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91.
92.
M-quantile models with application to poverty mapping 总被引:1,自引:0,他引:1
Nikos Tzavidis Nicola Salvati Monica Pratesi Ray Chambers 《Statistical Methods and Applications》2008,17(3):393-411
Over the last decade there has been growing demand for estimates of population characteristics at small area level. Unfortunately,
cost constraints in the design of sample surveys lead to small sample sizes within these areas and as a result direct estimation,
using only the survey data, is inappropriate since it yields estimates with unacceptable levels of precision. Small area models
are designed to tackle the small sample size problem. The most popular class of models for small area estimation is random
effects models that include random area effects to account for between area variations. However, such models also depend on
strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow
for outlier robust inference. An alternative approach to small area estimation that is based on the use of M-quantile models
was recently proposed by Chambers and Tzavidis (Biometrika 93(2):255–268, 2006) and Tzavidis and Chambers (Robust prediction
of small area means and distributions. Working paper, 2007). Unlike traditional random effects models, M-quantile models do
not depend on strong distributional assumption and automatically provide outlier robust inference. In this paper we illustrate
for the first time how M-quantile models can be practically employed for deriving small area estimates of poverty and inequality.
The methodology we propose improves the traditional poverty mapping methods in the following ways: (a) it enables the estimation
of the distribution function of the study variable within the small area of interest both under an M-quantile and a random
effects model, (b) it provides analytical, instead of empirical, estimation of the mean squared error of the M-quantile small
area mean estimates and (c) it employs a robust to outliers estimation method. The methodology is applied to data from the
2002 Living Standards Measurement Survey (LSMS) in Albania for estimating (a) district level estimates of the incidence of
poverty in Albania, (b) district level inequality measures and (c) the distribution function of household per-capita consumption
expenditure in each district. Small area estimates of poverty and inequality show that the poorest Albanian districts are
in the mountainous regions (north and north east) with the wealthiest districts, which are also linked with high levels of
inequality, in the coastal (south west) and southern part of country. We discuss the practical advantages of our methodology
and note the consistency of our results with results from previous studies. We further demonstrate the usefulness of the M-quantile
estimation framework through design-based simulations based on two realistic survey data sets containing small area information
and show that the M-quantile approach may be preferable when the aim is to estimate the small area distribution function. 相似文献
93.
We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have Dirichlet priors. We study a training set consisting of thousands of protein alignment pairs. The training data is used to set the prior hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is not applicable any more, there is no simple procedure to find the MAP path, and several iterative algorithms are considered and compared. The main goal of the paper is to test the Bayesian setup against the frequentist one, where the parameters of HMM are estimated using the training data. 相似文献
94.
Searches for faint signals in counting experiments are often encountered in particle physics and astrophysics, as well as in other fields. Many problems can be reduced to the case of a model with independent and Poisson-distributed signal and background. Often several background contributions are present at the same time, possibly correlated. We provide the analytic solution of the statistical inference problem of estimating the signal in the presence of multiple backgrounds, in the framework of objective Bayes statistics. The model can be written in the form of a product of a single Poisson distribution with a multinomial distribution. The first is related to the total number of events, whereas the latter describes the fraction of events coming from each individual source. Correlations among different backgrounds can be included in the inference problem by a suitable choice of the priors. 相似文献
95.
We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns. 相似文献
96.
Rhonda magel 《统计学通讯:模拟与计算》2013,42(3):917-925
We consider a test for the equality of k population medians, θi i=1,2,….,k, when it is believed a priori, that θ i: The observations are subject to right censorhip. The distributions of the censoring variables for each population are assumed to be equal. This test is compared with the general k-sample test proposed by Breslow 相似文献
97.
In earlier work (Gelfand and Smith, 1990 and Gelfand et al, 1990) a sampling based approach using the Gibbs sampler was offered as a means for developing marginal posterior densities for a wide range of Bayesian problems several of which were previously inaccessible. Our purpose here is two-fold. First we flesh out the implementation of this approach for calculation of arbitrary expectations of interest. Secondly we offer comparison with perhaps the most prominent approach for calculating posterior expectations, analytic approximation involving application of the LaPlace method. Several illustrative examples are discussed as well. Clear advantages for the sampling based approach emerge. 相似文献
98.
The likelihood ratio method is used to construct a confidence interval for a population mean when sampling from a population with certain characteristics found in many applications, such as auditing. Specifically, a sample taken from this type of population usually consists of a very large number of zero values, plus a small number of nonzero values that follow some continuous distribution. In this situation, the traditional confidence interval constructed for the population mean is known to be unreliable. This article derives confidence intervals based on the likelihood-ratio-test approach by assuming (1) a normal distribution (normal algorithm) and (2) an exponential distribution (exponential algorithm). Because the error population distribution is usually unknown, it is important to study the robustness of the proposed procedures. We perform an extensive simulation study to compare the percentage of confidence intervals containing the true population mean using the two proposed algorithms with the percentage obtained from the traditional method based on the central limit theorem. It is shown that the normal algorithm is the most robust procedure against many different distributional error assumptions. 相似文献
99.
Peter Wessman 《统计学通讯:理论与方法》2013,42(5):1143-1161
The surveillance of multivariate processes has received growing attention during the last decade. Several generalizations of well-known methods such as Shewhart, CUSUM and EWMA charts have been proposed. Many of these multivariate procedures are based on a univariate summarized statistic of the multivariate observations, usually the likelihood ratio statistic. In this paper we consider the surveillance of multivariate observation processes for a shift between two fully specified alternatives. The effect of the dimension reduction using likelihood ratio statistics are discussed in the context of sufficiency properties. Also, an example of the loss of efficiency when not using the univariate sufficient statistic is given. Furthermore, a likelihood ratio method, the LR method, for constructing surveillance procedures is suggested for multivariate surveillance situations. It is shown to produce univariate surveillance procedures based on the sufficient likelihood ratios. As the LR procedure has several optimality properties in the univariate, it is also used here as a benchmark for comparisons between multivariate surveillance procedures 相似文献
100.
《统计学通讯:理论与方法》2013,42(10):1969-1988
We propose an iterative method of estimation for discrete missing data problems that is conceptually different from the Expectation–Maximization (EM) algorithm and that does not in general yield the observed data maximum likelihood estimate (MLE). The proposed approach is based conceptually upon weighting the set of possible complete-data MLEs. Its implementation avoids the expectation step of EM, which can sometimes be problematic. In the simple case of Bernoulli trials missing completely at random, the iterations of the proposed algorithm are equivalent to the EM iterations. For a familiar genetics-oriented multinomial problem with missing count data and for the motivating example with epidemiologic applications that involves a mixture of a left censored normal distribution with a point mass at zero, we investigate the finite sample performance of the proposed estimator and find it to be competitive with that of the MLE. We give some intuitive justification for the method, and we explore an interesting connection between our algorithm and multiple imputation in order to suggest an approach for estimating standard errors. 相似文献