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21.
The family of cumulative paired -entropies offers a wide variety of ordinal dispersion measures, covering many well-known dispersion measures as a special case. After a comprehensive analysis of this family of entropies, we consider the corresponding sample versions and derive their asymptotic distributions for stationary ordinal time series data. Based on an investigation of their asymptotic bias, we propose a family of signed serial dependence measures, which can be understood as weighted types of Cohen’s , with the weights being related to the actual choice of . Again, the asymptotic distribution of the corresponding sample is derived and applied to test for serial dependence in ordinal time series. Using numerical computations and simulations, the practical relevance of the dispersion and dependence measures is investigated. We conclude with an environmental data example, where the novel -entropy-related measures are applied to an ordinal time series on the daily level of air quality. 相似文献
22.
We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations. 相似文献
23.
Noriya Kadota 《Mathematical Logic Quarterly》1993,39(1):217-227
We show the following results on Wainer's notation for a minimal subrecursive inaccessible ordinal τ: First, we give a constructive proof of the collapsing theorem. Secondly, we prove that the slow-growing hierarchy and the fast-growing hierarchy up to τ have elementary properties on increase and domination, which completes Wainer's proof that τ is a minimal subrecursive inaccessible. Our results are obtained by showing a strong normalization theorem for the term structure of the notation. MSC: 03D20, 03F15. 相似文献
24.
It is shown that the class of all possible families of -subsets of finite ordinals in admissible sets coincides with a class of all non-empty families closed under e-reducibility and . The construction presented has the property of being minimal under effective definability. Also, we describe the smallest (w.r.t. inclusion) classes of families of subsets of natural numbers, computable in hereditarily finite superstructures. A new series of examples is constructed in which admissible sets lack in universal -function. Furthermore, we show that some principles of classical computability theory (such as the existence of an infinite non-trivial enumerable subset, existence of an infinite computable subset, reduction principle, uniformization principle) are always satisfied for the classes of all -subsets of finite ordinals in admissible sets. 相似文献
25.
We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have discrete representatives when the ordinal scales are considered as totally ordered finite sets. We also show that those scale independent functions identify with the so-called order invariant functions, which have been described recently. In particular, this identification allows us to justify the continuity property for certain order invariant functions in a natural way.
Mathematics Subject Classifications (2000) Primary: 91C05, 91E45; Secondary: 06A99, 39A12.Jean-Luc Marichal: Partially supported by a grant from the David M. Kennedy Center for International Studies, Brigham Young University.Radko Mesiar: Partially supported by grants VEGA 1/0273/03 and APVT-20-023402. 相似文献
26.
We present a new method called UTAGMS–INT for ranking a finite set of alternatives evaluated on multiple criteria. It belongs to the family of Robust Ordinal Regression (ROR) methods which build a set of preference models compatible with preference information elicited by the Decision Maker (DM). The preference model used by UTAGMS–INT is a general additive value function augmented by two types of components corresponding to “bonus” or “penalty” values for positively or negatively interacting pairs of criteria, respectively. When calculating value of a particular alternative, a bonus is added to the additive component of the value function if a given pair of criteria is in a positive synergy for performances of this alternative on the two criteria. Similarly, a penalty is subtracted from the additive component of the value function if a given pair of criteria is in a negative synergy for performances of the considered alternative on the two criteria. The preference information elicited by the DM is composed of pairwise comparisons of some reference alternatives, as well as of comparisons of some pairs of reference alternatives with respect to intensity of preference, either comprehensively or on a particular criterion. In UTAGMS–INT, ROR starts with identification of pairs of interacting criteria for given preference information by solving a mixed-integer linear program. Once the interacting pairs are validated by the DM, ROR continues calculations with the whole set of compatible value functions handling the interacting criteria, to get necessary and possible preference relations in the considered set of alternatives. A single representative value function can be calculated to attribute specific scores to alternatives. It also gives values to bonuses and penalties. UTAGMS–INT handles quite general interactions among criteria and provides an interesting alternative to the Choquet integral. 相似文献
27.
王鸣鹤 《应用数学与计算数学学报》1998,(1)
1900年,希尔伯特第一问题提出:连续统能否良序?每一个数学家都会说:“它已在1904年被Zermelo的良序定理所解决”。本文建立了集合三分法,严格证明了一个良序集一定是一个可数集。同时揭露了良序定理及其它一些定理中证明的错误。因此,现代数学存在着第四次数学危机。 相似文献
28.
Rodolf Beran 《Annals of the Institute of Statistical Mathematics》2005,57(2):201-220
The balanced complete multi-way layout with ordinal or nominal factors is a fundamental data-type that arises in medical imaging,
agricultural field trials, DNA microassays, and other settings where analysis of variance (ANOVA) is an established tool.
ASP algorithms weigh competing biased fits in order to reduce risk through variance-bias tradeoff. The acronym ASP stands
for Adaptive Shrinkage of Penalty bases. Motivating ASP is a penalized least squares criterion that associates a separate
quadratic penalty term with each main effect and each interaction in the general ANOVA decomposition of means. The penalty
terms express plausible conjecture about the mean function, respecting the difference between ordinal and nominal factors.
Multiparametric asymptotics under a probability model and experiments on data elucidate how ASP dominates least squares, sometimes
very substantially. ASP estimators for nominal factors recover Stein's superior shrinkage estimators for one- and two-way
layouts. ASP estimators for ordinal factors bring out the merits of smoothed fits to multi-way layouts, a topic broached algorithmically
in work by Tukey.
This research was supported in part by National Science Foundation Grants DMS 0300806 and 0404547. 相似文献
29.
30.
讨论了相关次序矩阵的SOR迭代法,它的最佳松弛因子在1,2之间,我们可以用0.618法逼近它的最优值. 相似文献