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91.
《Journal of Statistical Computation and Simulation》2012,82(7):507-523
This paper is concerned with properties (bias, standard deviation, mean square error and efficiency) of twenty six estimators of the intraclass correlation in the analysis of binary data. Our main interest is to study these properties when data are generated from different distributions. For data generation we considered three over-dispersed binomial distributions, namely, the beta-binomial distribution, the probit normal binomial distribution and a mixture of two binomial distributions. The findings regarding bias, standard deviation and mean squared error of all these estimators, are that (a) in general, the distributions of biases of most of the estimators are negatively skewed. The biases are smallest when data are generated from the beta-binomial distribution and largest when data are generated from the mixture distribution; (b) the standard deviations are smallest when data are generated from the beta-binomial distribution; and (c) the mean squared errors are smallest when data are generated from the beta-binomial distribution and largest when data are generated from the mixture distribution. Of the 26, nine estimators including the maximum likelihood estimator, an estimator based on the optimal quadratic estimating equations of Crowder (1987), and an analysis of variance type estimator is found to have least amount of bias, standard deviation and mean squared error. Also, the distributions of the bias, standard deviation and mean squared error for each of these estimators are, in general, more symmetric than those of the other estimators. Our findings regarding efficiency are that the estimator based on the optimal quadratic estimating equations has consistently high efficiency and least variability in the efficiency results. In the important range in which the intraclass correlation is small (≤0 5), on the average, this estimator shows best efficiency performance. The analysis of variance type estimator seems to do well for larger values of the intraclass correlation. In general, the estimator based on the optimal quadratic estimating equations seems to show best efficiency performance for data from the beta-binomial distribution and the probit normal binomial distribution, and the analysis of variance type estimator seems to do well for data from the mixture distribution. 相似文献
92.
A simple transformation of classical binomial confidence limits provides exact confidence limits in situations where a confounding variable is present. An example is the multiple-choice test, where a correct answer may represent either knowledge or guesswork, the latter being the confounding variable. 相似文献
93.
Recently in Dutt (1973, (1975), intgral representations over (0,A) were obtained for upper and lover multivariate normal and the probilities. It was pointed out that these integral representaitons when evaluated by Gauss-Hermite uadrature yield rapid and accurate numerical results. Here integral representaitons, based on an integral formula due to Gurland (1948), are indicated for arbitrary multivariate probabilities. Application of this general representaion for computing multivariate x2 probabilities is discussed and numerical results using Gaussian quadrature are given for the bivariate and equicorre lated trivariate cases. Applications to the multivariate densities studied by Miller (1965) are also included 相似文献
94.
This article discusses a representation of Pearson's chi-square for independence in two-way contingency tables in terms of conditional probabilities of two categorical random variables and proposes a functional interpretation of Pearson's chi-square. This representation is suggested for use in the teaching of statistical independence between categorical variables. 相似文献
95.
《Journal of Statistical Computation and Simulation》2012,82(1-2):133-136
Estimation in logistic-normal models for correlated and overdispersed binomial data is complicated by the numerical evaluation of often intractable likelihood functions. Penalized quasilikelihood (PQL) estimators of fixed effects and variance components are known to be seriously biased for binary data. A simple correction procedure has been proposed to improve the performance of the PQL estimators. The proposed method is illustrated by analyzing infectious disease data. Its performance is compared, by means of simulations, with that of the Bayes approach using the Gibbs sampler. 相似文献
96.
D. B. Owen 《统计学通讯:模拟与计算》2013,42(4):389-419
Integrals of functions of the univariate, bivariate, trivariate and multivariate normal densities are given. Both indefinite and definite integrals are included. 相似文献
97.
T. P. Hettmansperger & Hoben Thomas 《Journal of the Royal Statistical Society. Series B, Statistical methodology》2000,62(4):811-825
We consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions. We require a vector of observations on each subject. This vector is mapped into a vector of 0s and 1s and summed. The resulting distribution of sums can be modelled as a mixture of binomials. We then work with the binomial mixture. The efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when, typically, the true underlying mixture distribution is different. It is shown that in many cases the approach based on simple binomial mixtures is superior. 相似文献
98.
Tomoaki Nishimura 《统计学通讯:理论与方法》2013,42(12):1867-1879
The generalized empirical likelihood (GEL) method produces a class of estimators of parameters defined via general estimating equations. This class includes several important estimators, such as empirical likelihood (EL), exponential tilting (ET), and continuous updating estimators (CUE). We examine the information geometric structure of GEL estimators. We introduce a class of estimators closely related to the class of minimum divergence (MD) estimators and show that there is a one-to-one correspondence between this class and the class GEL. 相似文献
99.
Piero Demetrio Falorsi Giorgio Alleva Fabio Bacchini Roberto Iannaccone 《Statistical Methods and Applications》2005,14(1):83-99
Various approaches to obtaining estimates based on preliminary data are outlined. A case is then considered which frequently
arises when selecting a subsample of units, the information for which is collected within a deadline that allows preliminary
estimates to be produced. At the moment when these estimates have to be produced it often occurs that, although the collection
of data on subsample units is still not complete, information is available on a set of units which does not belong to the
sample selected for the production of the preliminary estimates. An estimation method is proposed which allows all the data
available on a given date to be used to the full-and the expression of the expectation and variance are derived. The proposal
is based on two-phase sampling theory and on the hypothesis that the response mechanism is the result of random processes
whose parameters can be suitably estimated. An empirical analysis of the performance of the estimator on the Italian Survey
on building permits concludes the work.
The Sects. 1,2,3,4 and the technical appendixes have been developed by Giorgio Alleva and Piero Demetrio Falorsi; Sect. 5
has been done by Fabio Bacchini and Roberto Iannaccone.
Piero Demetrio Falorsi is chief statisticians at Italian National Institute of Statistics (ISTAT); Giorgio Alleva is Professor
of Statistics at University “La Sapienza” of Rome, Fabio Bacchini and Roberto Iannaccone are researchers at ISTAT. 相似文献
100.
The generalized regression (GREG) predictor is used for estimating a finite population total when the study variable is well‐related to the auxiliary variable. In 1997, Chaudhuri & Roy provided an optimal estimator for the variance of the GREG predictor within a class of non‐homogeneous quadratic estimators (H) under a certain superpopulation model M. They also found an inequality concerning the expected variances of the estimators of the variance of the GREG predictor belonging to the class H under the model M. This paper shows that the derivation of the optimal estimator and relevant inequality, presented by Chaudhuri & Roy, are incorrect. 相似文献