Model Selection for Gaussian Mixture Models

This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models. The proposed method is shown to be statistically consistent in determining of the number of components. A modified EM algorithm is developed to simultaneously select the number of components and to estimate the mixing weights, i.e. the mixing probabilities, and unknown parameters of Gaussian distributions. Simulations and a real data analysis are presented to illustrate the performance of the proposed method

Isospin and a possible interpretation of the newly observed X(1576)

Recently, the BES collaboration observed a broad resonant structure X(1576) with a large width being around 800 MeV and assigned its $J^{PC}$ number to $1^{--}$. We show that the isospin of this resonant structure should be assigned to 1. This state might be a molecule state or a tetraquark state. We study the consequences of a possible $K^*(892)$-${\bar \kappa}$ molecular interpretation. In this scenario, the broad width can easily be understood. By using the data of $B(J/\psi\to X\pi^0)\cdot B(X\to K^+K^-)$, the branching ratios $B(J/\psi\to X\pi^0)\cdot B(X\to \pi^+\pi^-)$ and $B(J/\psi\to X\pi^0)\cdot B(X\to K^+K^-\pi^+\pi^-)$ are further estimated in this molecular state scenario. It is shown that the $X\to \pi^+\pi^-$ decay mode should have a much larger branching ratio than the $X\to K^+K^-$ decay mode has. As a consequence, this resonant structure should also be seen in the $J/\psi\to \pi^+\pi^-\pi^0$ and $J/\psi\to K^+K^-\pi^+\pi^-\pi^0$ processes, especially in the former process. Carefully searching this resonant structure in the $J/\psi\to \pi^+\pi^-\pi^0$ and $J/\psi\to K^+K^-\pi^+\pi^-\pi^0$ decays should be important for understanding the structure of X(1567).Comment: 5 pages, ReVTeX4, 3 figures. Version accepted for publication as a brief report in Phys. Rev.

Sorting by Foot: Consumable Travel-for Local Public Good and Equilibrium Stratification

This paper reexamine Tiebout’s hypothesis of endogenous sorting in a competitive spatial equilibrium setup with both income and preference heterogeneity. Agents decide endogenously the number of trips to consume a travel-for congestable local public good. We show that the equilibrium configuration may be completely segregated, incompletely segregated or completely integrated, depending crucially on the scale of local public good services, relative market rents and the underlying income/preference/local tax parameters. Segregated equilibrium may feature endogenous sorting purely by income or by both income and preferences. Multiple equilibria may arise when the equilibrium configuration is incompletely segregated.Endogenous Sorting, Integrated/Segregated Equilibrium, Income/Preference Heterogeneity

"Spatial Competition in Variety and Number of Stores"

We propose location-then-variety competition for amulti-productandmulti-store oligopoly,in which the number of firms, the number of stores and their location, and the number of varieties are endogenously determined. We show that ascompared to price-then-variety competition, location-then-variety competition with multi-stores yields a much richer set of equilibrium outcomes, such as market segmentation, interlacing, sandwich and enclosure.

Welfare Analysis of the Number and Locations of Local Public Facilities

We develop a discrete or finite household model with congestable local public goods where the level of provision, the number of facilities and their locations are all endogenously determined in a purely normative context. We prove the existence of an equal-treatment identical-provision second best optimum, where all households are required to reach the same utility level, the provision of local public good is required to be the same at all facilities, and all facilities must serve the same number of consumers. Such an optimal public facility configuration may or may not be geographically centralized if there is only a single public facility site. Moreover, the optimal public facility configuration could be either concentrated (single site) or dispersed (multiple sites), depending crucially on the degree of congestability and the household valuation of the local public good as well as the commuting cost.Congestable Local Public Goods, Optimal Public Facility Configurations