介质波导中非均匀性散射的T矩阵方法

采用广泛应用于波散射分析的T矩阵方法,研究了介质波导中导波与非均匀性的相互作用问题。原理上讲,文中的分析适用于任意结构的介质波导和任意形状的非均匀性。当介质波导为单模圆柱光纤而非均匀性为球形时,得到的HE_11模传输和反射系数的解析表达式与文献中应用体积分方程法所得到的结果完全一致。     

单模光纤中非均匀性内有源分子的非弹性散射

根据有源分子的等效振荡偶极子模型,利用并矢格林函数方法及场的矢量柱波函数和矢量球波函数展开,本文处理了埋入在单模光纤中一个非均匀性內有源分子的非弹性散射问题。对于非均匀性为球形及单模光纤的情况,我们得到了非弹性IIE_(11)模散射系数的解析表达式,入射与散射奇/偶模之间的耦合问题也可同时考虑。     

Marginal inhomogeneity models for square contingency tables with nominal categories

For the analysis of square contingency tables with nominal categories, this paper proposes two kinds of models that indicate the structure of marginal inhomogeneity. One model states that the absolute values of log odds of the row marginal probability to the corresponding column marginal probability for each category i are constant for every i. The other model states that, on the condition that an observation falls in one of the off-diagonal cells in the square table, the absolute values of log odds of the conditional row marginal probability to the corresponding conditional column marginal probability for each category i are constant for every i. These models are used when the marginal homogeneity model does not hold, and the values of parameters in the models are useful for seeing the degree of departure from marginal homogeneity for the data on a nominal scale. Examples are given.     

Asymptotic properties of the inhomogeneous Lotka‐Von Foerster system

In this paper, we investigate an extension of the multistate stable population model, which makes allowances for migration. The model is formulated as an inhomogeneous system of first order partial differential equations with integral boundary conditions. First, we construct its classical solution. Next, we reformulate the system as an abstract inhomogeneous Cauchy problem on a Banach space, and give its mild solution by using the population semigroup. Our main purpose is to investigate the asymptotic behavior of the mild solution.     

Local Adaptivity of Kernel Estimates with Plug-in Local Bandwidth Selectors

In non-parametric function estimation selection of a smoothing parameter is one of the most important issues. The performance of smoothing techniques depends highly on the choice of this parameter. Preferably the bandwidth should be determined via a data-driven procedure. In this paper we consider kernel estimators in a white noise model, and investigate whether locally adaptive plug-in bandwidths can achieve optimal global rates of convergence. We consider various classes of functions: Sobolev classes, bounded variation function classes, classes of convex functions and classes of monotone functions. We study the situations of pilot estimation with oversmoothing and without oversmoothing. Our main finding is that simple local plug-in bandwidth selectors can adapt to spatial inhomogeneity of the regression function as long as there are no local oscillations of high frequency. We establish the pointwise asymptotic distribution of the regression estimator with local plug-in bandwidth.     

Hidden Second‐order Stationary Spatial Point Processes

In the existing statistical literature, the almost default choice for inference on inhomogeneous point processes is the most well‐known model class for inhomogeneous point processes: reweighted second‐order stationary processes. In particular, the K‐function related to this type of inhomogeneity is presented as the inhomogeneous K‐function. In the present paper, we put a number of inhomogeneous model classes (including the class of reweighted second‐order stationary processes) into the common general framework of hidden second‐order stationary processes, allowing for a transfer of statistical inference procedures for second‐order stationary processes based on summary statistics to each of these model classes for inhomogeneous point processes. In particular, a general method to test the hypothesis that a given point pattern can be ascribed to a specific inhomogeneous model class is developed. Using the new theoretical framework, we reanalyse three inhomogeneous point patterns that have earlier been analysed in the statistical literature and show that the conclusions concerning an appropriate model class must be revised for some of the point patterns.     

Statistical Inference for Transformation Inhomogeneous Point Processes

Abstract.  Statistical inference for exponential inhomogeneous Markov point processes by transformation is discussed. It is argued that the inhomogeneity parameter can be estimated, using a partial likelihood based on an inhomogeneous Poisson point process. The inhomogeneity parameter can thereby be estimated without taking the interaction into account, which simplifies the statistical analysis considerably. Data analysis and simulation experiments support the results.