Communications in Mathematics and Statistics最新文献

In this paper, we establish three circles theorem for volume of conformal metrics whose scalar curvatures are integrable in a critical (scaling invariant) norm. As applications, we analyze the asymptotic behavior of such metrics near isolated singularities and use it to show the residual terms of the Chern–Gauss–Bonnet formula are integers. Such strong rigidity implies a vanishing theorem on the integral value of the (Q_g) curvature, with application to the bi-Lipschitz equivalence problem for conformal metrics.

In this paper, we study continuous frames with symmetries from projective representations of compact groups. In particular, we study maximal spanning vectors in detail and we prove the existence of maximal spanning vectors for irreducible projective representations of compact abelian groups by a dimension counting method.

In the present paper, a scheme of path sampling is explored for stochastic diffusion processes. The core issue is the evaluation of the diffusion propagators (spatial–temporal Green functions) by solving the corresponding Kolmogorov forward equations with Dirac delta functions as initials. The technique can be further used in evaluating general functional of path integrals. The numerical experiments demonstrated that the simulation scheme based on this approach overwhelms the popular Euler scheme and Exact Algorithm in terms of accuracy and efficiency in fairly general settings. An example of likelihood inference for the diffusion driven Cox process is provided to show the scheme’s potential power in applications.

Censored data with functional predictors often emerge in many fields such as biology, neurosciences and so on. Many efforts on functional data analysis (FDA) have been made by statisticians to effectively handle such data. Apart from mean-based regression, quantile regression is also a frequently used technique to fit sample data. To combine the strengths of quantile regression and classical FDA models and to reveal the effect of the functional explanatory variable along with nonfunctional predictors on randomly censored responses, the focus of this paper is to investigate the semi-functional partial linear quantile regression model for data with right censored responses. An inverse-censoring-probability-weighted three-step estimation procedure is proposed to estimate parametric coefficients and the nonparametric regression operator in this model. Under some mild conditions, we also verify the asymptotic normality of estimators of regression coefficients and the convergence rate of the proposed estimator for the nonparametric component. A simulation study and a real data analysis are carried out to illustrate the finite sample performances of the estimators.

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.

Lutwak et al. (Adv Math 329:85–132, 2018) introduced the (L_p) dual curvature measure that unifies several other geometric measures in dual Brunn–Minkowski theory and Brunn–Minkowski theory. Motivated by works in Lutwak et al. (Adv Math 329:85–132, 2018), we consider the uniqueness and continuity of the solution to the (L_p) dual Minkowski problem. To extend the important work (Theorem A) of LYZ to the case for general convex bodies, we establish some new Minkowski-type inequalities which are closely related to the optimization problem associated with the (L_p) dual Minkowski problem. When (q< p), the uniqueness of the solution to the (L_p) dual Minkowski problem for general convex bodies is obtained. Moreover, we obtain the continuity of the solution to the (L_p) dual Minkowski problem for convex bodies.

Testing slope homogeneity is important in panel data modeling. Existing approaches typically take the summation over a sequence of test statistics that measure the heterogeneity of individual panels; they are referred to as Sum tests. We propose two procedures for slope homogeneity testing in large panel data models. One is called a Max test that takes the maximum over these individual test statistics. The other is referred to as a Combo test, which combines a certain Sum test (i.e., that of Pesaran and Yamagata in J Econom 142:50-93, 2008) and the proposed Max test together. We derive the limiting null distributions of the two test statistics, respectively, when both the number of individuals and temporal observations jointly diverge to infinity, and demonstrate that the Max test is asymptotically independent of the Sum test. Numerical results show that the proposed approaches perform satisfactorily.

Let (({mathcal {X}},d,mu )) be a doubling metric measure space in the sense of R. R. Coifman and G. Weiss, L a non-negative self-adjoint operator on (L^2({mathcal {X}})) satisfying the Davies–Gaffney estimate, and (X({mathcal {X}})) a ball quasi-Banach function space on ({mathcal {X}}) satisfying some extra mild assumptions. In this article, the authors introduce the Hardy type space (H_{X,,L}({mathcal {X}})) by the Lusin area function associated with L and establish the atomic and the molecular characterizations of (H_{X,,L}({mathcal {X}}).) As an application of these characterizations of (H_{X,,L}({mathcal {X}})), the authors obtain the boundedness of spectral multiplies on (H_{X,,L}({mathcal {X}})). Moreover, when L satisfies the Gaussian upper bound estimate, the authors further characterize (H_{X,,L}({mathcal {X}})) in terms of the Littlewood–Paley functions (g_L) and (g_{lambda ,,L}^*) and establish the boundedness estimate of Schrödinger groups on (H_{X,,L}({mathcal {X}})). Specific spaces (X({mathcal {X}})) to which these results can be applied include Lebesgue spaces, Orlicz spaces, weighted Lebesgue spaces, and variable Lebesgue spaces. This shows that the results obtained in the article have extensive generality.

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].