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931.
For a stable autoregressive process of order p with unknown vector parameter θ, it is shown that under a sequential sampling scheme with the stopping time defined by the trace of the observed Fisher information matrix, the least-squares estimator of θ is asymptotically normally distributed uniformly in θ belonging to any compact set in the parameter region. 相似文献
932.
二次损失下一般Gauss-Markov模型中可估函数的线性Minimax估计 总被引:4,自引:0,他引:4
设Y是具有均值Xβ和协方差阵σ~2V的n维随机向量,Sβ是线性可估函数,这里X,S和V≥0是已知矩阵,β∈R~p和σ~2>0是未知参数。本文在二次损失下研究了线性估计的Minimax性。在适当的假设下,得到了Sβ的唯一线性Minimax估计(有关唯一性在几乎处处意义下理解) 相似文献
933.
Jean-Yves Audibert 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2004,40(6):148-736
Numerous empirical results have shown that combining regression procedures can be a very efficient method. This work provides PAC bounds for the L2 generalization error of such methods. The interest of these bounds are twofold.First, it gives for any aggregating procedure a bound for the expected risk depending on the empirical risk and the empirical complexity measured by the Kullback–Leibler divergence between the aggregating distribution
and a prior distribution π and by the empirical mean of the variance of the regression functions under the probability
.Secondly, by structural risk minimization, we derive an aggregating procedure which takes advantage of the unknown properties of the best mixture
: when the best convex combination
of d regression functions belongs to the d initial functions (i.e. when combining does not make the bias decrease), the convergence rate is of order (logd)/N. In the worst case, our combining procedure achieves a convergence rate of order
which is known to be optimal in a uniform sense when
(see [A. Nemirovski, in: Probability Summer School, Saint Flour, 1998; Y. Yang, Aggregating regression procedures for a better performance, 2001]).As in AdaBoost, our aggregating distribution tends to favor functions which disagree with the mixture on mispredicted points. Our algorithm is tested on artificial classification data (which have been also used for testing other boosting methods, such as AdaBoost). 相似文献
934.
In this paper, we consider the estimation of time-varying ARMA models subject to Markovian changes in regime. We give explicit conditions ensuring consistency and asymptotic normality, as well as the limiting covariance matrix, of least squares and quasi-generalized least-squares estimators. 相似文献
935.
Assume X = (X1, …, Xp)′ is a normal mixture distribution with density w.r.t. Lebesgue measure, , where Σ is a known positive definite matrix and F is any known c.d.f. on (0, ∞). Estimation of the mean vector under an arbitrary known quadratic loss function
Q(θ, a) = (a − θ)′ Q(a − θ), Q a positive definite matrix, is considered. An unbiased estimator of risk is obatined for an arbitrary estimator, and a sufficient condition for estimators to be minimax is then achieved. The result is applied to modifying all the Stein estimators for the means of independent normal random variables to be minimax estimators for the problem considered here. In particular the results apply to the Stein class of limited translation estimators. 相似文献
936.
Let X ≡ (X1, …, Xt) have a multinomial distribution based on N trials with unknown vector of cell probabilities p ≡ (p1, …, pt). This paper derives admissibility and complete class results for the problem of simultaneously estimating p under entropy loss (EL) and squared error loss (SEL). Let
and f(x¦p) denote the (t − 1)-dimensional simplex, the support of X and the probability mass function of X, respectively. First it is shown that δ is Bayes w.r.t. EL for prior P if and only if δ is Bayes w.r.t. SEL for P. The admissible rules under EL are proved to be Bayes, a result known for the case of SEL. Let Q denote the class of subsets of
of the form T = j=1kFj where k ≥ 1 and each Fj is a facet of
which satisfies: F a facet of
such that F naFjF ncT. The minimal complete class of rules w.r.t. EL when N ≥ t − 1 is characterized as the class of Bayes rules with respect to priors P which satisfy P(
0) = 1, ξ(x) ≡ ∫ f(x¦p) P(dp) > 0 for all x in {x
: sup
0 f(x¦p) > 0} for some
0 in Q containing all the vertices of
. As an application, the maximum likelihood estimator is proved to be admissible w.r.t. EL when the estimation problem has parameter space Θ =
but it is shown to be inadmissible for the problem with parameter space Θ = (
minus its vertices). This is a severe form of “tyranny of boundary.” Finally it is shown that when N ≥ t − 1 any estimator δ which satisfies δ(x) > 0 x
is admissible under EL if and only if it is admissible under SEL. Examples are given of nonpositive estimators which are admissible under SEL but not under EL and vice versa. 相似文献
937.
938.
Jeffrey D. Hart 《Statistics & probability letters》1984,2(6):363-369
The ability of a kernel density estimator to resolve modes of the underlying density is investigated. For various bimodal densities and three different kernels, the smallest sample size required for the expectation of an optimally smoothed kernel estimator to be bimodal is determined. The optimality criterion employed is equivalent to asymptotic mean integrated squared error for sufficiently smooth densities. 相似文献
939.
删失数据平滑非参数分位估计 总被引:1,自引:0,他引:1
文中在随机右删失意义下,对于未知分布函数的分位点,基于PL估计给出了一种平滑的非参数核分位估计,推导出了该估计的逐点和一致强弱Bahadur类型表示定理,并由此结果获得了平滑分位计的渐近正态性及重对数律等深刻结果。 相似文献
940.
Qiquing Yu 《Annals of the Institute of Statistical Mathematics》1989,41(3):503-520
Consider both the calssical and some more general invariant decision problems of estimating a continuous distribution function, with the loss function {ie503-1} and a sample of sizen fromF. It is proved that any nonrandomized estimator can be approximated in Lebesgue measure by the more general invariant estimators. Some methods for investigating the finite sample problem are discussed. As an application, a proof that the best invariant estimator is minimax when the sample size is 1 is given. 相似文献