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Roberto Rossi Steven Prestwich S. Armagan Tarim Brahim Hnich 《European Journal of Operational Research》2014
We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach produces an upper and a lower bound for the associated cost. We apply this approach to three demand distributions in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist—e.g. based on maximum likelihood estimators—or Bayesian strategies. 相似文献
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Mohamedou Ould HayeAnne Philippe 《Statistics & probability letters》2011,81(9):1354-1364
Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclic effects. In particular, we extend the results of Ho and Hsing (1996), Mielniczuk (1997) and Hall and Hart (1990) to the stationary processes for which the singularities of the spectral density are not limited to the origin. We show that the convergence rates and the limiting distribution may be different in this context. 相似文献
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Attila Csenki 《Journal of multivariate analysis》1979,9(2):337-340
In a paper by Lai [(1976) Ann. Statist.4] a construction of sequences of confidence intervals for one-parameter exponential families is given, where the intersection of these intervals contains the true parameter value θ0 with a prescribed level of confidence and the respective interval bounds tend a.s. to θ0. In this paper an analogous result for multiparameter exponential families is proved. More presicely, sequences of convex confidence sets are obtained which shrink to the actual parameter value. 相似文献
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We propose a new and simple estimating equation for the parameters in median regression models with designed censoring variables, and then apply the empirical log likelihood ratio statistic to construct confidence region for the parameters. The empirical log likelihood ratio statistic is shown to have a standard chi-square distribution, which makes this method easy to implement. At the same time, another empirical log likelihood ratio statistic is proposed based on an existing estimating equation and the limiting distribution of the empirical likelihood ratio statistic is shown to be a sum of weighted chi-square distributions. We compare the performance of the empirical likelihood confidence region based on the new estimating equation, with that based on the existing estimating equation and a normal approximation method by simulation studies. 相似文献
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S. G. Giakoumatos I. D. Vrontos P. Dellaportas D. N. Politis 《Journal of computational and graphical statistics》2013,22(3):431-451
Abstract A new diagnostic procedure for assessing convergence of a Markov chain Monte Carlo (MCMC) simulation is proposed. The method is based on the use of subsampling for the construction of confidence regions from asymptotically stationary time series as developed in Politis, Romano, and Wolf. The MCMC subsampling diagnostic is capable of gauging at what point the chain has “forgotten” its starting points, as well as to indicate how many points are needed to estimate the parameters of interest according to the desired accuracy. Simulation examples are also presented showing that the diagnostic performs favorably in interesting cases. 相似文献
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Jürgen Dippon 《随机分析与应用》2013,31(5):765-798
Parallelization of stochastic approximation procedures can reduce computation and total observation time of a system. Concerning the number of all observations used by the pure sequential and the suggested parallel method a weak invariance principle implies the asymptotic equivalence of both methods. A loglog invariance principle and a rate of a.s. convergence result describe the pathwise properties. Due to the parallel design asymptotic confidence regions can readily be constructed either by computing the bootstrap distribution or the Gaussian limit distribution determined by the empirical covariance 相似文献
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Let
be an observation from a spherically symmetric distribution with unknown location parameter
. For a general non-negative function c, we consider the problem of estimating c(||x − θ||2) under the usual quadratic loss. For p ≥ 5, we give sufficient conditions for improving on the unbiased estimator γ0 of c(||x − θ||2) by competing estimators γ
s
= γ0 + s correcting γ0 with a suitable function s. The main condition relies on a partial differential inequality of the form k Δs + s
2 ≤ 0 for a certain constant k ≠ 0. Our approach unifies, in particular, the two problems of quadratic loss estimation and confidence statement estimation
and allows to derive new results for these two specific cases. Note that we formally establish our domination results (that
is, with no recourse to simulation).
相似文献