Communications in Mathematics and Statistics
Journal Prestige (SJR): 0.556 Citation Impact (citeScore): 1 Number of Followers: 3 Hybrid journal (It can contain Open Access articles) ISSN (Print) 21946701  ISSN (Online) 2194671X Published by SpringerVerlag [2468 journals] 
 SemiFunctional Partial Linear Quantile Regression Model with Randomly
Censored Responses
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Abstract: Abstract 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 meanbased 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 semifunctional partial linear quantile regression model for data with right censored responses. An inversecensoringprobabilityweighted threestep 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.
PubDate: 20240317

 A Global Torelli Theorem for Certain CalabiYau Threefolds

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Abstract: Abstract We establish a global Torelli theorem for the complete family of CalabiYau threefolds arising from cyclic triple covers of \({{\mathbb {P}}}^3\) branched along six stable hyperplanes.
PubDate: 20240301

 Second Maximal Invariant Subgroups and Solubility of Finite Groups

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Abstract: Abstract Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders. We prove that the fact of imposing specific properties on the second maximal Ainvariant subgroups of G determines that G is either soluble or isomorphic to a few nonsoluble groups such as PSL(2, 5) or SL(2, 5).
PubDate: 20240301

 Weak Solutions of McKean–Vlasov SDEs with Supercritical Drifts

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Abstract: Abstract Consider the following McKean–Vlasov SDE: $$\begin{aligned} \textrm{d} X_t=\sqrt{2}\textrm{d} W_t+\int _{{\mathbb {R}}^d}K(t,X_ty)\mu _{X_t}(\textrm{d} y)\textrm{d} t,\ \ X_0=x, \end{aligned}$$ where \(\mu _{X_t}\) stands for the distribution of \(X_t\) and \(K(t,x): {{\mathbb {R}}}_+\times {{\mathbb {R}}}^d\rightarrow {{\mathbb {R}}}^d\) is a timedependent divergence free vector field. Under the assumption \(K\in L^q_t({\widetilde{L}}_x^p)\) with \(\frac{d}{p}+\frac{2}{q}<2\) , where \({\widetilde{L}}^p_x\) stands for the localized \(L^p\) space, we show the existence of weak solutions to the above SDE. As an application, we provide a new proof for the existence of weak solutions to 2D Navier–Stokes equations with measure as initial vorticity.
PubDate: 20240301

 Identification and Estimation of Generalized Additive Partial Linear
Models with Nonignorable Missing Response
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Abstract: Abstract The generalized additive partial linear models (GAPLM) have been widely used for flexible modeling of various types of response. In practice, missing data usually occurs in studies of economics, medicine, and public health. We address the problem of identifying and estimating GAPLM when the response variable is nonignorably missing. Three types of monotone missing data mechanism are assumed, including logistic model, probit model and complementary loglog model. In this situation, likelihood based on observed data may not be identifiable. In this article, we show that the parameters of interest are identifiable under very mild conditions, and then construct the estimators of the unknown parameters and unknown functions based on a likelihoodbased approach by expanding the unknown functions as a linear combination of polynomial spline functions. We establish asymptotic normality for the estimators of the parametric components. Simulation studies demonstrate that the proposed inference procedure performs well in many settings. We apply the proposed method to the household income dataset from the Chinese Household Income Project Survey 2013.
PubDate: 20240301

 Incorporating Relative Error Criterion to Conformal Prediction for
Positive Data
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Abstract: Abstract Positive data are very common in many scientific fields and applications; for these data, it is known that estimation and inference based on relative error criterion are superior to that of absolute error criterion. In prediction problems, conformal prediction provides a useful framework to construct flexible prediction intervals based on hypothesis testing, which has been actively studied in the past decade. In view of the advantages of the relative error criterion for regression problems with positive responses, in this paper, we combine the relative error criterion (REC) with conformal prediction to develop a novel RECbased predictive inference method to construct prediction intervals for the positive response. The proposed method satisfies the finite sample global coverage guarantee and to some extent achieves the local validity. We conduct extensive simulation studies and two real data analysis to demonstrate the competitiveness of the new proposed method.
PubDate: 20240301

 On the $$\partial {{\bar{\partial }}}$$ Lemma and BottChern cohomology
with local coefficients
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Abstract: Abstract A Frölichertype inequality for BottChern cohomology and its relation with \(\partial {{\bar{\partial }}}\) lemma were introduced in [1]. In this paper, we generalize these results to the cohomology groups with coefficients in flat complex vector bundles.
PubDate: 20240301

 Efficient Fully Discrete SpectralGalerkin Scheme for the VolumeConserved
MultiVesicular PhaseField Model of Lipid Vesicles with Adhesion
Potential
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Abstract: Abstract In this work, we aim to develop an effective fully discrete SpectralGalerkin numerical scheme for the multivesicular phasefield model of lipid vesicles with adhesion potential. The essence of the scheme is to introduce several additional auxiliary variables and design some corresponding auxiliary ODEs to reformulate the system into an equivalent form so that the explicit discretization for the nonlinear terms can also achieve unconditional energy stability. Moreover, the scheme has a full decoupling structure and can avoid calculating variablecoefficient systems. The advantage of this scheme is its high efficiency and ease of implementation, that is, only by solving two independent linear biharmonic equations with constant coefficients for each phasefield variable, the scheme can achieve the secondorder accuracy in time, spectral accuracy in space, and unconditional energy stability. We strictly prove that the fully discrete energy stability that the scheme holds and give a detailed stepbystep implementation process. Further, numerical experiments are carried out in 2D and 3D to verify the convergence rate, energy stability, and effectiveness of the developed algorithm.
PubDate: 20240301

 Tool Path Planning with Confined Scallop Height Error Using Optimal
Connected Fermat Spirals
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Abstract: Abstract In CNC machining, the tool path planning of the cutter plays an important role. In this paper, we generate a spacefilling and continuous tool path for freeform surface represented by the triangular mesh with a confined scallop height. The tool path is constructed from connected Fermat spirals (CFS) but with fewer inflection points. Comparing with the newly developed CFS method, only about half of the number of inflection points are involved. Moreover, the kinematic constraints are simultaneously taken into account to increase the feedrates in machining. Finally, we use a microline trajectory technique to smooth the tool path. Experimental results and physical cutting tests are provided to illustrate and clarify our method.
PubDate: 20240301

 Generalized Varying Coefficient Mediation Models

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Abstract: Abstract Motivated by an analysis of causal mechanism from economic stress to entrepreneurial withdrawals through depressed affect, we develop a twolayer 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 finitesample performance of the proposed estimation method. A real data analysis based on the proposed model discovers some interesting behavioral economic phenomenon, that selfefficacy influences the deleterious impact of economic stress, both directly and indirectly through depressed affect, on business owners’ withdrawal intentions.
PubDate: 20240220

 Uniqueness and Continuity of the Solution to $$L_p$$ Dual Minkowski
Problem
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Abstract: Abstract 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 Minkowskitype 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.
PubDate: 20240208

 New Approaches for Testing Slope Homogeneity in Large Panel Data Models

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Abstract: Abstract 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 142:5093, 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.
PubDate: 20240125
DOI: 10.1007/s40304023003715

 Hardy Spaces Associated with Nonnegative Selfadjoint Operators and Ball
QuasiBanach Function Spaces on Doubling Metric Measure Spaces and Their
Applications
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Abstract: Abstract Let \(({\mathcal {X}},d,\mu )\) be a doubling metric measure space in the sense of R. R. Coifman and G. Weiss, L a nonnegative selfadjoint operator on \(L^2({\mathcal {X}})\) satisfying the Davies–Gaffney estimate, and \(X({\mathcal {X}})\) a ball quasiBanach 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.
PubDate: 20240119
DOI: 10.1007/s40304023003760

 Even Character Degrees and Ito–Michler Theorem

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Abstract: Abstract Let \(\textrm{Irr}_2(G)\) be the set of linear and evendegree irreducible characters of a finite group G. In this paper, we prove that G has a normal Sylow 2subgroup if \(\sum \limits _{\chi \in \textrm{Irr}_2(G)} \chi (1)^m/\sum \limits _{\chi \in \textrm{Irr}_2(G)} \chi (1)^{m1} < (1+2^{m1})/(1+2^{m2})\) for a positive integer m, which is the generalization of several recent results concerning the wellknown Ito–Michler theorem.
PubDate: 20240118
DOI: 10.1007/s40304023003680

 Optimal Convergence Rates in the Averaging Principle for Slow–Fast SPDEs
Driven by Multiplicative Noise
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Abstract: Abstract 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].
PubDate: 20240118
DOI: 10.1007/s40304023003635

 Directional Entropy and Pinsker $$\sigma $$ Algebra for $$\mathbb
{Z}^{2}$$ Actions
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Abstract: Abstract In this paper, we study the directional entropy along irrational directions in \(\mathbb {R}^2\) and present the structure of directional Pinsker \(\sigma \) algebra of \(\mathbb {Z}^2\) MPSs.
PubDate: 20240117
DOI: 10.1007/s4030402300369z

 A Class of Polynomial Modules over Map Lie Algebras

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Abstract: Abstract For any finitely generated unital commutative associative algebra \(\mathcal {R}\) over \(\mathbb {C}\) and any complex finitedimensional simple Lie algebra \(\mathfrak {g}\) with a fixed Cartan subalgebra \(\mathfrak {h}\) , we classify all \(\mathfrak {g}\otimes \mathcal {R}\) modules on \(U(\mathfrak {h})\) such that \(\mathfrak {h}\) as a subalgebra of \(\mathfrak {g}\otimes \mathcal {R}\) , acts on \(U(\mathfrak {h})\) by the multiplication. We construct these modules explicitly and study their module structures.
PubDate: 20240117
DOI: 10.1007/s40304023003564

 Multiply Robust Estimation of Quantile Treatment Effects with Missing
Responses
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Abstract: Abstract Causal inference and missing data have attracted significant research interests in recent years, while the current literature usually focuses on only one of these two issues. In this paper, we develop two multiply robust methods to estimate the quantile treatment effect (QTE), in the context of missing data. Compared to the commonly used average treatment effect, QTE provides a more complete picture of the difference between the treatment and control groups. The first one is based on inverse probability weighting, the resulting QTE estimator is rootn consistent and asymptotic normal, as long as the class of candidate models of propensity scores contains the correct model and so does that for the probability of being observed. The second one is based on augmented inverse probability weighting, which further relaxes the restriction on the probability of being observed. Simulation studies are conducted to investigate the performance of the proposed method, and the motivated CHARLS data are analyzed, exhibiting different treatment effects at various quantile levels.
PubDate: 20231229
DOI: 10.1007/s40304023003804

 Unadjusted Langevin Algorithm for Nonconvex Weakly Smooth Potentials

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Abstract: Abstract Discretization of continuoustime diffusion processes is a widely recognized method for sampling. However, the canonical Euler Maruyama discretization of the Langevin diffusion process, referred as unadjusted Langevin algorithm (ULA), studied mostly in the context of smooth (gradient Lipschitz) and strongly logconcave densities, is a considerable hindrance for its deployment in many sciences, including statistics and machine learning. In this paper, we establish several theoretical contributions to the literature on such sampling methods for nonconvex distributions. Particularly, we introduce a new mixture weakly smooth condition, under which we prove that ULA will converge with additional logSobolev inequality. We also show that ULA for smoothing potential will converge in \(L_{2}\) Wasserstein distance. Moreover, using convexification of nonconvex domain (Ma et al. in Proc Natl Acad Sci 116(42):20881–20885, 2019) in combination with regularization, we establish the convergence in Kullback–Leibler divergence with the number of iterations to reach \(\epsilon \) neighborhood of a target distribution in only polynomial dependence on the dimension. We relax the conditions of Vempala and Wibisono (Advances in Neural Information Processing Systems, 2019) and prove convergence guarantees under isoperimetry, and nonstrongly convex at infinity.
PubDate: 20231209
DOI: 10.1007/s4030402300350w

 AreaPreserving Parameterization with Tutte Regularization

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Abstract: Abstract Areapreserving parameterization is now widely applied, such as for remeshing and medical image processing. We propose an efficient and stable approach to compute areapreserving parameterization on simply connected open surfaces. From an initial parameterization, we construct an objective function of energy. This consists of an area distortion measure and a new regularization, termed as the Tutte regularization, combined into an optimization problem with sliding boundary constraints. The original areapreserving problem is decomposed into a series of subproblems to linearize the boundary constraints. We design an iteration framework based on the augmented Lagrange method to solve each linear constrained subproblem. Our method generates a highquality parameterization with areapreserving on facets. The experimental results demonstrate the efficacy of the designed framework and the Tutte regularization for achieving a fine parameterization.
PubDate: 20231201
DOI: 10.1007/s40304021002716
