Beta-Exponential Distribution (BED) is proposed by Nadarajah and Samuel Kotz which contains several well-known distributions. With the addition of two shape parameters, this distribution can fit a wider range of data and therefore has been widely used in life testing. However, there are few literature on the properties of order statitics from this distribution, especially the best linear unbiased estimation (BLUE) of the location-scale parameters. In this paper, a new algorithm is proposed by us to obtain closed-form expression for variance-covariance matrix of order statistics from this distribution and give the BLUE for the location-scale parameters for the first time. Compared with several other classical parameter estimation methods (MLE, trimmed L-moments (TL-moments), probability weighted moments (PWM)), BLUE is more suitable for location-scale parameter estimation under small sample size for this distribution. Besides, the explicit expressions for moments of order statistics under the independent identically distributed (IID) case and independent not identically distributed (INID) case are also derived. Furthermore, for BED with three parameters (two shape parameters and scale parameter), we propose an improved TL-moments estimation method based on order statistics isotone transformation under two different trimmed schemes ( and ) as well as an improved PWM estimation method and conduct simulation study to compare the performance of each new method with MLE. As a result, the improved TL-moments estimation () and the improved PWM estimation perform better than MLE on the whole.
Category is put to work in the non-associative realm in the article. We focus on a typical example of non-associative category. Its objects are octonionic bimodules, morphisms are octonionic para-linear maps, and compositions are non-associative in general. The octonionic para-linear map is the main object of octonionic Hilbert theory because of the octonionic Riesz representation theorem. An octonionic para-linear map f is in general not octonionic linear since it subjects to the rule
High-dimensional covariance matrices have attracted much attention of statisticians and econometricians during the past decades. Vast literature is devoted to the research in high-dimensional covariance matrices. However, most of them are for constant covariance matrices. In many applications, constant covariance matrices are not appropriate, e.g., in portfolio allocation, dynamic covariance matrices would make much more sense. Simply assuming each entry of a covariance matrix is a function of time to introduce a dynamic structure would not work. In this paper, we are going to introduce a class of high-dimensional dynamic covariance matrices in which a kind of additive structure is embedded. We will show the proposed high-dimensional dynamic covariance matrices have many advantages in applications. An estimation procedure is also proposed to estimate the proposed high-dimensional dynamic covariance matrices. Asymptotic properties are built to justify the proposed estimation procedure. Intensive simulation studies show the proposed estimation procedure works very well when sample size is finite. Finally, we apply the proposed high-dimensional dynamic covariance matrices, together with the proposed estimation procedure, to portfolio allocation. The results look very interesting.
By using the method of space mapping, basis functions of biquadratic polynomial spline spaces over the hierarchical T-meshes without limitation for level difference can be constructed. In this paper, the basis functions defined over hierarchical T-meshes with high level differences are adopted for the application in the isogeometric analysis problems with rapidly changing local features. Without subdividing redundant cells to ensure the level difference of the adjacent cells, the refinement becomes more local, and fewer cells are subdivided for each refinement of the hierarchical T-mesh. Therefore, the dimension of the biquadratic polynomial spline space over the hierarchical T-mesh can be reduced, the superfluous control points or coefficients can be avoided, and the quantity of calculations can be decreased. Numerical examples show that these basis functions can work well on physical domains with different boundaries for the application in IGA.
Time series of counts observed in practice often exhibit overdispersion or underdispersion, zero inflation and even heavy-tailedness (the tail probabilities are non-negligible or decrease very slowly). In this article, we propose a more flexible integer-valued GARCH model based on the generalized Conway–Maxwell–Poisson distribution to model time series of counts, which offers a unified framework to deal with overdispersed or underdispersed, zero-inflated and heavy-tailed time series of counts. This distribution generalizes the Conway–Maxwell–Poisson distribution by adding a parameter, which plays the role of controlling the length of the tail. We investigate basic properties of the proposed model and obtain estimators of parameters via the conditional maximum likelihood method. The numerical results with both simulated and real data confirm the good performance of the proposed model.
For designs of computer experiments, two important and desirable properties are projection uniformity and column-orthogonality. However, it is always a challenging task to construct designs with both properties. This paper constructs a series of designs which possess both (near) column-orthogonality and projection uniformity, called (nearly) column-orthogonal mappable nearly orthogonal arrays (MNOAs). Furthermore, we enhance the MNOAs’ projection uniformity on any one dimension by using the constructed (nearly) column-orthogonal MNOAs and rotation matrices. Compared with the existing results (such as Sun and Tang in J Am Stat Assoc 112:683–689, 2017), the newly constructed designs are able to accommodate more design columns and have a much better projection uniformity, for the same run sizes.
In this paper, we consider symbolic (hybrid trigonometric) parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in each block of functions are different. We prove that the varieties parametrizable in this way are exactly the class of real unirational varieties of any dimension. In addition, we provide symbolic algorithms to implicitize and to convert a hybrid trigonometric parametrization into a unirational one, and vice versa. We illustrate by some examples the applicability of having these different types of parametrizations, namely, hybrid trigonometric and unirational.
We discuss regression analysis of current status data with the additive hazards model when the failure status may suffer misclassification. Such data occur commonly in many scientific fields involving the diagnosis test with imperfect sensitivity and specificity. In particular, we consider the situation where the sensitivity and specificity are known and propose a nonparametric maximum likelihood approach. For the implementation of the method, a novel EM algorithm is developed, and the asymptotic properties of the resulting estimators are established. Furthermore, the estimated regression parameters are shown to be semiparametrically efficient. We demonstrate the empirical performance of the proposed methodology in a simulation study and show its substantial advantages over the naive method. Also an application to a motivated study on chlamydia is provided.