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21.
CHRISTOPHE BIERNACKI 《Scandinavian Journal of Statistics》2007,34(3):569-586
Abstract. In the context of the univariate Gaussian mixture with grouped data, it is shown that the global maximum of the likelihood may correspond to a situation where a Dirac lies in any non-empty interval. Existence of a domain of attraction near such a maximizer is discussed and we establish that the expectation-maximization (EM) iterates move extremely slowly inside this domain. These theoretical results are illustrated both by some Monte-Carlo experiments and by a real data set. To help practitioners identify and discard these potentially dangerous degenerate maximizers, a specific stopping rule for EM is proposed. 相似文献
22.
Louis-Paul Rivest 《Revue canadienne de statistique》1985,13(3):211-216
Let ?(1) and ?(2) be location-equivariant estimators of an unknown location parameter μ. It is shown that the test for H0: μ ≤ μ0 versus HA : μ > μ0 that rejects H0 if ?(1) is large is uniformly more powerful than the one that rejects H0 if ?(2) is large if and only if ?(2) is “more dispersed” than ?(1). A similar result is obtained for tests on scale using the star-shaped ordering. Examples are given. 相似文献
23.
Characterizing all possible chemical mixtures in drinking water is a potentially overwhelming project, and the task of assessing each mixture's net toxicity even more daunting. We propose that analyzing occurrence information on mixtures in drinking water may help to narrow the priorities and inform the approaches taken by researchers in mixture toxicology. To illustrate the utility of environmental data for refining the mixtures problem, we use a recent compilation of national ground-water-quality data to examine proposed U.S. Environmental Protection Agency (EPA) and Agency for Toxic Substances and Disease Registry (ATSDR) models of noncancer mixture toxicity. We use data on the occurrence of binary and ternary mixtures of arsenic, cadmium, and manganese to parameterize an additive model and compute hazard index scores for each drinking-water source in the data set. We also use partially parameterized interaction models to perform a bounding analysis estimating the interaction potential of several binary and ternary mixtures for which the toxicological literature is limited. From these results, we estimate a relative value of additional toxicological information for each mixture. For example, we find that according to the U.S. EPA's interaction model, the levels of arsenic and cadmium found in U.S. drinking water are unlikely to have synergistic cardiovascular effects, but the same mixture's potential for synergistic neurological effects merits further study. Similar analysis could in future be used to prioritize toxicological studies based on their potential to reduce scientific and regulatory uncertainty. Environmental data may also provide a means to explore the implications of alternative risk models for the toxicity and interaction of complex mixtures. 相似文献
24.
P.M. Robinson 《Journal of statistical planning and inference》1985,11(2):135-148
Samples of size n are drawn from a finite population on each of two occasions. On the first occasion a variate x is measured, and on the second a variate y. In estimating the population mean of y, the variance of the best linear unbiased combination of means for matched and unmatched samples is itself minimized, with respect to the sampling design on the second occasion, by a certain degree of matching. This optimal allocation depends on the population correlation coefficient, which previous authors have assumed known. We estimate the correlation from an initial matched sample, then an approximately optimal allocation is completed and an estimator formed which, under a bivariate normal superpopulation model, has model expected mean square error equal, apart from an error of order n-2, to the minimum enjoyed by any linear, unbiased estimator. 相似文献
25.
本文应用通用函数Y及其变分原理,为求解具有自由面流动问题提出了一种新方法。将物理平面变换成映象平面。在映象平面上,引出通用函数Y,并且写出关于Y的变分原理。用这个变分原理及有限元法求解自由面流动可克服边界未知的困难。文中以水坝闸门出流问题为例进行了计算,结果表明,该方法是非常有效的。 相似文献
26.
D. Firth & K. E. Bennett 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1998,60(1):3-21
In the estimation of a population mean or total from a random sample, certain methods based on linear models are known to be automatically design consistent, regardless of how well the underlying model describes the population. A sufficient condition is identified for this type of robustness to model failure; the condition, which we call 'internal bias calibration', relates to the combination of a model and the method used to fit it. Included among the internally bias-calibrated models, in addition to the aforementioned linear models, are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting. Other models can often be made robust by using a suboptimal fitting method. Thus the class of model-based, but design consistent, analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts. Particular applications discussed are the estimation of the size of a population subdomain, as arises in tax auditing for example, and the estimation of a bootstrap tail probability. 相似文献
27.
We propose a parametric test for bimodality based on the likelihood principle by using two-component mixtures. The test uses
explicit characterizations of the modal structure of such mixtures in terms of their parameters. Examples include the univariate
and multivariate normal distributions and the von Mises distribution. We present the asymptotic distribution of the proposed
test and analyze its finite sample performance in a simulation study. To illustrate our method, we use mixtures to investigate
the modal structure of the cross-sectional distribution of per capita log GDP across EU regions from 1977 to 1993. Although
these mixtures clearly have two components over the whole time period, the resulting distributions evolve from bimodality
toward unimodality at the end of the 1970s. 相似文献
28.
Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixture-of-Dirichlet-processes prior on the unknown error distribution. A Markov-chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data. 相似文献
29.
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
30.
Hedayat et al. [1988a. Sampling plans excluding contiguous units. J. Statist. Plann. Inference 19, 159–170; 1988b. Designs in survey sampling avoiding contiguous units. In: Krishnaiah, P.R., Rao, C.R. (Eds.). Handbook of Statistics, vol. 6. Elsevier, Amsterdam, pp. 575–583] first introduced balanced sampling designs for the exclusion of contiguous units. Sampling plans that excluded the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. There remain many open questions about the existence of such plans and their extension to plans excluding adjacent units. We present new generation techniques and new balanced sampling plans for the exclusion of adjacent units under finite, one-dimensional, circularly and linearly ordered populations. 相似文献