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921.
《统计学通讯:理论与方法》2013,42(12):2477-2512
Abstract To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address leptokurtic feature, volatility smile, and volatility clustering effects of the asset return distributions. However, analytical tractability remains a problem for most alternative models. In this article, we study a class of hidden Markov models including Markov switching models and stochastic volatility models, that can incorporate leptokurtic feature, volatility clustering effects, as well as provide analytical solutions to option pricing. We show that these models can generate long memory phenomena when the transition probabilities depend on the time scale. We also provide an explicit analytic formula for the arbitrage-free price of the European options under these models. The issues of statistical estimation and errors in option pricing are also discussed in the Markov switching models. 相似文献
922.
L.R. Haff 《统计学通讯:理论与方法》2013,42(7):2131-2144
Fisher's Linear Discriminant Function Can be used to classify an individual who has sampled from one of two multivariate normal Populations. In the following, this function is viewed as the other given his data vector it is assumed that the Population means and common covariance matrix are unknown. The vector of discriminant coeffients β(p×1) is the gradient of posterior log-odds and certain of its lineqar functions are directional derivatives which have a practical meaning. Accordingly, we treat the problems of estimating several linear functions of β The usual estimatoes of these functions are scaled versions of the unbiased estmators. In this Paper, these estimators are domainated by explicit alterenatives under a quadratic loss function. we reduce the problem of estimating β to that of estimating the inverse convariance matrix. 相似文献
923.
Finite mixture models, that is, weighted averages of parametric distributions, provide a powerful way to extend parametric families of distributions to fit data sets not adequately fit by a single parametric distribution. First-order finite mixture models have been widely used in the physical, chemical, biological, and social sciences for over 100 years. Using maximum likelihood estimation, we demonstrate how a first-order finite mixture model can represent the large variability in data collected by the U.S. Environmental Protection Agency for the concentration of Radon 222 in drinking water supplied from ground water, even when 28% of the data fall at or below the minimum reporting level. Extending the use of maximum likelihood, we also illustrate how a second-order finite mixture model can separate and represent both the variability and the uncertainty in the data set. 相似文献
924.
《Journal of Statistical Computation and Simulation》2012,82(15):3093-3105
ABSTRACTIn economics and government statistics, aggregated data instead of individual level data are usually reported for data confidentiality and for simplicity. In this paper we develop a method of flexibly estimating the probability density function of the population using aggregated data obtained as group averages when individual level data are grouped according to quantile limits. The kernel density estimator has been commonly applied to such data without taking into account the data aggregation process and has been shown to perform poorly. Our method models the quantile function as an integral of the exponential of a spline function and deduces the density function from the quantile function. We match the aggregated data to their theoretical counterpart using least squares, and regularize the estimation by using the squared second derivatives of the density function as the penalty function. A computational algorithm is developed to implement the method. Application to simulated data and US household income survey data show that our penalized spline estimator can accurately recover the density function of the underlying population while the common use of kernel density estimation is severely biased. The method is applied to study the dynamic of China's urban income distribution using published interval aggregated data of 1985–2010. 相似文献
925.
《Journal of Statistical Computation and Simulation》2012,82(4):251-272
Maximum likelihood, goodness-of-fit, and symmetric percentile estimators of the power transformation parameterp, are considered. The comparative robustness of each estimation procedure is evaluated when the transformed data can be made symmetric, but may not necessarily be normal. Seven types of symmetric distributions are considered as well as four contaminated normal distributions over a range of six p values for samples of size 25, 50, and 100. The results indicate that the maximum likelihood estimator was slightly better than the goodness-of-fit estimator, but both were greatly superior to the percentile estimator. In general, the procedures were robust to distributional symmetric departures from normality, but increasing kurtosis caused appreciable increases in variation for estimated p values. The variability of p was found to decrease more than exponentially with decreases in the underlying normal distribution coefficient of variation. The standard likelihood ratio confidence interval procedure was found not to be generally useful. 相似文献
926.
Patrick E.B. FitzGerald & Matthew W. Knuiman 《Australian & New Zealand Journal of Statistics》1998,40(3):305-316
This paper examines a number of methods of handling missing outcomes in regressive logistic regression modelling of familial binary data, and compares them with an EM algorithm approach via a simulation study. The results indicate that a strategy based on imputation of missing values leads to biased estimates, and that a strategy of excluding incomplete families has a substantial effect on the variability of the parameter estimates. Recommendations are made which depend, amongst other factors, on the amount of missing data and on the availability of software. 相似文献
927.
Consider a linear regression model with unknown regression parameters β0 and independent errors of unknown distribution. Block the observations into q groups whose independent variables have a common value and measure the homogeneity of the blocks of residuals by a Cramér‐von Mises q‐sample statistic Tq(β). This statistic is designed so that its expected value as a function of the chosen regression parameter β has a minimum value of zero precisely at the true value β0. The minimizer β of Tq(β) over all β is shown to be a consistent estimate of β0. It is also shown that the bootstrap distribution of Tq(β0) can be used to do a lack of fit test of the regression model and to construct a confidence region for β0 相似文献
928.
This article gives a unified account of nonparametric statistics, covering testing, estimating, multiple comparisons, analysis of variance and regression, for rounded-off data, with ties handled by the average scores method. The theory is illustrated by means of numerous applications to the Biomedical, Engineering and Behavioral Sciences. 相似文献
929.
Dallas R. Wingo 《统计学通讯:模拟与计算》2013,42(2):201-212
The log-likelihood function (LLF) of the single (location) parameter Cauchy distribution can exhibit up to n relative maxima, where n is the sample size. To compute the maximum likelihood estimate of the location parameter, previously published methods have advocated scanning the LLF over a suf-ficiently large portion of the real line to locate the absolute maximum. This note shows that, given an easily derived upper bound on the second derivative of the negative LLF, Brent's univariate numerical global optimization method can be used to locate the absolute maximum among several relative maxima of the LLF without performing an exhaustive search over the real line. 相似文献
930.
Benee F. Swindel 《统计学通讯:理论与方法》2013,42(11):1065-1075
Ridge regression is re-examined and ridge estimators based on prior information are introduced. A necessary and sufficient condition is given for such ridge estimators to yield estimators of every nonnull linear combination of the regression coefficients with smaller mean square error than that of the Gauss-Markov best linear unbiased estimator. 相似文献