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161.
Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion 总被引:1,自引:0,他引:1
Clifford M. Hurvich Jeffrey S. Simonoff & Chih-Ling Tsai 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1998,60(2):271-293
Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a criterion based on the Akaike information criterion (AIC), termed AICC , is derived and examined as a way to choose the smoothing parameter. Unlike plug-in methods, AICC can be used to choose smoothing parameters for any linear smoother, including local quadratic and smoothing spline estimators. The use of AICC avoids the large variability and tendency to undersmooth (compared with the actual minimizer of average squared error) seen when other 'classical' approaches (such as generalized cross-validation (GCV) or the AIC) are used to choose the smoothing parameter. Monte Carlo simulations demonstrate that the AICC -based smoothing parameter is competitive with a plug-in method (assuming that one exists) when the plug-in method works well but also performs well when the plug-in approach fails or is unavailable. 相似文献
162.
Interval-censored data arise in a wide variety of application and research areas such as, for example, AIDS studies (Kim et al ., 1993) and cancer research (Finkelstein, 1986; Becker & Melbye, 1991). Peto (1973) proposed a Newton–Raphson algorithm for obtaining a generalized maximum likelihood estimate (GMLE) of the survival function with interval-cen sored observations. Turnbull (1976) proposed a self-consistent algorithm for interval-censored data and obtained the same GMLE. Groeneboom & Wellner (1992) used the convex minorant algorithm for constructing an estimator of the survival function with "case 2" interval-censored data. However, as is known, the GMLE is not uniquely defined on the interval [0, ∞]. In addition, Turnbull's algorithm leads to a self-consistent equation which is not in the form of an integral equation. Large sample properties of the GMLE have not been previously examined because of, we believe, among other things, the lack of such an integral equation. In this paper, we present an EM algorithm for constructing a GMLE on [0, ∞]. The GMLE is expressed as a solution of an integral equation. More recently, with the help of this integral equation, Yu et al . (1997a, b) have shown that the GMLE is consistent and asymptotically normally distributed. An application of the proposed GMLE is presented 相似文献
163.
Tatsuya Kubokawa 《Revue canadienne de statistique》1990,18(1):59-62
For estimating powers of the generalized variance under a multivariate normal distribution with an unknown mean, the inadmissibility of the closest affine equivariant estimator is shown for the Pitman closeness criterion. 相似文献
164.
A. Stepanov 《Statistical Papers》2007,48(1):63-79
LetX
1,X
2, … be a sequence of i.i.d. random variables with some continuous distribution functionF. LetX(n) be then-th record value associated with this sequence and μ
n
−
, μ
n
+
be the variables that count the number of record values belonging to the random intervals(f−(X(n)), X(n)), (X(n), f+(X(n))), wheref−, f+ are two continuous functions satisfyingf−(x)<x, f+(x)>x. Properties of μ
n
−
, μ
n
+
are studied in the present paper. Some statistical applications connected with these variables are also provided. 相似文献
165.
Our aim is to estimate the unknown slope function in the functional linear model when the response Y is real and the random function X is a second-order stationary and periodic process. We obtain our estimator by minimizing a standard (and very simple) mean-square contrast on linear finite dimensional spaces spanned by trigonometric bases. Our approach provides a penalization procedure which allows to automatically select the adequate dimension, in a non-asymptotic point of view. In fact, we can show that our penalized estimator reaches the optimal (minimax) rate of convergence in the sense of the prediction error. We complete the theoretical results by a simulation study and a real example that illustrates how the procedure works in practice. 相似文献
166.
Dong Wan Shin 《Statistics》2015,49(1):209-223
Stationary bootstrapping is applied to panel cointegration tests which are based on the ordinary least-squares estimator and the seemingly unrelated regression (SUR) estimator of the residual unit root. Large sample validity of stationary bootstrapping is established. A finite sample experiment reveals that size performances of the bootstrap tests are much less sensitive to cross-sectional correlation than those of existing tests and a test based on the SUR estimator has substantially better power than existing tests. 相似文献
167.
Sedigheh Mirzaei Salehabadi Debasis Sengupta Rituparna Das 《Scandinavian Journal of Statistics》2015,42(1):290-305
Menarche, the onset of menstruation, is an important maturational event of female childhood. Most of the studies of age at menarche make use of dichotomous (status quo) data. More information can be harnessed from recall data, but such data are often censored in a informative way. We show that the usual maximum likelihood estimator based on interval censored data, which ignores the informative nature of censoring, can be biased and inconsistent. We propose a parametric estimator of the menarcheal age distribution on the basis of a realistic model of the recall phenomenon. We identify the additional information contained in the recall data and demonstrate theoretically as well as through simulations the advantage of the maximum likelihood estimator based on recall data over that based on status quo data. 相似文献
168.
Gaëlle Chagny 《Scandinavian Journal of Statistics》2015,42(2):336-360
In this work, we develop a method of adaptive non‐parametric estimation, based on ‘warped’ kernels. The aim is to estimate a real‐valued function s from a sample of random couples (X,Y). We deal with transformed data (Φ(X),Y), with Φ a one‐to‐one function, to build a collection of kernel estimators. The data‐driven bandwidth selection is performed with a method inspired by Goldenshluger and Lepski (Ann. Statist., 39, 2011, 1608). The method permits to handle various problems such as additive and multiplicative regression, conditional density estimation, hazard rate estimation based on randomly right‐censored data, and cumulative distribution function estimation from current‐status data. The interest is threefold. First, the squared‐bias/variance trade‐off is automatically realized. Next, non‐asymptotic risk bounds are derived. Lastly, the estimator is easily computed, thanks to its simple expression: a short simulation study is presented. 相似文献
169.
170.