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1.
GeD spline estimation of multivariate Archimedean copulas   总被引:1,自引:0,他引:1  
A new multivariate Archimedean copula estimation method is proposed in a non-parametric setting. The method uses the so-called Geometrically Designed splines (GeD splines) to represent the cdf of a random variable Wθ, obtained through the probability integral transform of an Archimedean copula with parameter θ. Sufficient conditions for the GeD spline estimator to possess the properties of the underlying theoretical cdf, K(θ,t), of Wθ, are given. The latter conditions allow for defining a three-step estimation procedure for solving the resulting non-linear regression problem with linear inequality constraints. In the proposed procedure, finding the number and location of the knots and the coefficients of the unconstrained GeD spline estimator and solving the constraint least-squares optimisation problem are separated. Thus, the resulting spline estimator is used to recover the generator and the related Archimedean copula by solving an ordinary differential equation. The proposed method is truly multivariate, it brings about numerical efficiency and as a result can be applied with large volumes of data and for dimensions d≥2, as illustrated by the numerical examples presented.  相似文献   

2.
The land cover fractions (LCFs) and spectral reflectance of photosynthetic vegetation (PV), nonphotosynthetic vegetation (NPV), and bare soil were measured at 58 sites in semi-arid and arid regions of Mongolia in the summers of 2005 and 2006. These data sets allowed a detailed assessment of the impact of measurement geometry as represented by the solar zenith angle θs, sensor view zenith angle θv and azimuth view angle ? in the estimation of LCF values by means of the spectral unmixing model (SUM). The bidirectional distribution function (BRDF) was fitted to the reflectance data and then used to produce reflectance at various measurement geometries. LCFs from these reflectance data for a given combination of θs, θv, and ? were compared with visually determined LCFs. It was found that θs in the range of 30-45° produced a better agreement of LCFs. For θv, the agreement is not very sensitive to the choice of angle for the range 30-70°, although θv = 50° showed a slightly better performance. The azimuth view angle does not have strong influences to the LCF estimation, except for the case of ? = 180° (view toward the sun), which does not allow precise fitting of BRDF function over a tall vegetation site. Overall, this study verified the results of earlier studies obtained mostly for the American continents that SUM is capable of producing LCF estimates accurately and also found that its accuracy was, in general, much better than that by the more traditional approach of the supervised classification method (SCM) applied to images of a digital camera.  相似文献   

3.
This paper deals with the J-spectral factorization for general discrete rational matrices. A simple approach based on the Kalman filtering in Krein space is proposed. The main idea is to construct a stochastic state space filtering model in Krein space such that the spectral matrix of the output is equal to the rational matrix to be factorized. The spectral factor is then easily derived by using the generalized Kalman filtering in Krein space, which is similar to the H2 spectral factorization. Our approach unifies the treatment of the H2 spectral factorization and the J-spectral factorization. The applications of the derived results in H and risk-sensitive estimation for both nonsingular and singular systems are demonstrated.  相似文献   

4.
This article studies a locally optimal test φ for testing H0:θθ0 versus H1:θ<θ0 for the lifetime parameter θ in an exponential distribution based on type-I censored data. Certain properties associated with φ are addressed. We compare the performance of φ with that of Spurrier and Wei’s [Spurrier, J.D., Wei, L.J., 1980. A test of the parameter of the exponential distribution in the type-I censoring case. J. Amer. Statist. Assoc. 75, 405-409] test φSW, which is based on the MLE of θ. The exact powers and asymptotic powers of φ and φSW are computed. The numerical results indicate that the power of φ is better than that of φSW when θ(0<θ<θ0) is close to θ0.  相似文献   

5.
For a sequence of independent, identically distributed random variables any limiting point process for the time normalized exceedances of high levels is a Poisson process. However, for stationary dependent sequences, under general local and asymptotic dependence restrictions, any limiting point process for the time normalized exceedances of high levels is a compound Poisson process, i.e., there is a clustering of high exceedances, where the underlying Poisson points represent cluster positions, and the multiplicities correspond to the cluster sizes. For such classes of stationary sequences there exists the extremal indexθ, 0?θ?1, directly related to the clustering of exceedances of high values. The extremal index θ is equal to one for independent, identically distributed sequences, i.e., high exceedances appear individually, and θ>0 for “almost all” cases of interest. The estimation of the extremal index through the use of the Generalized Jackknife methodology, possibly together with the use of subsampling techniques, is performed. Case studies in the fields of environment and finance will illustrate the performance of the new extremal index estimator comparatively to the classical one.  相似文献   

6.
This study deals with the classical and Bayesian estimation of the parameters of a k-components load-sharing parallel system model in which each component's lifetime follows Lindley distribution. Initially, the failure rate of each of the k components in the system is h(t,θ1) until the first component failure. However, upon the first failure within the system, the failure rates of the remaining (k − 1) surviving components change to h(t,θ2) and remain the same until next failure. After second failure, the failure rates of (k − 2) surviving components change to h(t,θ3) and finally when the (k − 1)th component fails, the failure rate of the last surviving component becomes h(t,θk). In classical set up, the maximum likelihood estimates of the load share parameters, system reliability and hazard rate functions along with their standard errors are computed. 100 × (1 − γ)% confidence intervals and two bootstrap confidence intervals for the parameters have also been constructed. Further, by assuming Jeffrey's invariant and gamma priors of the unknown parameters, Bayes estimates along with their posterior standard errors and highest posterior density credible intervals of the parameters are obtained. Markov Chain Monte Carlo technique such as Metropolis–Hastings algorithm has been utilized to generate draws from the posterior densities of the parameters.  相似文献   

7.
Given angular data θ1,…,θn∈[0,2π) a common objective is to estimate the density. In case that a kernel estimator is used, bandwidth selection is crucial to the performance. A “plug-in rule” for the bandwidth, which is based on the concentration of a reference density, namely, the von Mises distribution is obtained. It is seen that this is equivalent to the usual Euclidean plug-in rule in the case where the concentration becomes large. In case that the concentration parameter is unknown, alternative methods are explored which are intended to be robust to departures from the reference density. Simulations indicate that “wrapped estimators” can perform well in this context. The methods are applied to a real bivariate dataset concerning protein structure.  相似文献   

8.
In this paper, we consider the robust Hurwitz stability analysis problems of a single parameter-dependent matrix A(θ)?A0+θA1 over θ∈[-1,1], where A0,A1Rn×n with A0 being Hurwitz stable. In particular, we are interested in the degree N of the polynomial parameter-dependent Lyapunov matrix (PPDLM) of the form that ensures the robust Hurwitz stability of A(θ) via . On the degree of PPDLMs, Barmish conjectured in early 90s that if there exists such P(θ), then there always exists a first-degree PPDLM P(θ)=P0+θP1 that meets the desired conditions, regardless of the size or rank of A0 and A1. The goal of this paper is to falsify this conjecture. More precisely, we will show a pair of the matrices A0,A1R3×3 with A0+θA1 being Hurwitz stable for all θ∈[-1,1] and prove rigorously that the desired first-degree PPDLM does not exist for this particular pair. The proof is based on the recently developed techniques to deal with parametrized LMIs in an exact fashion and related duality arguments. From this counter-example, we can conclude that the conjecture posed by Barmish is not valid when n?3 in general.  相似文献   

9.
On the structure of generalized rough sets   总被引:3,自引:0,他引:3  
In this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that
1.
Any reflexive binary relation determines a topology.
2.
If θ is a reflexive and symmetric relation on a set X, then O={AX|θ-(A)=A} is a topology such that A is open if and only if it is closed.
3.
Conversely, for every topological space (X,O) satisfying the condition that A is open if and only if it is closed, there exists a reflexive and symmetric relation R such that O={AX|R-(A)=A}.
4.
Let θ be an equivalence relation on X. For any pseudo ω-closed subset A of Xθ(A) is an ω-closed set if and only if ω(xx, … , x) ∈ θ(A) for any x ∈ X.
Moreover we consider properties of generalized rough sets.  相似文献   

10.
We consider an uncapacitated 2-hierarchal location-allocation problem where p1 level 1 facilities and p2 level 2 facilities are to be located among n(?p1 + p2) potential locations so as to minimize the total weighted travel distance to the facilities when θ, (0 ? θ ? 1) fraction of the demand from a level 1 facility is referred to a level 2 facility. At most one facility may be located at any location. In this model, a level 2 facility provides services in addition to services provided by a level 1 facility.The problem is formulated as a mathematical programming problem, relaxed and solved by a subgradient optimization procedure. The proposed procedure is illustrated with an example.  相似文献   

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