Saddlepoint-Based Bootstrap Inference for Quadratic Estimating Equations

Abstract.  We propose an easy to implement method for making small sample parametric inference about the root of an estimating equation expressible as a quadratic form in normal random variables. It is based on saddlepoint approximations to the distribution of the estimating equation whose unique root is a parameter's maximum likelihood estimator (MLE), while substituting conditional MLEs for the remaining (nuisance) parameters. Monotoncity of the estimating equation in its parameter argument enables us to relate these approximations to those for the estimator of interest. The proposed method is equivalent to a parametric bootstrap percentile approach where Monte Carlo simulation is replaced by saddlepoint approximation. It finds applications in many areas of statistics including, nonlinear regression, time series analysis, inference on ratios of regression parameters in linear models and calibration. We demonstrate the method in the context of some classical examples from nonlinear regression models and ratios of regression parameter problems. Simulation results for these show that the proposed method, apart from being generally easier to implement, yields confidence intervals with lengths and coverage probabilities that compare favourably with those obtained from several competing methods proposed in the literature over the past half-century.     

Bayesian analysis of threshold autoregressions

A nonasymptotic Bayesian approach is developed for analysis of data from threshold autoregressive processes with two regimes. Using the conditional likelihood function, the marginal posterior distribution for each of the parameters is derived along with posterior means and variances. A test for linear functions of the autoregressive coefficients is presented. The approach presented uses a posterior p-value averaged over the values of the threshold. The one-step ahead predictive distribution is derived along with the predictive mean and variance. In addition, equivalent results are derived conditional upon a value of the threshold. A numerical example is presented to illustrate the approach.     

金融科技、财务风险与公司治理

以沪深A股上市企业2011—2020年数据为研究样本，运用固定效应模型，研究金融科技与公司治理水平的关系以及财务风险在其中的中介作用。结果表明：金融科技能够显著提高公司治理水平，企业财务风险在两者之间发挥部分中介作用；金融科技对会计信息披露质量优秀企业的治理水平影响最大，对会计信息披露质量不合格企业的治理水平没有显著影响；相对于内部控制存在缺陷的企业，金融科技对内部控制不存在缺陷的企业促进作用更大。为此，政府应对金融科技企业给予足够的政策支持，完善金融监管体系；企业应加大运用金融科技的力度，提高会计信息披露质量，减少企业内部控制缺陷，降低企业财务风险，以提高公司治理水平，促进企业高质量发展。     

On concurrence of several linear regressions and applications to problems of enzyme kinetics

In comparing several regressions E(y_ij) =α_i + β_ix_ij i = 1, 2, ..., k, j = 1,2, ..., n_i, researchers are generally interested in the following five problems: whether they have (1) equal slope, (2) equal intercept, (3) coincidence, (4) common intersection on X-axis, and (5) common intersection on (X,Y) - plane. Problems (1) - (3) can be put into the framework of the general linear hypothesis and the F-test can be used. However, problems (4) and (5) cannot be put into the general linear hypothesis because they are ratios of parameters. Hence, in this paper we consider the generalized likelihood ratio test for hypothesis testing. An application to an enzyme kinetics problem in Aniline Metabolism is demonstrated     

浅谈企业会计监督

会计监督作为一种经济监督形式或活动，是经济监督系统中的一个组成部分，其本身又构成一个完整体系。会计监督要充分发挥其职能作用，需建立良好的运行机制。本文首先分析了会计监督的内容及重要性，提出当前企业会计监督存在的问题及原因，然后提出加强会计监督的措施与对策。     

一类地下水水质污染问题广义解的唯一性及对初值和自由项的连续依赖性

本文讨论了一类地下水水质污染问题，其数学模型为一组非线性双曲—抛物耦合方程组，并证明了在相应初边值条件下广义解的唯一性及对初值和自由项的连续依赖性．     

Influence Diagnostics of Semiparametric Nonlinear Reproductive Dispersion Models

This article proposes a semiparametric nonlinear reproductive dispersion model (SNRDM) which is an extension of nonlinear reproductive dispersion model and semiparametric regression model. Maximum penalized likelihood estimators (MPLEs) of unknown parameters and nonparametric functions in SNRDMs are presented. Some novel diagnostic statistics such as Cook distance and difference deviance for parametric and nonparametric parts are developed to identify influence observations in SNRDMs on the basis of case-deletion method, and some formulae readily computed with the MPLEs algorithm for diagnostic measures are given. The equivalency of case-deletion models and mean-shift outlier models in SNRDM is investigated. A simulation study and a real example are used to illustrate the proposed diagnostic measures.     

A cubic smoothing spline based lack of fit test for nonlinear regression models

The use of a statistic based on cubic spline smoothing is considered for testing nonlinear regression models for lack of fit. The statistic is defined to be the Euclidean squared norm of the smoothed residual vector obtained from fitting the nonlinear model, The asymptotic distribution of the statistic is derived under suitable smooth local alternatives and a numerical example is presented.     

一类n阶非线性微分方程多点边值问题解的存在性

利用Leray-Schauder度理论建立了n阶非线性微分方程y(n)=f(x,y,y′,…,y(n-1)),n≥3,满足多点边界条件yn-1(0)-hyn-2(0)=0,y(i)(ηi)=0,i=0,1,…,n-3,y(n-1)(1)+ky(n-2)(1)=0.的多点边值问题的解存在性的几个充分条件,并给出了应用举例.     

气泡振动Noltingk-Neppiras方程的解析解的存在性

从Noltingk—Neppiras方程出发，考察了存在外加声场情况下的单气泡非线性振动方程。从理论上证明了该气泡振动方程周期解的存在性，并给出了方程的解析解。