Maximum Likelihood Inference for Log-linear Models Subject to Constraints of Double Monotone Dependence

To model an hypothesis of double monotone dependence between two ordinal categorical variables A and B usually a set of symmetric odds ratios defined on the joint probability function is subject to linear inequality constraints. Conversely in this paper two sets of asymmetric odds ratios defined, respectively, on the conditional distributions of A given B and on the conditional distributions of B given A are subject to linear inequality constraints. If the joint probabilities are parameterized by a saturated log-linear model, these constraints are nonlinear inequality constraints on the log-linear parameters. The problem here considered is a non-standard one both for the presence of nonlinear inequality constraints and for the fact that the number of these constraints is greater than the number of the parameters of the saturated log-linear model.This work has been supported by the COFIN 2002 project, references 2002133957_002, 2002133957_004. Preliminary findings have been presented at SIS (Società Italiana di Statistica) Annual Meeting, Bari, 2004.     

Bayesian regression under combinations of constraints

A Bayesian method for regression under several types of constraints is proposed. The constraints can be range-restricted and include shape restrictions, constraints on the value of the regression function, smoothness conditions and combinations of these types of constraints. The support of the prior distribution is included in the set of piecewise linear functions. It is shown that the proposed prior can be arbitrarily close to the distribution induced by the addition of a polynomial plus an (m−1)-fold integrated Brownian motion. Hence, despite its piecewise linearity, the regression function behaves (approximately) like an m−1 times continuously differentiable random function. Furthermore, thanks to the piecewise linear property, many combinations of constraints can easily be considered. The regression function is estimated by the posterior mode computed by a simulated annealing algorithm. The constraints on the shape and the values of the regression function are taken into account thanks to the proposal distribution, while the smoothness condition is handled by the acceptation step. Simulations from the posterior distribution are obtained by a Gibbs sampling algorithm.     

Inequality Constraints in the Univariate GARCH Model

To keep the conditional variances generated by the GARCH (p, q) model nonnegative, Bollerslev imposed nonnegativity constraints on the parameters of the process. We show that these constraints can be substantially weakened and so should not be imposed in estimation. We also provide empirical examples illustrating the importance of relaxing these constraints.     

Change-Point Detection in Two-Phase Regression with Inequality Constraints on the Regression Parameters

Two-phase regression models with inequality constraints on the regression coefficients and with a small number of measurements is considered. A new test based on the likelihood ratio in linear model with inequality constraints for the presence of a change-point is proposed. Numerical approximations to the powers against various alternatives are given and compared with the powers of the likelihood ratio test in the two-phase regression models without inequality constraints, the backwards CUSUM test, and the k-linear-r-ahead recursive residuals tests. Performance of related likelihood based estimators of the change-point is briefly studied in a Monte Carlo experiment.     

Characterization of singular balanced fractional sm factorial designs derivable from balanced arrays with maximum number of constraints

An upper bound on the maximum number of constraints for s-symbol balanced arrays is derived. It is shown that balanced fractional s^m factorial designs derived from some balanced arrays with the maximum possible number of constraints become singular.     

Shape-Constrained Kernel-Weighted Least Squares: Estimating Production Functions for Chilean Manufacturing Industries

ABSTRACT

In this article, we examine a novel way of imposing shape constraints on a local polynomial kernel estimator. The proposed approach is referred to as shape constrained kernel-weighted least squares (SCKLS). We prove uniform consistency of the SCKLS estimator with monotonicity and convexity/concavity constraints and establish its convergence rate. In addition, we propose a test to validate whether shape constraints are correctly specified. The competitiveness of SCKLS is shown in a comprehensive simulation study. Finally, we analyze Chilean manufacturing data using the SCKLS estimator and quantify production in the plastics and wood industries. The results show that exporting firms have significantly higher productivity.     

Admissible Linear Predictors in the Superpopulation Model with Respect to Inequality Constraints

Admissibility of linear predictors of the linear quantity Qy is investigated under a general linear regression superpopulation model with some inequality constraints. The relation between admissible homogeneous and inhomogeneous linear predictors is characterized. Further, necessary and sufficient conditions for a linear predictor to be admissible in two cases of inequality constraints in the classes of homogeneous and inhomogeneous linear predictors are given, respectively.     

Some resolvable orthogonal arrays with two symbols

A method of constructing a resolvable orthogonal array (4λk2,2) which can be partitioned into λ orthogonal arrays (4,k 2,1) is proposed. The number of constraints kfor this type of orthogonal array is at most 3λ. When λ=2 or a multiple of 4, an orthogonal array with the maximum number of constraints of 3λ can be constructed. When λ=4n+2(n≧1) an orthogonal array with 2λ+2 constraints can be constructed. When λ is an odd number, orthogonal arrays can be constructed for λ=3,5,7, and 9 with k=4,8,12, and 13 respectively.     

Robust empirical likelihood for linear models under median constraints

In this paper, we consider the application of the empirical likelihood for

linear models under median constraints in view of robustness. For two simple median constraints, it is shown that conditions to ensure the consistency of the empirical likelihood confidence regions can be surprisingly relaxed compared with the normal approach under L norm. However, the coverage accuracy of the empirical likelihood confidence regions based on simple median constrains cannot be improved because of the discontinuity of the constraints. Therefore, a smoothed version of median constraint is proposed and a general theory is established to ensure its validity.     

环境约束下的化石能源跨期开采路径比较研究

考虑化石能源开发和使用的环境外部性与代际外部性,在动态最优开采模型基础上构建含有环境污染因子的跨期配置模型,比较考虑环境制约因素前后的开采路径,证明环境约束对化石能源消耗有复杂影响,环境作为政策工具可以调节化石能源开采强度,在一定程度上缓解了资源的稀缺性和延长了资源耗竭时间,为具有经济价值的可再生能源的出现赢得时间。应用中国相关历史数据,发现实际上环境约束没有抑制化石能源消耗,偏离了理论分析预期目标。据此提出加快矿产资源税费改革、加大环境污染治理投资、优化投资结构、建立科学环境补偿制度、促进技术进步的政策建议。     

Inequality Constrained State-Space Models

ABSTRACT

The standard Kalman filter cannot handle inequality constraints imposed on the state variables, as state truncation induces a nonlinear and non-Gaussian model. We propose a Rao-Blackwellized particle filter with the optimal importance function for forward filtering and the likelihood function evaluation. The particle filter effectively enforces the state constraints when the Kalman filter violates them. Monte Carlo experiments demonstrate excellent performance of the proposed particle filter with Rao-Blackwellization, in which the Gaussian linear sub-structure is exploited at both the cross-sectional and temporal levels.     

Nonparametric likelihood and doubly robust estimating equations for marginal and nested structural models

This article considers Robins's marginal and nested structural models in the cross‐sectional setting and develops likelihood and regression estimators. First, a nonparametric likelihood method is proposed by retaining a finite subset of all inherent and modelling constraints on the joint distributions of potential outcomes and covariates under a correctly specified propensity score model. A profile likelihood is derived by maximizing the nonparametric likelihood over these joint distributions subject to the retained constraints. The maximum likelihood estimator is intrinsically efficient based on the retained constraints and weakly locally efficient. Second, two regression estimators, named hat and tilde, are derived as first‐order approximations to the likelihood estimator under the propensity score model. The tilde regression estimator is intrinsically and weakly locally efficient and doubly robust. The methods are illustrated by data analysis for an observational study on right heart catheterization. The Canadian Journal of Statistics 38: 609–632; 2010 © 2010 Statistical Society of Canada     

Sliced inverse regression under linear constraints

We consider the semiparametric regression model introduced by Li (1991) and add to this model some linear constraints on the slope parameters. These constraints can be identifiability conditions or they may carry additional in¬formations on the slope parameters. Using a geometric argument, we develop a method to estimate the slope parameters. This link-free and distribution-free method splits in two steps: the first is a Sliced Inverse Regression (SIR); Canonical Analysis is used at the second step to transform the SIR estimates so that they satisfy the constraints. We establish yn-consistency and obtain the asymptotic distribution of the estimates.

This estimation method is applied to the general sample selection model which is very useful in Econometrics. A simulation study shows that the method performs well in the example considered.     

Constructing optimal designs with constraints

We construct constrained approximate optimal designs by maximizing a criterion subject to constraints. We approach this problem by transforming the constrained optimization problem to one of maximizing three functions of the design weights simultaneously. We used a class of multiplicative algorithms, indexed by a function f(·). These algorithms are shown to satisfy the basic constraints on the design weights of nonnegativity and summation to unity. We also investigate techniques for improving convergence rates by means of some suitable choices of the function f(·).     

A three-population constrained discrimination procedure

ABSTRACT

Classification rules with a reserve judgment option provide a way to satisfy constraints on the misclassification probabilities when there is a high degree of overlap among the populations. Constructing rules which maximize the probability of correct classification while satisfying such constraints is a difficult optimization problem. This paper uses the form of the optimal solution to develop a relatively simple and computationally fast method for three populations which has a non parametric quality in controlling the misclassification probabilities. Simulations demonstrate that this procedure performs well.     

Construction of uniform designs for mixture experiments with complex constraints

Abstract

Mixture experiments have attracted increasingly attention due to their great practical value in production and living, while uniform designs over irregular experimental regions have become a hot topic in the area of experimental designs in the past two decades. Noting that the experimental region of a mixture experiment with q components under some constraints is in fact a (q ? 1)-dimensional geometry, this article proposes a new method for searching nearly uniform designs for mixture experiments with any complex constraints. Two examples with some tables and figures are given to illustrate this method.     

Simple Computation of Maximum Likelihood Estimates in Latent Class Model with Equality and Constant Constraints

A simple computational method for estimation of parameters via a type of EM algorithm is proposed in restricted latent class analysis, where equality and constant constraints are considered. These constraints create difficulty in estimation. In order to simply and stably estimate parameters in restricted latent class analysis, a simple computational method using only first-order differentials is proposed, where the step-halving method is adopted. A simulation study shows that in almost all cases the new method gives parameter sequences monotonously increasing the Q-function in the EM algorithm. Analysis of real data is provided.     

融资约束如何影响劳动收入份额

本文基于流动资本的视角,新古典要素分配模型中引入融资约束,分析了企业流动资本约束对劳动收入份额影响机制;进一步建立相应的计量模型,采用1998-2007年中国工业企业数据实证考察了融资约束对劳动收入份额的影响效应。研究表明与流动资本紧密相关的内源融资约束对于劳动收入份额的变化具有显著的负向影响,尤其是对于非国有企业表现更为明显;外源融资约束的加强在一定程度上则可能减少企业流动资本的挤占,从而增加劳动收入份额;企业垄断能力的变化及其实收资本中不同所有制所属份额,都将显著改变融资约束影响要素收入份额的程度。     

Testing for generalized linear mixed models with cluster correlated data under linear inequality constraints

Generalized linear mixed models (GLMMs) are often used for analyzing cluster correlated data, including longitudinal data and repeated measurements. Full unrestricted maximum likelihood (ML) approaches for inference on both fixed‐and random‐effects parameters in GLMMs have been extensively studied in the literature. However, parameter orderings or constraints may occur naturally in practice, and in such cases, the efficiency of a statistical method is improved by incorporating the parameter constraints into the ML estimation and hypothesis testing. In this paper, inference for GLMMs under linear inequality constraints is considered. The asymptotic properties of the constrained ML estimators and constrained likelihood ratio tests for GLMMs have been studied. Simulations investigated the empirical properties of the constrained ML estimators, compared to their unrestricted counterparts. An application to a recent survey on Canadian youth smoking patterns is also presented. As these survey data exhibit natural parameter orderings, a constrained GLMM has been considered for data analysis. The Canadian Journal of Statistics 40: 243–258; 2012 © 2012 Crown in the right of Canada     

环境规制、政府支持与重污染行业的融资约束

利用2003—2009年A股上市公司数据,以Almeida等的现金-现金流量模型为基础,从融资约束角度,研究环境规制对重污染行业的影响。结果表明：环境规制放宽了重污染行业中央国企的融资约束程度;未对地方国企产生显著性影响,但加大了非国有企业的融资约束;所在地为地方政府环境政策支持度高的地区的企业,因环境规制而加重了融资约束,而对支持度较低地区的企业,融资约束状况却得以改善。结论支持了政府官员作为理性经济人的公共选择理论和对地方国企支持的政治庇护理论,表明考虑到地方政府利益的中央-地方政府环境规制实施机制的重要性。