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1.
We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution
tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma distributions
is transfered to GPD. Posterior estimates are then computed by Gibbs samplers with Hastings-Metropolis steps. Accurate Bayes
credibility intervals are also defined, they provide assessment of the quality of the extreme events estimates. An empirical
Bayesian method is used in this work, but the suggested approach could incorporate prior information. It is shown that the
obtained quasi-conjugate Bayes estimators compare well with the GPD standard estimators when simulated and real data sets
are studied.
AMS 2000 Subject Classification Primary—62G32, 62F15, 62G09 相似文献
2.
In model-based clustering, a situation in which true class labels are unknown and that is therefore also referred to as unsupervised
learning, observations are typically classified by the Bayes modal rule. In this study, we assess whether alternative classifiers
from the classification or supervised-learning literature—developed for situations in which class labels are known—can improve
the Bayes rule. More specifically, we investigate the performance of bootstrap-based aggregate (bagging) rules after adapting
these to the model-based clustering context. It is argued that specific issues, such as the label-switching problem, have
to be carefully addressed when using bootstrap methods in model-based clustering. Our two Monte Carlo studies show that classification
based on the Bayes rule is rather stable and difficult to improve by bootstrap-based aggregate rules, even for sparse data.
An empirical example illustrates the various approaches described in this paper. 相似文献
3.
Black-Litterman模型能够有效的解决均值-方差模型对输入(尤其是预期收益率)过于敏感的问题,从而使得其在实践中得到了广泛的应用。采用风险平价策略构造市场均衡组合,并采用基于货币周期的资产轮动收益构造主观观点组合,在将主观观点信心水平进行适当简化后,形成了改进后的Black-Litterman模型。利用我国资本市场上股票、商品和债券三种大类资产数据对改进后的Black-Litterman模型进行实证检验后发现:通过相对信心水平的调节,改进后的Black-Litterman模型能够对市场均衡组合和主观观点组合进行有效的平衡,且相对于其他资产配置组合及单种资产买入持有策略,Black-Litterman组合无论是在风险控制还是收益率上都表现的更为出色。实证结论充分说明了Black-Litterman模型的有效性,同时也从市场均衡组合、主观观点及信心水平三个方向指明了模型改进的方向。 相似文献
4.
Summary The Bayesian estimation on lifetime data under fuzzy environments is proposed in this paper. In order to apply the Bayesian
approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian
estimation method will be used to create the fuzzy Bayes point estimator by invoking the well-known theorem called “Resolution
Identity” in fuzzy set theory. On the other hand, we also provide computational procedures to evaluate the membership degree
of any given Bayes point estimate. In order to achieve this purpose, we transform the original problem into a nonlinear programming
problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation.
Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINDO. 相似文献
5.
6.
Minimax nonhomogeneous linear estimators of scalar linear parameter functions are studied in the paper under restrictions
on the parameters and variance-covariance matrix. The variance-covariance matrix of the linear model under consideration is
assumed to be unknown but from a specific set R of nonnegativedefinite matrices. It is shown under this assumption that, without
any restriction on the parameters, minimax estimators correspond to the least-squares estimators of the parameter functions
for the “worst” variance-covariance matrix. Then the minimax mean-square error of the estimator is derived using the Bayes
approach, and finally the exact formulas are derived for the calculation of minimax estimators under elliptical restrictions
on the parameter space and for two special classes of possible variance-covariance matrices R. For example, it is shown that
a special choice of a constant q
0
and a matrixW
0 defining one of the above classes R leads to the well known Kuks—Olman admissible estimator (see [16]) with a known variance-covariance
matrixW
0. Bibliography:32 titles.
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 79–92. 相似文献
7.
Value-at-Risk, despite being adopted as the standard risk measure in finance, suffers severe objections from a practical point
of view, due to a lack of convexity, and since it does not reward diversification (which is an essential feature in portfolio
optimization). Furthermore, it is also known as having poor behavior in risk estimation (which has been justified to impose
the use of parametric models, but which induces then model errors). The aim of this paper is to chose in favor or against
the use of VaR but to add some more information to this discussion, especially from the estimation point of view. Here we
propose a simple method not only to estimate the optimal allocation based on a Value-at-Risk minimization constraint, but
also to derive—empirical—confidence intervals based on the fact that the underlying distribution is unknown, and can be estimated
based on past observations. 相似文献
8.
The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of system reliability based on Exponential distribution by invoking the well-known theorem called “Resolution Identity” in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINGO (LINDO). 相似文献
9.
Olav Kallenberg 《Acta Appl Math》2007,96(1-3):271-282
The aim of this paper is to convey the basic ideas regarding some local hitting and conditioning properties of random measures.
Some very general results are obtainable in the special case of simple point processes. Though much of this theory has no
counterpart for general random measures, similar results do exist in two cases of special interest—for local time random measures
and for Dawson–Watanabe superprocesses. This is an informal account of some of the basic hitting and conditioning properties
common to all three cases. Precise statements and proofs will be provided elsewhere. 相似文献
10.
Dulce Rosas Jordi Castro Lídia Montero 《Computational Optimization and Applications》2009,44(2):289-313
The purpose of the traffic assignment problem is to obtain a traffic flow pattern given a set of origin-destination travel
demands and flow dependent link performance functions of a road network. In the general case, the traffic assignment problem
can be formulated as a variational inequality, and several algorithms have been devised for its efficient solution. In this
work we propose a new approach that combines two existing procedures: the master problem of a simplicial decomposition algorithm
is solved through the analytic center cutting plane method. Four variants are considered for solving the master problem. The
third and fourth ones, which heuristically compute an appropriate initial point, provided the best results. The computational
experience reported in the solution of real large-scale diagonal and difficult asymmetric problems—including a subset of the
transportation networks of Madrid and Barcelona—show the effectiveness of the approach. 相似文献
11.
《Advances in Applied Mathematics》1986,7(2):170-181
We exhibit a compound sequential Bayes portfolio selection algorithm based solely on the past which not only lives off market fluctuations but follows the drift as well. In fact, this sequential portfolio performs as well (up to first order terms in the exponent) as the optimal portfolio based on advance knowledge of the n-period empirical distribution of the market. Moreover, to first order in the exponent, the capital resulting from this portfolio will be no less than the best of the available stocks. This is a result that holds for every sample sequence. Thus bull markets and bear markets can not fool the investor into over-committing or under-committing his capital to the risky alternatives available to him. The goal is accomplished by a choice of portfolio which is robust with respect to futures that may differ drastically from the past. 相似文献
12.
Panagiotis Xidonas George Mavrotas Constantin Zopounidis John Psarras 《European Journal of Operational Research》2011
A fundamental principle of modern portfolio theory is that comparisons between portfolios are generally made using two criteria, corresponding to the first two moments of return distributions, namely the expected return and portfolio variance. According to this model and according to most of the portfolio models derived from the stochastic dominance approach, the group of portfolios open to comparisons is divided into two parts: on the one hand there are the efficient portfolios (those that are not dominated by any other portfolio in the group), and on the other, those that are dominated. In other words, these models do not solve for one optimal portfolio, but rather solve for an efficient set of portfolios, among which the investor must choose, given his preference system. One criticism over these models, which has often been addressed both by practitioners and academics, is that they fail to embody the objectives of the decision maker (DM), through the various stages of the decision process. Our purpose in this article is to present an integrated and innovative methodological approach for the construction and selection of equity portfolios, which will take into account the inherent multidimensional nature of the problem, while allowing the DM to incorporate his preferences in the decision process. The proposed approach, which grounds its basis on the field of multiple criteria decision making (MCDM) and more specifically on multiobjective mathematical programming (MMP), is implemented in the IPSSIS (Integrated Portfolio Synthesis and Selection Information System) decision support system (DSS). The validity of the proposed approach is tested through an illustrative application in the Athens Stock Exchange (ASE). 相似文献
13.
14.
Marco Castrillón López Jerrold E. Marsden 《Annals of Global Analysis and Geometry》2008,34(3):263-285
Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after
spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in
an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think
of this class of field theories as including examples such as a “sea of rigid bodies” with and appropriate interbody coupling
potential. 相似文献
15.
A two-parameter distribution was revisited by Chen (2000) [7]. This distribution can have a bathtub-shaped or increasing failure rate function which enables it to fit real lifetime data sets. Maximum likelihood and Bayes estimates of the two unknown parameters are discussed in this paper. It is assumed in the Bayes case that the unknown parameters have gamma priors. Explicit forms of Bayes estimators cannot be obtained. Different approximations are used to establish point estimates and two sided Bayesian probability intervals for the parameters. Monte Carlo simulations are applied to the comparison between the maximum likelihood estimates and the approximate Bayes estimates obtained under non-informative prior assumptions. Analysis of a real data set is also been presented for illustrative purposes. 相似文献
16.
Dominique Fourdrinier William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2003,55(4):803-816
We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In
3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988,
On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual
estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized
Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly,
that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax
estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes
estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator
of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss.
Research supported by NSF Grant DMS-97-04524. 相似文献
17.
Thomas Galtier 《Extremes》2011,14(2):157-166
In this note upcrossing intensity of a level u by a non-Gaussian process—the Laplace Moving Average (LMA)—is estimated by means of a saddle point approximation of Rice’s
formula. A LMA-process is defined by power spectral density, skewness and kurtosis parameters. The method is illustrated by
measurements of sea surface elevation and stresses in a vessel. 相似文献
18.
Approaches for classifying resolvable balanced incomplete block designs (RBIBDs) are surveyed. The main approaches can roughly
be divided into two types: those building up a design parallel class by parallel class and those proceeding point by point.
With an algorithm of the latter type — and by refining ideas dating back to 1917 and the doctoral thesis by Pieter Mulder
— it is shown that the list of seven known resolutions of 2-(28, 4, 1) designs is complete; these objects are also known as
the resolutions of unitals on 28 points.
This research was supported in part by the Academy of Finland, Grants No. 107493, 110196, and 117499. 相似文献
19.
In this paper we study the asymptotic behavior of Bayes estimators for hidden Markov models as the number of observations
goes to infinity. The theorem that we prove is similar to the Bernstein—von Mises theorem on the asymptotic behavior of the
posterior distribution for the case of independent observations. We show that our theorem is applicable to a wide class of
hidden Markov models. We also discuss the implication of the theorem’s assumptions for several models that are used in practical
applications such as ion channel kinetics.
相似文献
20.
E. Welzl 《Discrete and Computational Geometry》2001,25(3):351-364
Let S be a set of n points in d -space, no i+1 points on a common (i-1) -flat for 1 ≤ i ≤ d . An oriented (d-1) -simplex spanned by d points in S is called a j-facet of S if there are exactly j points from S on the positive side of its affine hull. We show: (*) {\em For j ≤ n/2 - 2 , the total number of (≤ j) -facets (i.e. the number of i -facets with 0 ≤ i ≤ j ) in 3-space is maximized in convex position (where these numbers are known).} A large part of this presentation is a preparatory
review of some basic properties of the collection of j -facets—some with their proofs—and of relations to well-established concepts and results from the theory of convex polytopes
(h -vector, Dehn—Sommerville relations, Upper Bound Theorem, Generalized Lower Bound Theorem). The relations are established
via a duality closely related to the Gale transform—similar to previous works by Lee, by Clarkson, and by Mulmuley.
A central definition is as follows. Given a directed line ℓ and a j -facet F of S , we say that {\it ℓ enters F } if ℓ intersects the relative interior of F in a single point, and if ℓ is directed from the positive to the negative side of F . One of the results reviewed is a tight upper bound of j+d-1 \choose d-1 on the maximum number of j -facets entered by a directed line.
Based on these considerations, we also introduce a vector for a point relative to a point set, which—intuitively speaking—expresses
``how interior' the point is relative to the point set. This concept allows us to show that statement (*) above is equivalent
to the Generalized Lower Bound Theorem for d -polytopes with at most d+4 vertices.
Received May 21, 1999, and in revised form July 6, 2000. Online publication January 17, 2001. 相似文献