In analyzing semi-continuous data, two-part model is a widely appreciated tool, in which two components are enclosed to characterize the mixing proportion of zeros and the actual level of positive values in semi-continuous data. The primary interest underlying such a model is primarily to exploit the dependence of the observed covariates on the semi-continuous variables; as such, the exploitation of unobserved heterogeneity is sometimes ignored. In this paper, we extend the conventional two-part regression model to much more general situations where multiple latent factors are considered to interpret the latent heterogeneity arising from the absence of covariates. A structural equation is constructed to describe the interrelationships between the latent factors. Moreover, a general statistical analysis procedure is developed to accommodate semi-continuous, ordered and unordered data simultaneously. A procedure for parameter estimation and model assessment is developed under a Bayesian framework. Empirical results including a simulation study and a real example are presented to illustrate the proposed methodology.
We study the solutions of elliptic Yang–Mills equation and we give a description of their asymptotic behaviors in dimensions . These solutions serve as the ground state solutions for super-critical Yang–Mills heat flow equation; thus, this result provides the background for potential blow-up research.
Issues concerning spatial dependence among cross-sectional units in econometrics have received more and more attention, while in statistical modeling, rarely can the analysts have a priori knowledge of the dependency relationship of the response variable with respect to independent variables. This paper proposes an automatic structure identification and variable selection procedure for semiparametric spatial autoregressive model, based on the generalized method of moments and the smooth-threshold estimating equations. The novel method is easily implemented without solving any convex optimization problems. Model identification consistency is theoretically established in the sense that the proposed method can automatically separate the linear and zero components from the varying ones with probability approaching to one. Detailed issues on computation and turning parameter selection are discussed. Some Monte Carlo simulations are conducted to demonstrate the finite sample performance of the proposed procedure. Two empirical applications on Boston housing price data and New York leukemia data are further considered.
In this paper, the averaging principle is researched for slow–fast stochastic partial differential equations driven by multiplicative noises. The optimal orders for the slow component that converges to the solution of the corresponding averaged equation have been obtained by using the Poisson equation method under some appropriate conditions. More precisely, the optimal orders are 1/2 and 1 for the strong and weak convergences, respectively. It is worthy to point that two kinds of strong convergence are studied here and the stronger one of them answers an open question by Bréhier in [3, Remark 4.9].
In this paper, we derive an averaging principle for a fast–slow system of stochastic differential equations (SDEs) involving distribution-dependent coefficients driven by both fractional Brownian motion (fBm) and standard Brownian motion (Bm). We first establish the existence and uniqueness of solutions of the fast–slow system and the corresponding averaging equation. Then, we show that the slow component strongly converges to the solution of the associated averaged equation.
This article is focused on the problem to measure and test the conditional mean dependence of a response variable on a predictor variable. A local influence detection approach is developed combining with the martingale difference divergence (MDD) metric, and an efficient wild bootstrap implementation is given. The obtained new metric of the conditional mean dependence holds the merits of MDD, while it is more sensitive than the original one, and leads to a powerful test to nonlinear relationships. It is shown by simulations that the proposed test can achieve higher power for general conditional mean dependence relationships even in high-dimensional settings. Theoretical asymptotic properties of the local influence test statistic are given, and a real data analysis is also presented for further illustration. The localization idea could be combined with other conditional mean dependence metrics.
Motivated by an analysis of causal mechanism from economic stress to entrepreneurial withdrawals through depressed affect, we develop a two-layer generalized varying coefficient mediation model. This model captures the bridging effects of mediators that may vary with another variable, by treating them as smooth functions of this variable. It also allows various response types by introducing the generalized varying coefficient model in the first layer. The varying direct and indirect effects are estimated through spline expansion. The theoretical properties of the estimated direct and indirect coefficient functions including estimation biases, asymptotic distributions and so forth, are explored. Simulation studies validate the finite-sample performance of the proposed estimation method. A real data analysis based on the proposed model discovers some interesting behavioral economic phenomenon, that self-efficacy influences the deleterious impact of economic stress, both directly and indirectly through depressed affect, on business owners’ withdrawal intentions.
In this work, we construct and study a family of robust nonparametric estimators for a regression function based on kernel methods. The data are functional, independent and identically distributed, and are linked to a single-index model. Under general conditions, we establish the pointwise and uniform almost complete convergence, as well as the asymptotic normality of the estimator. We explicitly derive the asymptotic variance and, as a result, provide confidence bands for the theoretical parameter. A simulation study is conducted to illustrate the proposed methodology.