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61.
62.
John E. Kolassa 《Scandinavian Journal of Statistics》1997,24(4):523-530
This paper discusses recovery of information regarding logistic regression parameters in cases when maximum likelihood estimates of some parameters are infinite. An algorithm for detecting such cases and characterizing the divergence of the parameter estimates is presented. A method for fitting the remaining parameters is also presented . All of these methods rely only on sufficient statistics rather than less aggregated quantities, as required for inference according to the method of Kolassa & Tanner (1994). These results are applied to approximate conditional inference via saddlepoint methods. Specifically, the double saddlepoint method of Skovgaard (1987) is adapted to the case when the solution to the saddlepoint equations exists as a point at infinity 相似文献
63.
S. T. Boris Choy & Adrian F. M. Smith 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1997,59(2):463-474
Pericchi and Smith considered a normal location parameter problem with double-exponential and Student t prior distributions. These two prior distributions both belong to the class of scale mixtures of normal distributions and are useful in providing a robust analysis of the normal location parameter problem. In this paper we extend the analysis to other scale mixtures of normal distributions, such as the exponential power and the symmetric stable distributions. 相似文献
64.
We propose a new stochastic approximation (SA) algorithm for maximum-likelihood estimation (MLE) in the incomplete-data setting. This algorithm is most useful for problems when the EM algorithm is not possible due to an intractable E-step or M-step. Compared to other algorithm that have been proposed for intractable EM problems, such as the MCEM algorithm of Wei and Tanner (1990), our proposed algorithm appears more generally applicable and efficient. The approach we adopt is inspired by the Robbins-Monro (1951) stochastic approximation procedure, and we show that the proposed algorithm can be used to solve some of the long-standing problems in computing an MLE with incomplete data. We prove that in general O(n) simulation steps are required in computing the MLE with the SA algorithm and O(n log n) simulation steps are required in computing the MLE using the MCEM and/or the MCNR algorithm, where n is the sample size of the observations. Examples include computing the MLE in the nonlinear error-in-variable model and nonlinear regression model with random effects. 相似文献
65.
介绍了夸克胶子等离子体(QGP)的动力论基础,讨论了在半经典近似下的QGP输运方程的阿贝尔优势近似和线性近似,指出了超越阿贝尔优势和线性近似的可能途径 相似文献
66.
The paper gives the saddlepoint approximation for the distribution function of the sample quantile. A comparison of the saddlepoint approximations for the distribution functions of the sample quantile and the bootstrap quantile shows that the error of the bootstrap approximation to the distribution of the sample quantile obtained by Singh (1981) as an absolute error is actually a relative error. 相似文献
67.
A tutorial on adaptive MCMC 总被引:1,自引:0,他引:1
We review adaptive Markov chain Monte Carlo algorithms (MCMC) as a mean to optimise their performance. Using simple toy examples
we review their theoretical underpinnings, and in particular show why adaptive MCMC algorithms might fail when some fundamental
properties are not satisfied. This leads to guidelines concerning the design of correct algorithms. We then review criteria
and the useful framework of stochastic approximation, which allows one to systematically optimise generally used criteria,
but also analyse the properties of adaptive MCMC algorithms. We then propose a series of novel adaptive algorithms which prove
to be robust and reliable in practice. These algorithms are applied to artificial and high dimensional scenarios, but also
to the classic mine disaster dataset inference problem. 相似文献
68.
Given observations on an m × n lattice, approximate maximum likelihood estimates are derived for a family of models including direct covariance, spatial moving average, conditional autoregressive and simultaneous autoregressive models. The approach involves expressing the (approximate) covariance matrix of the observed variables in terms of a linear combination of neighbour relationship matrices, raised to a power. The structure is such that the eigenvectors of the covariance matrix are independent of the parameters of interest. This result leads to a simple Fisher scoring type algorithm for estimating the parameters. The ideas are illustrated by fitting models to some remotely sensed data. 相似文献
69.
Wagner Hugo Bonat Paulo Justiniano Ribeiro Jr Walmes Marques Zeviani 《Journal of applied statistics》2015,42(2):252-266
Beta regression is a suitable choice for modelling continuous response variables taking values on the unit interval. Data structures such as hierarchical, repeated measures and longitudinal typically induce extra variability and/or dependence and can be accounted for by the inclusion of random effects. In this sense, Statistical inference typically requires numerical methods, possibly combined with sampling algorithms. A class of Beta mixed models is adopted for the analysis of two real problems with grouped data structures. We focus on likelihood inference and describe the implemented algorithms. The first is a study on the life quality index of industry workers with data collected according to an hierarchical sampling scheme. The second is a study assessing the impact of hydroelectric power plants upon measures of water quality indexes up, downstream and at the reservoirs of the dammed rivers, with a nested and longitudinal data structure. Results from different algorithms are reported for comparison including from data-cloning, an alternative to numerical approximations which also allows assessing identifiability. Confidence intervals based on profiled likelihoods are compared with those obtained by asymptotic quadratic approximations, showing relevant differences for parameters related to the random effects. In both cases, the scientific hypothesis of interest was investigated by comparing alternative models, leading to relevant interpretations of the results within each context. 相似文献
70.
Bernstein polynomials have many interesting properties. In statistics, they were mainly used to estimate density functions and regression relationships. The main objective of this paper is to promote further use of Bernstein polynomials in statistics. This includes (1) providing a high-level approximation of the moments of a continuous function of a random variable , and (2) proving Jensen’s inequality concerning a convex function without requiring second differentiability of the function. The approximation in (1) is demonstrated to be quite superior to the delta method, which is used to approximate the variance of with the added assumption of differentiability of the function. Two numerical examples are given to illustrate the application of the proposed methodology in (1). 相似文献