Tonghui Wang

Active microwave imaging. I. 2-D forward and inverse scattering methods

Active microwave imaging (MWI) for the detection of breast tumors is an emerging technique to complement existing X-ray mammography. The potential advantages of MWI arise mainly from the high contrast of electrical properties between tumors and normal breast tissue. However, this high contrast also increases the difficulty of forming an accurate image because of increased multiple scattering. To address this issue, we develop fast forward methods based on the combination of the extended Born approximation, conjugate- and biconjugate-gradient methods, and the fast Fourier transform. We propose two nonlinear MWI algorithms to improve the resolution for the high-contrast media encountered in microwave breast-tumor detection. Numerical results show that our algorithms can accurately model and invert for the high-contrast media in breast tissue. The outcome of the inversion algorithms is a high-resolution digital image containing the physical properties of the tissue and potential tumors.

Distribution of matrix quadratic forms under skew-normal settings

For a class of skew-normal matrix distributions, the density function, moment generating function and independence conditions are obtained. The noncentral skew Wishart distribution is defined, and the necessary and sufficient conditions under which a quadratic form is noncentral skew Wishart distributed random matrix are established. A new version of Cochran’s theorem is given. For illustration, our main results are applied to two examples.

Multivariate dependence concepts through copulas

In this paper, multivariate dependence concepts such as affiliation, association and positive lower orthant dependent are studied in terms of copulas. Relationships among these dependent concepts are obtained. An affiliation is a notion of dependence among the elements of a random vector. It has been shown that the affiliation property is preserved using linear interpolation of subcopula. Also our results are applied to the multivariate skew-normal copula. As an application, the dependence concepts used in auction with affiliated signals are discussed. Several examples are given for illustration of the main results.

A measure of mutual complete dependence in discrete variables through subcopula

Siburg and Stoimenov 12 gave a measure of mutual complete dependence of continuous variables which is different from Spearmans ? and Kendalls ?. In this paper, a similar measure of mutual complete dependence is applied to discrete variables. Also two measures for functional relationships, which are not bijection, are investigated. For illustration of our main results, several examples are given.

Some Applications of One-sided Skew Distributions

In this paper, we introduce a class of skew distributions which could be used to describe data in economics and business when certain assumptions about the elements in a population are satisfied. Examples are given to show the fitness of the distributions on data sets in economics.

Dependence and Association Concepts through Copulas

In this paper, dependence concepts such as affiliation, left-tail decreasing, right-tail increasing, positively regression dependent, and positively quadrant dependent are studied in terms of copulas. Relationships among these dependent concepts are obtained. An affiliation is a notion of dependence between two positively dependent random variables and some measures of it are provided. It has been shown that the affiliation property is preserved using bilinear extensions of subcopula. As an application, the affiliation property of skew-normal copula is investigated. For illustration of dependent concepts and their relationships, several examples are given.

Risk Measures and Asset Pricing Models with New Versions of Wang Transform

To provide incentive for active risk managements, tail-preserving and coherent distortion risk measures are needed in the actuarial and financial fields. In this paper we propose new versions of Wang transform using two different forms of skew-normal distribution functions, and prove that the related risk measures in Choquet integral form are coherent and degree-two tail-preserving for usual bi-atomic risk distributions. Also under some plausible conditions, the portfolio optimization is explored for the capital asset pricing model where the pricing strategy uses the new Wang transforms as the distortion functions.

The Multivariate Extended Skew Normal Distribution and Its Quadratic Forms

In this paper, the class of multivariate extended skew normal distributions is introduced. The properties of this class of distributions, such as, the moment generating function, probability density function, and independence are discussed. Based on this class of distributions, the extended noncentral skew chi-square distribution is defined and its properties are investigated. Also the necessary and sufficient conditions, under which a quadratic form of the model has an extended noncentral skew chi-square distribution, are obtained. For illustration of our main results, several examples are given.

On Consistency of Estimators Based on Random Set Vector Observations

In this paper, the characterization of the joint distribution of random set vector by the belief function is investigated. A routine of calculating the bivariate coarsening at random model of finite random sets is obtained. In the context of reliable computations with imprecise data, we show that the maximum likelihood estimators of parameters in CAR model are consistent. Several examples are given to illustrate our results.

Semi-heuristic poverty measures used by economists: Justification motivated by fuzzy techniques

To properly gauge the extent of poverty in a country or in a region, economists use semi-heuristic poverty measures such as the Foster-Greer-Thorbecke (FGT) metric. These measures are used because it was empirically shown that they capture the commonsense meaning of the extent of poverty better than previously proposed measures. However, without a theoretical justification, we cannot guarantee that these semi-heuristic measures will work in other situations as well. So, it is desirable to look for poverty measures which can be theoretically justified. In this paper, we first use fuzzy techniques to provide a commonsense interpretation of FGT poverty measures, and then show that how this informal interpretation can be transformed into a formal justification of the FGT property measures - from certain reasonable assumptions.