Improved methods for moment restriction models with data combination and an application to two-sample instrumental variable estimation

Combining-100 information from multiple samples is often needed in biomedical and economic studies, but differences between these samples must be appropriately taken into account in the analysis of the combined data. We study the estimation for moment restriction models with data combined from two samples under an ignorability-type assumption while allowing for different marginal distributions of variables common to both samples. Suppose that an outcome regression (OR) model and a propensity score (PS) model are specified. By leveraging semi-parametric efficiency theory, we derive an augmented inverse probability-weighted (AIPW) estimator that is locally efficient and doubly robust with respect to these models. Furthermore, we develop calibrated regression and likelihood estimators that are not only locally efficient and doubly robust but also intrinsically efficient in achieving smaller variances than the AIPW estimator when the PS model is correctly specified but the OR model may be mispecified. As an important application, we study the two-sample instrumental variable problem and derive the corresponding estimators while allowing for incompatible distributions of variables common to the two samples. Finally, we provide a simulation study and an econometric application on public housing projects to demonstrate the superior performance of our improved estimators. The Canadian Journal of Statistics 48: 259–284; 2020 © 2019 Statistical Society of Canada     

二维机翼非定常气动反命题的欧拉解法

提出在映象坐标下求解二维非定常欧拉方程获取二维振荡机翼的气动反命题解，给出了非定常气动反问题的边界条件和求解方法．该方法克服了以往基于势函数方程解反命题的局限，统一了亚音、跨音与超音流反问题的解法，并避免了非定常尾涡面的直接求解与反问题未知边界的不确定性．     

一类实对称矩阵的逆特征值问题

本文主要讨论了如下形式的矩阵的逆特征值问题。即对给定的n个实数λ_1＜λ_2＜…＜λ_n与n-1个实数μ_1＜μ_2＜…＜μ_(n-1),满足λ_1＜μ_1＜λ_2＜…＜λ_(n-1)＜μ_(n-1)＜λ_n，在α_2＜α_3＜…＜α_(n-1)的条件下，存在唯一的一个矩阵A_n是以λ_i为其特征值，且其截边矩阵的特征值为μ_1，μ_2，…μ_(n-1)     

On a class of bivariate mixed Sarmanov distributions

Multivariate distributions are more and more used to model the dependence encountered in many fields. However, classical multivariate distributions can be restrictive by their nature, while Sarmanov's multivariate distribution, by joining different marginals in a flexible and tractable dependence structure, often provides a valuable alternative. In this paper, we introduce some bivariate mixed Sarmanov distributions with the purpose to extend the class of bivariate Sarmanov distributions and to obtain new dependency structures. Special attention is paid to the bivariate mixed Sarmanov distribution with Poisson marginals and, in particular, to the resulting bivariate Sarmanov distributions with negative binomial and with Poisson‐inverse Gaussian marginals; these particular types of mixed distributions have possible applications in, for example modelling bivariate count data. The extension to higher dimensions is also discussed. Moreover, concerning the dependency structure, we also present some correlation formulas.     

Determining the birth function for an age structured population

This paper deals with an inverse problem in age‐structured population dynamics, namely the recovery of the unknown birth function from the additional or overposed data consisting of the total population over a time interval equal to the maximum life span of the species. Conditions on the data are given to guarantee the existence and uniqueness of a solution, and the question of continuous dependence of the birth function on the data is addressed. Some numerical simulations are presented to indicate that one can in fact use the methods of the paper to reconstruct the birth function.     

Confidence intervals for the closed population size under inverse sampling without replacement

Inverse sampling is an appropriate design for the second phase of capture-recapture experiments which provides an exactly unbiased estimator of the population size. However, the sampling distribution of the resulting estimator tends to be highly right skewed for small recapture samples, so, the traditional Wald-type confidence intervals appear to be inappropriate. The objective of this paper is to study the performance of interval estimators for the population size under inverse recapture sampling without replacement. To this aim, we consider the Wald-type, the logarithmic transformation-based, the Wilson score, the likelihood ratio and the exact methods. Also, we propose some bootstrap confidence intervals for the population size, including the with-replacement bootstrap (BWR), the without replacement bootstrap (BWO), and the Rao–Wu’s rescaling method. A Monte Carlo simulation is employed to evaluate the performance of suggested methods in terms of the coverage probability, error rates and standardized average length. Our results show that the likelihood ratio and exact confidence intervals are preferred to other competitors, having the coverage probabilities close to the desired nominal level for any sample size, with more balanced error rate for exact method and shorter length for likelihood ratio method. It is notable that the BWO and Rao–Wu’s rescaling methods also may provide good intervals for some situations, however, those coverage probabilities are not invariant with respect to the population arguments, so one must be careful to use them.     

Pairwise directions estimation for multivariate response regression data

This article concerns the analysis of multivariate response data with multi-dimensional covariates. Based on local linear smoothing techniques, we propose an iteratively adaptive estimation method to reduce the dimensions of response variables and covariates. Two weighted estimation strategies are incorporated in our approach to provide initial estimates. Our proposal is also extended to curve response data for a data-adaptive basis function searching. Instead of focusing on goodness of fit, we shift the problem to reveal the data structure and basis patterns. Simulation studies with multivariate response and curve data are conducted for our pairwise directions estimation (PDE) approach in comparison with sliced inverse regression of Li et al. [Dimension reduction for multivariate response data. J Amer Statist Assoc. 2003;98:99–109]. The results demonstrate that the proposed PDE method is useful for data with responses approximating linear or bending structures. Illustrative applications to two real datasets are also presented.     

子矩阵约束下矩阵方程XA=B的对称非负定解

利用矩阵的广义逆及奇异值分解 ,给出了子矩阵约束下线性矩阵方程XA =B有对称非负定解的充分必要条件 ,并在有解时 ,给出了相应解的一般表达式     

Asymmetry and Gradient Asymmetry Functions: Density-Based Skewness and Kurtosis

Abstract.  Functional measures of skewness and kurtosis, called asymmetry and gradient asymmetry functions, are described for continuous univariate unimodal distributions. They are defined and interpreted directly in terms of the density function and its derivative. Asymmetry is defined by comparing distances from points of equal density to the mode. Gradient asymmetry is defined, in novel fashion, as asymmetry of an appropriate function of the density derivative. Properties and illustrations of asymmetry and gradient asymmetry functions are presented. Estimation of them is considered and illustrated with an example. Scalar summary skewness and kurtosis measures associated with asymmetry and gradient asymmetry functions are discussed.