continuously seek for simple and better proofs of the theorem and its extensions. In this article, we present a simple proof of a unified theorem on the independence of linear and quadratic functions in general normal variates. 相似文献
154.
In this article, we develop a new Rosenthal Inequality for uniform random permutation sums of random variables with finite third moments and apply it to obtain a sharp non-uniform bound for the combinatorial central limit theorem using the Stein's method and the exchangeable pair techniques. The obtained bound is shown to be sharper than other existing bounds. 相似文献
155.
《统计学通讯:理论与方法》2012,41(13-14):2570-2587
In a Gauss–Markov Model (GMM) with fixed constraints, all the relevant estimators perfectly satisfy these constraints. As soon as they become stochastic, most estimators are allowed to satisfy them only approximately, thereby leaving room for nonvanishing residuals to describe the deviation from the prior information. Sometimes, however, linear estimators may be preferred that are able to perfectly reproduce the prior information in form of stochastic constraints, including their variances and covariances. As typical example may be considered the case where a geodetic network ought to be densified without changing the higher-order point coordinates that are usually introduced together with their variances and (some) covariances. Traditional estimators are based on the “Helmert” or “S-transformation,” respectively an adaptation of the fixed-constraints Least-Squares estimator. Here we show that neither approach generates the optimal reproducing estimator, which will be presented in detail and compared with the other reproducing estimators in terms of their MSE-risks. 相似文献
156.
Abstract. Functional measures of skewness and kurtosis, called asymmetry and gradient asymmetry functions, are described for continuous univariate unimodal distributions. They are defined and interpreted directly in terms of the density function and its derivative. Asymmetry is defined by comparing distances from points of equal density to the mode. Gradient asymmetry is defined, in novel fashion, as asymmetry of an appropriate function of the density derivative. Properties and illustrations of asymmetry and gradient asymmetry functions are presented. Estimation of them is considered and illustrated with an example. Scalar summary skewness and kurtosis measures associated with asymmetry and gradient asymmetry functions are discussed. 相似文献
157.
158.
159.
This paper extends the concept of risk unbiasedness for applying to statistical prediction and nonstandard inference problems, by formalizing the idea that a risk unbiased predictor should be at least as close to the “true” predictant as to any “wrong” predictant, on the average. A novel aspect of our approach is measuring closeness between a predicted value and the predictant by a regret function, derived suitably from the given loss function. The general concept is more relevant than mean unbiasedness, especially for asymmetric loss functions. For squared error loss, we present a method for deriving best (minimum risk) risk unbiased predictors when the regression function is linear in a function of the parameters. We derive a Rao–Blackwell type result for a class of loss functions that includes squared error and LINEX losses as special cases. For location-scale families, we prove that if a unique best risk unbiased predictor exists, then it is equivariant. The concepts and results are illustrated with several examples. One interesting finding is that in some problems a best unbiased predictor does not exist, but a best risk unbiased predictor can be obtained. Thus, risk unbiasedness can be a useful tool for selecting a predictor. 相似文献
160.
Monica K. Hurdal Juan B. Gutierrez Christian Laing Deborah A. Smith 《Journal of Combinatorial Optimization》2008,15(3):257-275
We describe geometric invariants that characterize the shape of curves and surfaces in 3D space: curvature, Gauss integrals
and moments. We apply these invariants to neuroimaging data to determine if they have application for automatically classifying
and parcellating cortical data. The curves of sulci and gyri on the cortical surface can be obtained by reconstructing cortical
surface representations of the human brain from magnetic resonance imaging (MRI) data. We reconstructed gray matter surfaces
for 15 subjects, traced 10 sulcal curves on each surface and computed geometric invariants for each curve. These geometric
features were used classify the curves into sulcal and hemispheric classes. The best classification results were obtained
when moment-based features were computed on the sulcal curves in native space. Gauss integral measures showed that they were
useful for differentiating the hemispheric location of a single sulcus. These promising results may indicate that moment invariants
are useful for characterizing shape on a global scale. Gauss integral invariants are potentially useful measures for characterizing
cortical shape on a local, rather than global scale. Gauss integrals have found biological significance in characterizing
proteins so it is worthwhile to consider their possible application to neuroscientific data. 相似文献