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711.
It is known that linear regression models have immense applications in various areas such as engineering technology, economics and social sciences. In this paper, we investigate the asymptotic properties of M-estimator in multivariate linear regression model based on a class of random errors satisfying a generalised Bernstein-type inequality. By using the generalised Bernstein-type inequality, we obtain a general result on almost sure convergence for a class of random variables and then obtain the strong consistency for the M-estimator in multivariate linear regression models under some mild conditions. The result extends or improves some existing ones in the literature. Moreover, we also consider the case when the dimension $p$ tends to infinity by establishing the rate of almost sure convergence for a class of random variables satisfying generalised Bernstein-type inequality. Some numerical simulations are also provided to verify the validity of the theoretical results. 相似文献
712.
Continuous-time autoregressive processes have been applied successfully in many fields and are particularly advantageous in the modeling of irregularly spaced or high-frequency time series data. A convenient nonlinear extension of this model are continuous-time threshold autoregressions (CTAR). CTAR allow for greater flexibility in model parameters and can represent a regime switching behavior. However, so far only Gaussian CTAR processes have been defined, so that this model class could not be used for data with jumps, as frequently observed in financial applications. Hence, as a novelty, we construct CTAR processes with jumps in this paper. Existence of a unique weak solution and weak consistency of an Euler approximation scheme is proven. As a closed form expression of the likelihood is not available, we use kernel-based particle filtering for estimation. We fit our model to the Physical Electricity Index and show that it describes the data better than other comparable approaches. 相似文献
713.
Herv Moulin 《Econometrica : journal of the Econometric Society》2000,68(3):643-684
In a rationing problem, each agent demands a quantity of a certain commodity and the available resources fall short of total demand. A rationing method solves this problem at every level of resources and individual demands. We impose three axioms: Consistency—with respect to variations of the set of agents—Upper Composition and Lower Composition—with respect to variations of the available resources. In the model where the commodity comes in indivisible units, the three axioms characterize the family of priority rules, where individual demands are met lexicographically according to an exogeneous ordering of the agents. In the (more familiar) model where the commodity is divisible, these three axioms plus Scale Invariance—independence of the measurement unit—characterize a rich family of methods. It contains exactly three symmetric methods, giving equal shares to equal demands: these are the familiar proportional, uniform gains, and uniform losses methods. The asymmetric methods in the family partition the agents into priority classes; within each class, they use either the proportional method or a weighted version of the uniform gains or uniform losses methods. 相似文献
714.
Tanujit Chakraborty Gauri Kamat Ashis Kumar Chakraborty 《Australian & New Zealand Journal of Statistics》2023,65(2):101-126
Frequentist and Bayesian methods differ in many aspects but share some basic optimal properties. In real-life prediction problems, situations exist in which a model based on one of the above paradigms is preferable depending on some subjective criteria. Nonparametric classification and regression techniques, such as decision trees and neural networks, have both frequentist (classification and regression trees (CARTs) and artificial neural networks) as well as Bayesian counterparts (Bayesian CART and Bayesian neural networks) to learning from data. In this paper, we present two hybrid models combining the Bayesian and frequentist versions of CART and neural networks, which we call the Bayesian neural tree (BNT) models. BNT models can simultaneously perform feature selection and prediction, are highly flexible, and generalise well in settings with limited training observations. We study the statistical consistency of the proposed approaches and derive the optimal value of a vital model parameter. The excellent performance of the newly proposed BNT models is shown using simulation studies. We also provide some illustrative examples using a wide variety of standard regression datasets from a public available machine learning repository to show the superiority of the proposed models in comparison to popularly used Bayesian CART and Bayesian neural network models. 相似文献
715.
Grit is a non-cognitive construct based on personality theory that fosters individuals to perform better and achieve their goals. Previous researchers validated the psychometric properties of grit for adults and older adolescents but ignored that for early adolescents. An inappropriate measurement model may mislead researchers and teachers to misapprehend grit measures. This study aimed to identify the most appropriate grit model for early adolescents. Three factorial models (i.e., two-factor, one-factor, and bi-factor models) were evaluated and compared. Subsequently, we tested the measurement invariance (MI) and mean differences of grit across grade and gender groups. Participants were 672 junior high students (51% boys, aged 12–15) in Taiwan. The results showed that the two-factor model was the best grit model. This finding revealed that adolescents tend to comprehend grit with two distinct concepts, consistency in interest (CI) and perseverance of effort (PE), instead of a single compound. In addition, the results showed that the two-factor model retained strong invariance for grade and gender, justifying the comparison of grit scores over grade and gender groups for junior high students. Moreover, we did not find any group difference in the facets of grit by gender and grades. This result showed that grit is a stable personality for junior high students. The relationships between grit constructs and criteria, such as conscientiousness and academic achievements, were tested and discussed. 相似文献