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991.
In conditional logspline modelling, the logarithm of the conditional density function, log f(y|x), is modelled by using polynomial splines and their tensor products. The parameters of the model (coefficients of the spline functions) are estimated by maximizing the conditional log-likelihood function. The resulting estimate is a density function (positive and integrating to one) and is twice continuously differentiable. The estimate is used further to obtain estimates of regression and quantile functions in a natural way. An automatic procedure for selecting the number of knots and knot locations based on minimizing a variant of the AIC is developed. An example with real data is given. Finally, extensions and further applications of conditional logspline models are discussed. 相似文献
992.
The generalized likelihood plays an important role in parametric inference for prediction and empirical Bayesian models. This paper emphasizes the utility of the generalized likelihood as a summarization procedure in general prediction models. Properties of the generalized likelihood when used in this setting, and examples of its use as a data analytic tool are given in a series of numerical examples. 相似文献
993.
T. J. Sweeting 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1999,61(4):849-861
We obtain approximate Bayes–confidence intervals for a scalar parameter based on directed likelihood. The posterior probabilities of these intervals agree with their unconditional coverage probabilities to fourth order, and with their conditional coverage probabilities to third order. These intervals are constructed for arbitrary smooth prior distributions. A key feature of the construction is that log-likelihood derivatives beyond second order are not required, unlike the asymptotic expansions of Severini. 相似文献
994.
K. V. Mardia & I. L. Dryden 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1999,61(4):913-926
The complex Watson distribution is an important simple distribution on the complex sphere which is used in statistical shape analysis. We describe the density, obtain the integrating constant and provide large sample approximations. Maximum likelihood estimation and hypothesis testing procedures for one and two samples are described. The particular connection with shape analysis is discussed and we consider an application examining shape differences between normal and schizophrenic brains. We make some observations about Bayesian shape inference and finally we describe a more general rotationally symmetric family of distributions. 相似文献
995.
On the use of corrections for overdispersion 总被引:3,自引:0,他引:3
J. K. Lindsey 《Journal of the Royal Statistical Society. Series C, Applied statistics》1999,48(4):553-561
In studying fluctuations in the size of a blackgrouse ( Tetrao tetrix ) population, an autoregressive model using climatic conditions appears to follow the change quite well. However, the deviance of the model is considerably larger than its number of degrees of freedom. A widely used statistical rule of thumb holds that overdispersion is present in such situations, but model selection based on a direct likelihood approach can produce opposing results. Two further examples, of binomial and of Poisson data, have models with deviances that are almost twice the degrees of freedom and yet various overdispersion models do not fit better than the standard model for independent data. This can arise because the rule of thumb only considers a point estimate of dispersion, without regard for any measure of its precision. A reasonable criterion for detecting overdispersion is that the deviance be at least twice the number of degrees of freedom, the familiar Akaike information criterion, but the actual presence of overdispersion should then be checked by some appropriate modelling procedure. 相似文献
996.
The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines 总被引:10,自引:0,他引:10
Arnas P. Verbyla Brian R. Cullis Michael G. Kenward & Sue J. Welham 《Journal of the Royal Statistical Society. Series C, Applied statistics》1999,48(3):269-311
In designed experiments and in particular longitudinal studies, the aim may be to assess the effect of a quantitative variable such as time on treatment effects. Modelling treatment effects can be complex in the presence of other sources of variation. Three examples are presented to illustrate an approach to analysis in such cases. The first example is a longitudinal experiment on the growth of cows under a factorial treatment structure where serial correlation and variance heterogeneity complicate the analysis. The second example involves the calibration of optical density and the concentration of a protein DNase in the presence of sampling variation and variance heterogeneity. The final example is a multienvironment agricultural field experiment in which a yield–seeding rate relationship is required for several varieties of lupins. Spatial variation within environments, heterogeneity between environments and variation between varieties all need to be incorporated in the analysis. In this paper, the cubic smoothing spline is used in conjunction with fixed and random effects, random coefficients and variance modelling to provide simultaneous modelling of trends and covariance structure. The key result that allows coherent and flexible empirical model building in complex situations is the linear mixed model representation of the cubic smoothing spline. An extension is proposed in which trend is partitioned into smooth and non-smooth components. Estimation and inference, the analysis of the three examples and a discussion of extensions and unresolved issues are also presented. 相似文献
997.
We consider the use of Monte Carlo methods to obtain maximum likelihood estimates for random effects models and distinguish between the pointwise and functional approaches. We explore the relationship between the two approaches and compare them with the EM algorithm. The functional approach is more ambitious but the approximation is local in nature which we demonstrate graphically using two simple examples. A remedy is to obtain successively better approximations of the relative likelihood function near the true maximum likelihood estimate. To save computing time, we use only one Newton iteration to approximate the maximiser of each Monte Carlo likelihood and show that this is equivalent to the pointwise approach. The procedure is applied to fit a latent process model to a set of polio incidence data. The paper ends by a comparison between the marginal likelihood and the recently proposed hierarchical likelihood which avoids integration altogether. 相似文献
998.
The kth ( ) power expectile regression (ER) can balance robustness and effectiveness between the ordinary quantile regression and ER simultaneously. Motivated by a longitudinal ACTG 193A data with nonignorable dropouts, we propose a two-stage estimation procedure and statistical inference methods based on the kth power ER and empirical likelihood to accommodate both the within-subject correlations and nonignorable dropouts. Firstly, we construct the bias-corrected generalized estimating equations by combining the kth power ER and inverse probability weighting approaches. Subsequently, the generalized method of moments is utilized to estimate the parameters in the nonignorable dropout propensity based on sufficient instrumental estimating equations. Secondly, in order to incorporate the within-subject correlations under an informative working correlation structure, we borrow the idea of quadratic inference function to obtain the improved empirical likelihood procedures. The asymptotic properties of the corresponding estimators and their confidence regions are derived. The finite-sample performance of the proposed estimators is studied through simulation and an application to the ACTG 193A data is also presented. 相似文献
999.
1000.