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31.
Saul Blumentthal 《统计学通讯:理论与方法》2013,42(11):3607-3628
Data which is grouped and truncated is considered. We are given numbers n1<…<nk=n and we observe Xni ),i=1,…k, and the tottal number of observations available (N> nk is unknown. If the underlying distribution has one unknown parameter θ which enters as a scale parameter, we examine the form of the equations for both conditional, unconditional and modified maximum likelihood estimators of θ and N and examine when these estimators will be finite, and unique. We also develop expressions for asymptotic bias and search for modified estimators which minimize the maximum asymptotic bias. These results are specialized tG the zxponential distribution. Methods of computing the solutions to the likelihood equatims are also discussed. 相似文献
32.
MATHIAS VETTER 《Scandinavian Journal of Statistics》2012,39(4):757-771
Abstract. In this study we are concerned with inference on the correlation parameter ρ of two Brownian motions, when only high‐frequency observations from two one‐dimensional continuous Itô semimartingales, driven by these particular Brownian motions, are available. Estimators for ρ are constructed in two situations: either when both components are observed (at the same time), or when only one component is observed and the other one represents its volatility process and thus has to be estimated from the data as well. In the first case it is shown that our estimator has the same asymptotic behaviour as the standard one for i.i.d. normal observations, whereas a feasible estimator can still be defined in the second framework, but with a slower rate of convergence. 相似文献
33.
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the model fits the data well. Sometimes, few observations of a measurement process might be recorded in applications and so selecting a high quantile of the sample as the threshold leads to almost no exceedances. In this paper we propose extensions of the generalised Pareto distribution that incorporate an additional shape parameter while keeping the tail behaviour unaffected. The inclusion of this parameter offers additional structure for the main body of the distribution, improves the stability of the modified scale, tail index and return level estimates to threshold choice and allows a lower threshold to be selected. We illustrate the benefits of the proposed models with a simulation study and two case studies. 相似文献
34.
In regression, detecting anomalous observations is a significant step for model-building process. Various influence measures based on different motivational arguments are designed to measure the influence of observations through different aspects of various regression models. The presence of influential observations in the data is complicated by the existence of multicollinearity. The purpose of this paper is to assess the influence of observations in the Liu [9] and modified Liu [15] estimators by using the method of approximate case deletion formulas suggested by Walker and Birch [14]. A numerical example using a real data set used by Longley [10] and a Monte Carlo simulation are given to illustrate the theoretical results. 相似文献
35.
J.A. Hartigan 《统计学通讯:理论与方法》2013,42(8):2745-2756
Product partition models assume that observations in different components of a random partition of the data are independent given the partition. If the probability distribution of random partitions is in a certain product form prior to making the observations, it is also in product form given the observations. The product model thus provides a convenient machinery for allowing the data to weight the partitions likely to hold; and inference about particular future observations may then be made by first conditioning on the partition, and then averaging over all partitions. This model is applied to fatalities in manned rocket launches, using data from the SOYUZ, APOLLO, SHUTTLE, and post-Challenger SHUTTLE programs in the Soviet Union and the United States. The combination of these data suggest that the chance of a fatality in the next shuttle, launch is about .03, after allowing for the possibility that the older programs are of slight relevance to the present shuttle program. 相似文献
36.
Results are developed concerning the asymptotic behaviour of the Bayes classification rule as the number of unclassified observations grows without bound. It is shown that unclassified observations serve only to estimate the individual population parameters in an unlabeled sense and do not provide information about the labels that are attached to the populations. Prior construction is approached through investigation of prior odds over regions of the joint parameter space (across all populations) deemed likely to contain the true joint parameter vector. It is shown that consideration of these prior odds can lead to more robust a posteriori classification of individual observations. 相似文献
37.
38.
Ahmadou Alioum Daniel Commenges Rodolphe Thiébaut François Dabis for the Groupe d'Epidémiologie Clinique du Syndrome d'Immunodéficience Acquise en Aquitaine 《Journal of the Royal Statistical Society. Series C, Applied statistics》2005,54(4):739-752
Summary. Cohort studies of individuals infected with the human immunodeficiency virus (HIV) provide useful information on the past pattern of HIV diagnoses, progression of the disease and use of antiretroviral therapy. We propose a new method for using individual data from an open prevalent cohort study to estimate the incidence of HIV, by jointly modelling the HIV diagnosis, the inclusion in the cohort and the progression of the disease in a Markov model framework. The estimation procedure involves the construction of a likelihood function which takes into account the probability of observing the total number of subjects who are enrolled in the cohort and the probabilities of passage through the stages of disease for each observed subject conditionally on being included in the cohort. The estimator of the HIV infection rate is defined as the function which maximizes a penalized likelihood, and the solution of this maximization problem is approximated on a basis of cubic M -splines. The method is illustrated by using cohort data from a hospital-based surveillance system of HIV infection in Aquitaine, a region of south-western France. A simulation study is performed to study the ability of the model to reconstruct the incidence of HIV from prevalent cohort data. 相似文献
39.
ARNAUD GLOTER 《Scandinavian Journal of Statistics》2006,33(1):83-104
Abstract. We consider the estimation of unknown parameters in the drift and diffusion coefficients of a one-dimensional ergodic diffusion X when the observation is a discrete sampling of the integral of X at times i Δ , i = 1 ,…, n . Assuming that the sampling interval tends to 0 while the total length time interval tends to infinity, we first prove limit theorems for functionals associated with our observations. We apply these results to obtain a contrast function. The associated minimum contrast estimators are shown to be consistent and asymptotically Gaussian with different rates for drift and diffusion coefficient parameters. 相似文献
40.
Use of a suitable stopping rule yields exact uniformly most powerful tests and minimum variance unbiased estimators of various parameters of a Markov branching model with or without immigration. The population model discussed includes the pure birth, simple epidemic, immigration-death, M/M/ 1 queue, linear birth-death and a branching diffusion process, among others, as special cases. 相似文献