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301.
In the literature of information theory, Shannon entropy plays an important role and in the context of reliability theory, order statistics and record values are used for statistical modeling. The aim of this article is characterizing the parent distributions based on Shannon entropy of order statistics and record values. It is shown that the equality of the Shannon information in order statistics or record values can determine uniquely the parent distribution. The exponential distribution is characterized through maximizing Shannon entropy of record values under some constraints. The results are useful in the modeling problems. 相似文献
302.
This article is concerned with the problem of constructing A-optimal design for polynomial regression with analytic weight function on the interval [m ? a, m + a], m, a > 0. It is shown that the structure of the optimal design depends on a and weight function only, as a close to 0. Moreover, if the weight function is an analytic function a, then a scaled version of optimal support points, and weights are analytic functions of a at a = 0. We make use of a Taylor expansion to provide a recursive procedure for calculating the A-optimal designs. Examples are presented to illustrate the procedures for computing the optimal designs. 相似文献
303.
The approximate D s -optimal design for discriminating between linear and quadratic log contrast models for experiments with mixtures suggested by Aitchison and Bacon-Shone (1984) is investigated, where the experimental domain is restricted further as in Chan (1992). It is found that for a symmetric subspace of the finite dimensional simplex, there is a D s -optimal design with the nice structure that puts a weight 1/2 k?1 on the centroid of this subspace and the remaining weight is uniformly distributed on the vertices of the experimental domain. Finally, the D s -efficiency of the D-optimal design for quadratic model and the design given by Aitchison and Bacon-Shone (1984) are also discussed. 相似文献
304.
Best Quadratic Unbiased Prediction in a General Linear Model with Stochastic Regression Coefficients
In this article, we discuss on how to predict a combined quadratic parametric function of the form β′ H β + hσ2 in a general linear model with stochastic regression coefficients denoted by y = X β + e . Firstly, the quadratic predictability of β′ H β + hσ2 is investigated to obtain a quadratic unbiased predictor (QUP) via a general method of structuring an unbiased estimator. This QUP is also optimal in some situations and therefore we hope it will be a fine predictor. To show this idea, we apply the Lagrange multipliers method to this problem and finally reach the expected conclusion through permutation matrix techniques. 相似文献
305.
AbstractIn this article, when it is suspected that regression coefficients may be restricted to a subspace, we discuss the parameter estimation of regression coefficients in a multiple regression model. Then, in order to improve the preliminary test almost ridge estimator, we study the positive-rule Stein-type almost unbiased ridge estimator based on the positive-rule stein-type shrinkage estimator and almost unbiased ridge estimator. After that, quadratic bias and quadratic risk values of the new estimator are derived and compared with some relative estimators. And we also discuss the option of parameter k. Finally, we perform a real data example and a Monte Carlo study to illustrate theoretical results. 相似文献
306.
ABSTRACTPartially varying coefficient single-index models (PVCSIM) are a class of semiparametric regression models. One important assumption is that the model error is independently and identically distributed, which may contradict with the reality in many applications. For example, in the economical and financial applications, the observations may be serially correlated over time. Based on the empirical likelihood technique, we propose a procedure for testing the serial correlation of random error in PVCSIM. Under some regular conditions, we show that the proposed empirical likelihood ratio statistic asymptotically follows a standard χ2 distribution. We also present some numerical studies to illustrate the performance of our proposed testing procedure. 相似文献
307.
S. Huda 《统计学通讯:模拟与计算》2013,42(1):309-323
For polynomial regression over spherical regions, the d-th order As-optimal designs for γ-th order models are derived for 4 ≥ d > γ≥l. Efficiencies of these designs with respect to the γ-th order A-optimal designs are obtained. Furthermore, the effects of estimating intermediate m-th order models on these efficiencies are examined for d > m > γ 相似文献
308.
Karim F. Hirji 《统计学通讯:模拟与计算》2013,42(3):1197-1227
Multinomial goodness-of-fit tests arise in a diversity of milieu. The long history of the problem has spawned a multitude of asymptotic tests. If the sample size relative to the number of categories is small, the accuracy of these tests is compromised. In that case, an exact test is a prudent option. But such tests are computationally intensive and need efficient algorithms. This paper gives a conceptual overview, and empirical comparisons of two avenues, namely the network and fast Fourier transform (FFT) algorithms, for an exact goodness-of-fit test on a multinomial. We show that a recursive execution of a polynomial product forms the basis of both these approaches. Specific details to implement the network method, and techniques to enhance the efficiency of the FFT algorithm are given. Our empirical comparisons show that for exact analysis with the chi-square and likelihood ratio statistics, the network-cum-polynomial multiplication algorithm is the more efficient and accurate of the two. 相似文献
309.
S. Huda 《统计学通讯:理论与方法》2013,42(9):2965-2985
For polynomial regression over spherical regions the d-th order Ds-optimal designs for the λ-th order models are derived for 1 ≤ λ ≤ d ≤ 4. Efficiencies of these designs with respect to the λ-th order D-optimal designs are obtained. The effects of estimating addtional parameters due to an m-th order model (d ≥ m >>λ) on the efficiencies are investigated. 相似文献
310.
Making use of a characterization of multivariate normality by Hermitian polynomials, we propose a multivariate normality test. The approach is then applied to time series analysis by constructing a test for Gaussianity of a stationary univariate series. Simulation study shows that the proposed test has reasonable power and outperforms other tests available in the literature when the innovation series of the time series is symmetric, but non-Gaussian. 相似文献