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2.
Tim Futing Liao 《Journal of the Royal Statistical Society. Series A, (Statistics in Society)》2004,167(1):125-139
Summary. Social data often contain missing information. The problem is inevitably severe when analysing historical data. Conventionally, researchers analyse complete records only. Listwise deletion not only reduces the effective sample size but also may result in biased estimation, depending on the missingness mechanism. We analyse household types by using population registers from ancient China (618–907 AD) by comparing a simple classification, a latent class model of the complete data and a latent class model of the complete and partially missing data assuming four types of ignorable and non-ignorable missingness mechanisms. The findings show that either a frequency classification or a latent class analysis using the complete records only yielded biased estimates and incorrect conclusions in the presence of partially missing data of a non-ignorable mechanism. Although simply assuming ignorable or non-ignorable missing data produced consistently similarly higher estimates of the proportion of complex households, a specification of the relationship between the latent variable and the degree of missingness by a row effect uniform association model helped to capture the missingness mechanism better and improved the model fit. 相似文献
3.
The HastingsMetropolis algorithm is a general MCMC method for sampling from a density known up to a constant. Geometric convergence of this algorithm has been proved under conditions relative to the instrumental (or proposal) distribution. We present an inhomogeneous HastingsMetropolis algorithm for which the proposal density approximates the target density, as the number of iterations increases. The proposal density at the n th step is a non-parametric estimate of the density of the algorithm, and uses an increasing number of i.i.d. copies of the Markov chain. The resulting algorithm converges (in n ) geometrically faster than a HastingsMetropolis algorithm with any fixed proposal distribution. The case of a strictly positive density with compact support is presented first, then an extension to more general densities is given. We conclude by proposing a practical way of implementation for the algorithm, and illustrate it over simulated examples. 相似文献
4.
It is often of interest to find the maximum or near maxima among a set of vector‐valued parameters in a statistical model; in the case of disease mapping, for example, these correspond to relative‐risk “hotspots” where public‐health intervention may be needed. The general problem is one of estimating nonlinear functions of the ensemble of relative risks, but biased estimates result if posterior means are simply substituted into these nonlinear functions. The authors obtain better estimates of extrema from a new, weighted ranks squared error loss function. The derivation of these Bayes estimators assumes a hidden‐Markov random‐field model for relative risks, and their behaviour is illustrated with real and simulated data. 相似文献
5.
A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed. 相似文献
6.
In this paper, a new multivariate zero-inflated binomial (MZIB) distribution is proposed to analyse the correlated proportional data with excessive zeros. The distributional properties of purposed model are studied. The Fisher scoring algorithm and EM algorithm are given for the computation of estimates of parameters in the proposed MZIB model with/without covariates. The score tests and the likelihood ratio tests are derived for assessing both the zero-inflation and the equality of multiple binomial probabilities in correlated proportional data. A limited simulation study is performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates and to compare the nominal levels and powers of both score tests and likelihood ratio tests. The whitefly data is used to illustrate the proposed methodologies. 相似文献
7.
A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: easy Bayesian computing for real parameter spaces 总被引:2,自引:0,他引:2
Cajo J. F. Ter Braak 《Statistics and Computing》2006,16(3):239-249
Differential Evolution (DE) is a simple genetic algorithm for numerical optimization in real parameter spaces. In a statistical
context one would not just want the optimum but also its uncertainty. The uncertainty distribution can be obtained by a Bayesian
analysis (after specifying prior and likelihood) using Markov Chain Monte Carlo (MCMC) simulation. This paper integrates the
essential ideas of DE and MCMC, resulting in Differential Evolution Markov Chain (DE-MC). DE-MC is a population MCMC algorithm,
in which multiple chains are run in parallel. DE-MC solves an important problem in MCMC, namely that of choosing an appropriate
scale and orientation for the jumping distribution. In DE-MC the jumps are simply a fixed multiple of the differences of two
random parameter vectors that are currently in the population. The selection process of DE-MC works via the usual Metropolis
ratio which defines the probability with which a proposal is accepted. In tests with known uncertainty distributions, the
efficiency of DE-MC with respect to random walk Metropolis with optimal multivariate Normal jumps ranged from 68% for small
population sizes to 100% for large population sizes and even to 500% for the 97.5% point of a variable from a 50-dimensional
Student distribution. Two Bayesian examples illustrate the potential of DE-MC in practice. DE-MC is shown to facilitate multidimensional
updates in a multi-chain “Metropolis-within-Gibbs” sampling approach. The advantage of DE-MC over conventional MCMC are simplicity,
speed of calculation and convergence, even for nearly collinear parameters and multimodal densities. 相似文献
8.
WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES 总被引:2,自引:0,他引:2
In this paper, we establish strong laws for weighted sums of negatively associated (NA) random variables which have a higher‐order moment condition. Some results of Bai Z.D. & Cheng P.E. (2000) [Marcinkiewicz strong laws for linear statistics. Statist. and Probab. Lett. 43, 105–112,] and Sung S.K. (2001) [Strong laws for weighted sums of i.i.d. random variables, Statist. and Probab. Lett. 52, 413–419] are sharpened and extended from the independent identically distributed case to the NA setting. Also, one of the results of Li D.L. et al. (1995) [Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab. 8, 49–76,] is complemented and extended. 相似文献
9.
Manufacturers want to assess the quality andreliability of their products. Specifically, they want to knowthe exact number of failures from the sales transacted duringa particular month. Information available today is sometimesincomplete as many companies analyze their failure data simplycomparing sales for a total month from a particular departmentwith the total number of claims registered for that given month.This information—called marginal count data—is, thus,incomplete as it does not give the exact number of failures ofthe specific products that were sold in a particular month. Inthis paper we discuss nonparametric estimation of the mean numbersof failures for repairable products and the failure probabilitiesfor nonrepairable products. We present a nonhomogeneous Poissonprocess model for repairable products and a multinomial modeland its Poisson approximation for nonrepairable products. A numericalexample is given and a simulation is carried out to evaluatethe proposed methods of estimating failure probabilities undera number of possible situations. 相似文献
10.
Hoben Thomas & Thomas P. Hettmansperger 《Journal of the Royal Statistical Society. Series C, Applied statistics》2001,50(4):435-448
Psychological theories often posit the existence of several different states. Individuals are viewed as belonging to one of the states at a given age, but with development pass to another state. A main problem in evaluating such theories is representing the transition from one state to another over age. A stochastic transition framework is proposed which should be useful in many different settings. The model is illustrated with data from a cognitive development task. 相似文献