Quantile regression of right-censored length-biased data using the Buckley–James-type method

Length-biased data are encountered frequently due to prevalent cohort sampling in follow-up studies. Quantile regression provides great flexibility for assessing covariate effects on survival time, and is a useful alternative to Cox’s proportional hazards model and the accelerated failure time (AFT) model for survival analysis. In this paper, we develop a Buckley–James-type estimator for right-censored length-biased data under a quantile regression model. The problem of informative right-censoring of length-biased data induced by prevalent cohort sampling must be handled. Following on from the generalization of the Buckley–James-type estimator under the AFT model proposed by Ning et al. (Biometrics 67:1369–1378, 2011), we propose a Buckley–James-type estimating equation for regression coefficients in the quantile regression model and develop an iterative algorithm to obtain the estimates. The resulting estimator is consistent and asymptotically normal. We evaluate the performance of the proposed estimator on finite samples using extensive simulation studies. Analysis of real data is presented to illustrate our proposed methodology.     

Optimal value bounds in nonlinear programming with interval data

We consider nonlinear programming problems the input data of which are not fixed, but vary in some real compact intervals. The aim of this paper is to determine bounds of the optimal values. We propose a general framework for solving such problems. Under some assumption, the exact lower and upper bounds are computable by using two non-interval optimization problems. While these two optimization problems are hard to solve in general, we show that for some particular subclasses they can be reduced to easy problems. Subclasses that are considered are convex quadratic programming and posynomial geometric programming.     

Additive–multiplicative hazards model with current status data

The additive–multiplicative hazards (AMH) regression model specifies an additive and multiplicative form on the hazard function for the counting process associated with a multidimensional covariate process, which contains the Cox proportional hazards model and the additive hazards model as its special cases. In this paper, we study the AMH model with current status data, where the cumulative hazard hazard function is assumed to be nonparametric and is estimated using B-splines with monotonicity constraint on the functional, while a simultaneous sieve maximum likelihood estimation is proposed to estimate regression parameters. The proposed estimator for the parameter vector is shown to be asymptotically normal and semiparametric efficient. The B-splines estimator of the functional of the cumulative hazard function is shown to achieve the optimal nonparametric rate of convergence. A simulation study is conducted to examine the finite sample performance of the proposed estimators and algorithm, and a real data example is presented for illustration.     

Reissner–Mindlin plate model with uncertain input data

A Reissner–Mindlin model of a plate resting on unilateral rigid piers and a unilateral elastic foundation is considered. Since the material coefficients of the orthotropic plate, stiffness of the foundation, and the lateral loading are uncertain, a method of the worst scenario (anti-optimization) is employed to find maximal values of some quantity of interest.The state problem is formulated in terms of a variational inequality with a monotone operator. Using mixed-interpolated finite elements, approximations are proposed for the state problem and for the worst scenario problem. The solvability of the problems and a convergence of approximations is proved.     

The Vlasov–Poisson–Fokker–Planck equation in an interval with kinetic absorbing boundary conditions

We study the initial–boundary value problem for the Vlasov–Poisson–Fokker–Planck equations in an interval with absorbing boundary conditions. We first prove the existence of weak solutions of the linearized equation in an interval with absorbing boundary conditions. Moreover, the weak solution converges to zero exponentially in time. Then we extend the above results to the fully nonlinear Vlasov–Poisson–Fokker–Planck equations in an interval with absorbing boundary conditions; the existence and the longtime behavior of weak solutions. Finally, we prove that the weak solution is actually a classical solution by showing the hypoellipticity of the solution away from the grazing set and the Hölder continuity of the solution up to the grazing set.     

Improving discrimination in data envelopment analysis: PCA–DEA or variable reduction

Within the data envelopment analysis context, problems of discrimination between efficient and inefficient decision-making units often arise, particularly if there are a relatively large number of variables with respect to observations. This paper applies Monte Carlo simulation to generalize and compare two discrimination improving methods; principal component analysis applied to data envelopment analysis (PCA–DEA) and variable reduction based on partial covariance (VR). Performance criteria are based on the percentage of observations incorrectly classified; efficient decision-making units mistakenly defined as inefficient and inefficient units defined as efficient. A trade-off was observed with both methods improving discrimination by reducing the probability of the latter error at the expense of a small increase in the probability of the former error. A comparison of the methodologies demonstrates that PCA–DEA provides a more powerful tool than VR with consistently more accurate results. PCA–DEA is applied to all basic DEA models and guidelines for its application are presented in order to minimize misclassification and prove particularly useful when analyzing relatively small datasets, removing the need for additional preference information.     

Quasilinear Lane–Emden equations with absorption and measure data

We study the existence of solutions to the equation −_Δpu+g(x,u)=μ$-{\mathrm{\Delta }}_{p}u+g(x,u)=\mu$ when g(x,.)$g(x,.)$ is a nondecreasing function and μ   a measure. We characterize the good measures, i.e. the ones for which the problem has a renormalized solution. We study particularly the cases where g(x,u)=|x|^−β|u|^q−1u$g(x,u)={|x|}^{-\beta }{|u|}^{q-1}u$ and g(x,u)=sgn(u)(e^τ|u|λ−1)$g(x,u)=\mathrm{sgn}(u)(e^{\tau {|u|}^{\lambda }}-1)$. The results state that a measure is good if it is absolutely continuous with respect to an appropriate Lorentz–Bessel capacities.     

Reformulations of input–output oriented DEA tests with diversification

We deal with diversification-consistent data envelopment analysis (DEA) tests suitable for accessing financial efficiency of investment opportunities. We will show that under nonnegative inputs and outputs, input–output oriented tests with variable return to scale introduced by M. Branda (2013) [7] are equivalent to input oriented tests with nonincreasing return to scale proposed by J.D. Lamb and K.-H. Tee (2012) [14]. Moreover, we will derive a linear programming formulation of the tests with CVaR deviations.     

Global well-posedness for the Navier–Stokes–Boussinesq system with axisymmetric data

In this paper we prove the global well-posedness for a three-dimensional Boussinesq system with axisymmetric initial data. This system couples the Navier–Stokes equation with a transport-diffusion equation governing the temperature. Our result holds uniformly with respect to the heat conductivity coefficient κ?0$\kappa ?0$ which may vanish.     

Quantile regression with ℓ 1—regularization and Gaussian kernels

The quantile regression problem is considered by learning schemes based on ? ₁—regularization and Gaussian kernels. The purpose of this paper is to present concentration estimates for the algorithms. Our analysis shows that the convergence behavior of ? ₁—quantile regression with Gaussian kernels is almost the same as that of the RKHS-based learning schemes. Furthermore, the previous analysis for kernel-based quantile regression usually requires that the output sample values are uniformly bounded, which excludes the common case with Gaussian noise. Our error analysis presented in this paper can give satisfactory convergence rates even for unbounded sampling processes. Besides, numerical experiments are given which support the theoretical results.     

Ott–Sudan–Ostrovskiy type equations on a segment with large initial data

We study the global existence and asymptotic behavior of solutions to the initial-boundary value problem for the nonlinear nonlocal Ott–Sudan–Ostrovskiy type equations on a segment

Factor analysis for paired ranked data with application on parent–child value orientation preference data

Ranking data appear in everyday life and arise in many fields of study such as marketing, psychology and politics. Very often, the key objective of analyzing and modeling ranking data is to identify underlying factors that affect the individuals’ choice behavior. Factor analysis for ranking data is one of the most widely used methods to tackle the aforementioned problem. Recently, Yu et al. [J R Stat Soc Ser A (Statistics in Society) 168:583–597, 2005] have developed factor models for ranked data in which each individual is asked to rank a set of items. However, paired ranked data may arise when the same set of items are ranked by a pair of judges such as a couple in a family. This paper extended the factor model to accommodate such paired ranked data. The Monte Carlo expectation-maximization algorithm was used for parameter estimation, at which the E-step is implemented via the Gibbs Sampler. For model assessment and selection, a tailor-made method called the bootstrap predictive checks approach was proposed. Simulation studies were conducted to illustrate the proposed estimation and model selection method. The proposed method was applied to analyze a parent–child partially ranked data collected from a value priorities survey carried out in the United States.     

Inverse boundary spectral problem for non–selfadjoint maxwells–s equations with incomplete data

The inverse boundary spectral problem for selfadjoint Maxwell–s equations is to reconstruct unknown coefficient functions in Maxwell– equations from the knowledge of the boundary spectral data, i.e. fromt eh eigenvalues and the boudnary value of the eigenfunctions. Since the spectrum of non–selfadjoint Maxwell–s operator consists of normal eigenvalues and an interval, the complete boundary spectral data can be defind only in a very complicated way. In this article we show that the coefficients can be reconstructed from incomplete data, that is, from the large eigenvalues and the boundary values of the generalized eigenfunctions. Particularly, we do not need the nfinit–dimensional data corresponding to the non–discrete spectrum.     

Convergence of a non-monotone scheme for Hamilton–Jacobi–Bellman equations with discontinous initial data

We prove the convergence of a non-monotonous scheme for a one-dimensional first order Hamilton–Jacobi–Bellman equation of the form v _t + max _α (f(x, α)v _x ) = 0, v(0, x) = v ₀(x). The scheme is related to the HJB-UltraBee scheme suggested in Bokanowski and Zidani (J Sci Comput 30(1):1–33, 2007). We show for general discontinuous initial data a first-order convergence of the scheme, in L ¹-norm, towards the viscosity solution. We also illustrate the non-diffusive behavior of the scheme on several numerical examples.