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211.
ABSTRACT It is known that the Fisher information in any set of order statistics can be simplified to a sum of double integrals. In this article, we show that it can be further simplified to a sum of single integrals for the scale parameter of an exponential distribution. Moreover, we use the result and provide a simple method of obtaining the optimal spacing of order statistics. 相似文献
212.
In many phenomena described by stochastic processes, the implementation of an alarm system becomes fundamental to predict the occurrence of future events. In this work we develop an alarm system to predict whether a count process will upcross a certain level and give an alarm whenever the upcrossing level is predicted. We consider count models with parameters being functions of covariates of interest and varying on time. This article presents classical and Bayesian methodology for producing optimal alarm systems. Both methodologies are illustrated and their performance compared through a simulation study. The work finishes with an empirical application to a set of data concerning the number of sunspot on the surface of the sun. 相似文献
213.
Ryszard Zieliński 《统计学通讯:理论与方法》2013,42(7):980-992
“Nonparametric” in the title is used to say that observations X 1,…,X n come from an unknown distribution F ∈ ? with ? being the class of all continuous and strictly increasing distribution functions. The problem is to estimate the quantile of a given order q ∈ (0,1) of the distribution F. The class ? of distributions is very large; it is so large that even X nq:n , where nq is an integer, may be very poor estimator of the qth quantile. To assess the performance of estimators no properties based on moments may be used: expected values of estimators should be replaced by their medians, their variances—by some characteristics of concentration of distributions around the median. If an estimator is median-biased for one of distributions, the bias of the estimator may be infinitely large for other distributions. In the note optimal estimators with respect to various criteria of optimality are presented. The pivotal function F(T) of the estimator T is introduced which enables us to apply the classical statistical approach. 相似文献
214.
S. Stylianou 《统计学通讯:理论与方法》2013,42(10):1776-1784
A conference matrix is a square matrix C with zeros on the diagonal and ±1s off the diagonal, such that C T C = CC T = (n ? 1)I, where I is the identity matrix. Conference matrices are an important class of combinatorial designs due to their many applications in several fields of science, including statistical-experimental designs, telecommunications, elliptic geometry, and more. In this article, conference matrices and their full foldover design are combined together to obtain an alternative method for screening active factors in complicated problems. This method provides a model-independent estimate of the set of active factors and also gives a linearity test for the underlying model. 相似文献
215.
This note mainly aims to illustrate that some quadratic problems are robust in a sense with respect to the probabilistic distributions involved. The secondary moments of the quadratic forms of a multivariate t distribution are calculated. Then, the resulting formulae are applied to the quadratic problems of quadratic sufficiency and quadratic prediction. It is shown by revisiting the two problems that the same conclusions hold when the multivariate normal distribution is replaced with a multivariate t distribution. 相似文献
216.
In this article, we introduce a new method for the volatility function estimation of continuous-time diffusion process dX t = μ(X t )dt + σ(X t )dW t , which is based on combining the idea of local linear smoother and variable bandwidth. We give the expressions for the conditional MSE and MISE of the estimator and obtain the optimal variable bandwidth. An explicit formula for the optimal variable bandwidth is presented by minimizing the MISE, which extends the related results in Fan and Gijbels (1992), etc. Finally, some simulations show that the performance of the proposed estimator with optimal variable bandwidth is often much better than that of the local linear estimator with invariable bandwidth. 相似文献
217.
Shaoyong Hu 《统计学通讯:理论与方法》2014,43(1):151-164
In this article, we discuss about the stochastic comparisons and optimal allocation for policy limits and deductibles. We order the total retained losses of a policyholder in the usual stochastic order under more general conditions of X i (i = 1,…, n), based on which the optimal allocation of policy limits and deductibles are achieved in some special cases. Several results in Cheung (2007) and Lu and Meng (2011) are generalized here. 相似文献
218.
219.
Haifeng Xu 《统计学通讯:理论与方法》2013,42(2):506-519
ABSTRACTIn this paper, assuming that there exist omitted variables in the specified model, we analytically derive the exact formula for the mean squared error (MSE) of a heterogeneous pre-test (HPT) estimator whose components are the ordinary least squares (OLS) and feasible ridge regression (FRR) estimators. Since we cannot examine the MSE performance analytically, we execute numerical evaluations to investigate small sample properties of the HPT estimator, and compare the MSE performance of the HPT estimator with those of the FRR estimator and the usual OLS estimator. Our numerical results show that (1) the HPT estimator is more efficient when the model misspecification is severe; (2) the HPT estimator with the optimal critical value obtained under the correctly specified model can be safely used even when there exist omitted variables in the specified model. 相似文献
220.
Minimizing Upper Bound of Ruin Probability Under Discrete Risk Model with Markov Chain Interest Rate
This article focuses on minimal upper bound of ruin probability for a discrete time risk model with Markov chain interest rate and stochastic investment return. The interest rate of bond market is assumed to be a stationary Markov chain, and the return process of a stock market can be negative. This article presents two kinds of methods for minimizing the upper bound of ruin probability. One method relies on recursive equations for finite time ruin probabilities and inductive approach, the other one depends on martingale approach. Numerical examples show that the martingale approach is better than the inductive one. 相似文献