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981.
982.
Non-parametric Estimation of the Residual Distribution 总被引:2,自引:0,他引:2
Consider a heteroscedastic regression model Y = m ( X ) +σ( X )ε, where the functions m and σ are "smooth", and ε is independent of X . An estimator of the distribution of ε based on non-parametric regression residuals is proposed and its weak convergence is obtained. Applications to prediction intervals and goodness-of-fit tests are discussed. 相似文献
983.
Nasser Davarzani 《统计学通讯:理论与方法》2013,42(13):2362-2375
In this article, we consider the right random censoring scheme in a discrete setup when the lifetime and censoring variables are independent and have geometric distributions with means 1/θ1 and 1/θ2, respectively. We first obtain the Maximum Likelihood and Method of Moment estimators of the unknown parameters. We also find the Bayes and Posterior Regret Gamma Minimax estimators of the parameters for the two cases when the prior distributions are dependent and independent, assuming a squared error loss function. We then discuss the Proportional Hazard model, and obtain Maximum Likelihood estimators of the unknown parameters and derive the Bayes estimators assuming squared error loss using Markov Chain Monte Carlo methods. 相似文献
984.
In this article, we propose a class of additive transformation models for recurrent event data, which includes the additive rates model as a special case. The new models offer great flexibility in formulating the effects of covariates on the mean function of recurrent events. Estimating equation approaches are developed for the model parameters, and asymptotic properties of the resulting estimators are established. In addition, a model checking procedure is presented to assess the adequacy of the model. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a bladder cancer study is presented. 相似文献
985.
《统计学通讯:理论与方法》2013,42(11):2373-2384
The number of sterile couples in a retrospective study of the number of cycles to conception is necessarily zero; this is not so for a prospective study. The paper puts forward a modification of Weinberg and Gladen's beta geometric model for cycles to conception that is suitable for both types of investigation. The probability that a couple achieves conception at the xth cycle, but not earlier, is assumed to take the form Rx = (1 ? ρ)/(1 ? m x?1 ρ/u), instead of μ/(1 ? θ + θx). The set of parameter restraints (0 < m < 1, 0< ρ < 1, 1 < u) is appropriate for retrospective data, whilst the alternative set of restraints (1 < m, 1 < ρ, 0 < u < 1) is appropriate for prospective data. The decrease in Rx over time can be interpreted not only as a time effect, but also as a heterogeneity effect by replacing Weinberg and Gladen's beta mixture of geometric distributions by a q-beta mixture. 相似文献
986.
Ordinal regression is used for modelling an ordinal response variable as a function of some explanatory variables. The classical technique for estimating the unknown parameters of this model is Maximum Likelihood (ML). The lack of robustness of this estimator is formally shown by deriving its breakdown point and its influence function. To robustify the procedure, a weighting step is added to the Maximum Likelihood estimator, yielding an estimator with bounded influence function. We also show that the loss in efficiency due to the weighting step remains limited. A diagnostic plot based on the Weighted Maximum Likelihood estimator allows to detect outliers of different types in a single plot. 相似文献
987.
B. Lecoutre 《统计学通讯:理论与方法》2013,42(10):2437-2446
The usual F-test of the analysis of variance is reconsidered within the Bayesian framework, In terms of predictive distributions, This leads to the notion of semi-Bayesian significance test, so called because it consists in only probabilizing the space of nuisance parameters, thus bringing a general principle for “eliminating” nuisance parameters, or more exactly incorporating information about these parameters. The approach is shown to extend the F-tests, by allowing the testing of hypotheses of non-zero effects. 相似文献
988.
A unified approach is developed for testing hypotheses in the general linear model based on the ranks of the residuals. It complements the nonparametric estimation procedures recently reported in the literature. The testing and estimation procedures together provide a robust alternative to least squares. The methods are similar in spirit to least squares so that results are simple to interpret. Hypotheses concerning a subset of specified parameters can be tested, while the remaining parameters are treated as nuisance parameters. Asymptotically, the test statistic is shown to have a chi-square distribution under the null hypothesis. This result is then extended to cover a sequence of contiguous alternatives from which the Pitman efficacy is derived. The general application of the test requires the consistent estimation of a functional of the underlying distribution and one such estimate is furnished. 相似文献
989.
Chang-Ha Hwang 《统计学通讯:理论与方法》2013,42(8):2197-2215
In discriminant analysis, the dimension of the hyperplane which population mean vectors span is called the dimensionality. The procedures commonly used to estimate this dimension involve testing a sequence of dimensionality hypotheses as well as model fitting approaches based on (consistent) Akaike's method, (modified) Mallows' method and Schwarz's method. The marginal log-likelihood (MLL) method is developed and the asymptotic distribution of the dimensionality estimated by this method for normal populations is derived. Furthermore a modified marginal log-likelihood (MMLL) method is also considered. The MLL method is not consistent for large samples and two modified criteria are proposed which attain asymptotic consistency. Some comments are made with regard to the robustness of this method to departures from normality. The operating characteristics of the various methods proposed are examined and compared. 相似文献
990.
This article studies robustification strategies for the linear model in the presence of outliers. The advantages of an internal analysis of the robustness of least squares for a given sample are pointed out. The application of this methodology is illustrated by building an explicit model of the determinants of rental housing values in the Madrid Metropolitan Area. 相似文献