The generalized varying coefficient partially linear model with a growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation and inference. When the number of parameters grows with sample size, the existence and asymptotic normality of the profile likelihood estimator are establ...

The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation and inference. When the number of parameters grows with sample size, the existence and asymptotic normality of the profile likelihood estimator are establis...

Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. We consider a pseudo-profile likelihood approach to estimation and testing for single-index quantile regression models. We establish the asymptotic normality of the index coefficient estimator as well as the optimal conve...

We consider reaction-diffusion systems on the infinite line that exhibit a family of spectrally stable spatially periodic wave trains u0(kx− ωt; k) that are parameterized by the wave number k. We prove stable diffusive mixing of the asymptotic states u0(kx + φ±; k) as x → ±∞ with different phases φ− 6= φ+ at infinity for solutions that initially converge to these states as x → ±∞. The proof is ...

in this paper we discuss on the fixed points of asymptotic contractions and boyd-wong type contractions in uniform spaces equipped with an e-distance. a new version ofkirk's fixed point theorem is given for asymptotic contractions and boyd-wong type contractions is investigated in uniform spaces.

We prove a definitive theorem on the asymptotic stability of point vortex solutions to full Euler equation in 2 dimensions. More precisely, we show that small, Gevrey smooth, and compactly supported perturbation leads global solution 2D, which converges weakly as $t\to\infty$ radial profile with respect vortex. The position vortex, is time dependent, stabilizes rapidly becomes center final, pro...

We develop a model of information exchange through communication and investigate its implications for information aggregation in large societies. An underlying state determines payoffs from different actions. Agents decide which others to form a costly communication link with incurring the associated cost. After receiving a private signal correlated with the underlying state, they exchange info...

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metr...