Stein-rules and Testing in Generalized Mean Reverting Processes with Multiple Change-points

In this thesis, we consider inference problems about the drift parameter vector in generalized mean reverting processes with multiple and unknown change-points. In particular, we study the case where the parameter may satisfy uncertain restrictions. As compared to the results in the literature, we generalize some findings in five ways. First, we consider a statistical model which incorporates uncertain prior information and the uncertain restriction includes as a special case the nonexistence of the change-points. Second, we derive the unrestricted estimator (UE) and the restricted estimator~(RE), and we study their asymptotic properties. Specifically, in the context of a known number of change-points, we derive the joint asymptotic normality of the UE and the RE, under the set of local alternative hypotheses. Third, we derive a test for testing the hypothesized restriction and we derive its asymptotic local power. We also prove that the proposed test is consistent. Fourth, we construct a class of shrinkage type estimators (SEs) which includes as special cases the UE, RE, and classical SEs. Fifth, we derive the relative risk dominance of the proposed estimators. More precisely, we prove that the SEs dominate the UE. The novelty of the derived results consists in the fact that the dimensions of the proposed estimators are random variables. Finally, we present some simulation results which corroborate the established theoretical findings

Two Higgs Doublets Model in Gauge-Higgs Unification framework

We discuss the realization of two Higgs doublets model in the framework of 6 dimensional Gauge-Higgs Unification model with a simple Lie group G_M. Two Higgs SU(2)_L doublets can emerge at the low energy effective theory, and the quartic coupling terms in the scalar potential, essential for the electroweak symmetry breaking, are now G_M gauge invariant and permissive. A realistic two Higgs doublets model can possibly be obtained only when two of the root vectors associated with the would-be Higgs doublets and the root vector for SU(2)_L form an isosceles triangle with vertex angle either of Pi/3, Pi/2, or 2Pi/3. Moreover, depending on G_M, the scalar potential of resulting two Higgs doublets model can admit only a few limited forms. The mass spectrum of the physical Higgs and the weak mixing angle are briefly discussed.Comment: 5 Pages and 1 figure. Matches published version in PR

Hot Surface Ignition of A Composite Fuel Droplet

The present study examines the characteristics of conductive heating (up to ignition temperature) of a composite fuel droplet based on coal, liquid petroleum products, and water. In this paper, we have established the difference between heat transfer from a heat source to a fuel droplet in case of conductive (hot surface) and convective (hot gas) heat supply. The Leidenfrost effect influences on heat transfer characteristics significantly due to the gas gap between a composite fuel droplet and a hot surface

A Secular Interpretation of God in Christianity under Holographic Theory

God is the core of Christian religion, where the whole Christian faith and creed rest upon. While the relationship between the mortal and God is the fundamental question that makes Christianity distinguish from other religions. This paper aims to discover the secular meaning of God, such as in China, with the perspective of relationship between God and mortal and the theory of holographic theory, which brings atheists a better comprehension of human beings and the universe through a religious philosophy