Errors of misclassification in discrimination of dimensional coherent elliptic random field observations

The problem of classification of dimensional coherent elliptic random field observations into one of two populations specified by different regression mean models and common stationary scale matrix is considered, under the further assumption that the observations to be classified are dependent on the training samples. In this statistical frame, the behaviour of linear discriminant function is studied and an asymptotic expression for the distribution function of the probabilities of misclassification is derived.     

On Regression Sampling in Statistical Auditing: Bad Answers to the Wrong Questions?

This paper criticizes the use of regression in audit samples to obtain confidence intervals for the error rate. Also the methodology to evaluate methods by simulation studies using real–life populations is criticized. This is done from a Bayesian viewpoint, which goes as far as stating that in this type of research the wrong questions are answered. A fundamental discussion on the role of model building, illustrated by the use of models in auditing, forms the centre of the paper.     

Experiments with mixtures: Optimal allocations for becker’s models

Extending Scheffé’s simplex-centroid design for experiments with mixtures, we introduce aweighted simplex-centroid design for a class of mixture models. Becker’s homogeneous functions of degree one belong to this class. By applying optimal design theory, we obtainA-, D- andI-optimal allocations of observations for Becker’s models.     

Further thoughts on simplicity and complexity in population projection models

"This article is a review of--and response to--a special issue of Mathematical Population Studies that focused on the relative performance of simpler vs. more complex population projection models. I do not attempt to summarize or comment on each of the articles in the special issue, but rather present an additional perspective on several points: definitions of simplicity and complexity, empirical evidence regarding population forecast accuracy, the costs and benefits of disaggregation, the potential benefits of combining forecasts, criteria for evaluating projection models, and issues of economic efficiency in the production of population projections."     

Heteroskedasticity-consistent covariance matrix estimators for spatial autoregressive models

In the presence of heteroskedasticity, conventional test statistics based on the ordinary least squares (OLS) estimator lead to incorrect inference results for the linear regression model. Given that heteroskedasticity is common in cross-sectional data, the test statistics based on various forms of heteroskedasticity-consistent covariance matrices (HCCMs) have been developed in the literature. In contrast to the standard linear regression model, heteroskedasticity is a more serious problem for spatial econometric models, generally causing inconsistent extremum estimators of model coefficients. This paper investigates the finite sample properties of the heteroskedasticity-robust generalized method of moments estimator (RGMME) for a spatial econometric model with an unknown form of heteroskedasticity. In particular, it develops various HCCM-type corrections to improve the finite sample properties of the RGMME and the conventional Wald test. The Monte Carlo results indicate that the HCCM-type corrections can produce more accurate results for inference on model parameters and the impact effects estimates in small samples.     

A characterization of gamma mixtures of stable laws motivated by limit theorems

This pape; is concerned with distributional solutions of X₁+…+ X_m^d= U(X₁+…+ X_m+n) where the X's are iid and independent of U which takes values in [0,1]. When U is a constant the only possible non-trivial solutions lie in the class of semi-stable laws, and they are stable under a simple regularity condition. This material is reviewed. A unified account is given of some results known for the case where U has a beta (α, 1) law, apparently the only other case allowing explicit identification of all possible solutions.     

Variational Bayes approximation of factor stochastic volatility models

Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area, because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian inference for factor stochastic volatility models is usually done by Markov chain Monte Carlo methods (often by particle Markov chain Monte Carlo methods), which are usually slow for high dimensional or long time series because of the large number of parameters and latent states involved. Our article makes two contributions. The first is to propose a fast and accurate variational Bayes methods to approximate the posterior distribution of the states and parameters in factor stochastic volatility models. The second is to extend this batch methodology to develop fast sequential variational updates for prediction as new observations arrive. The methods are applied to simulated and real datasets, and shown to produce good approximate inference and prediction compared to the latest particle Markov chain Monte Carlo approaches, but are much faster.     

Generalized smooth finite mixtures

We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite mixture of component models with covariate-dependent mixing weights. The component densities can belong to any parametric family, with each model parameter being a deterministic function of covariates through a link function. Our MCMC methodology allows for Bayesian variable selection among the covariates in the mixture components and in the mixing weights. The model’s parameterization and variable selection prior are chosen to prevent overfitting. We use simulated and real data sets to illustrate the methodology.     

A characterization of admissible linear estimators of fixed and random effects in linear models

In the paper the problem of simultaneous linear estimation of fixed and random effects in the mixed linear model is considered. A necessary and sufficient conditions for a linear estimator of a linear function of fixed and random effects in balanced nested and crossed classification models to be admissible are given.     

Patterns and dynamics of population heterogeneity in mixtures models

Mixtures of distributions are a common modelling tool for durations of social phenomena, especially when the population is believed to be heterogeneous. We discuss heterogeneity patterns which can be captured by various mixing distributions in continuous and discrete time. Particular attention is given to recidivism data which Kaplan modeled by beta-mixtures of geometric distributions. We also investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration. It is shown that not all mixture models display decreasing heterogeneity over time.     

Bayesian inference in time series models using kernel quasi likelihoods

The paper takes up Bayesian inference in time series models when essentially nothing is known about the distribution of the dependent variable given past realizations or other covariates. It proposes the use of kernel quasi likelihoods upon which formal inference can be based. Gibbs sampling with data augmentation is used to perform the computations related to numerical Bayesian analysis of the model. The method is illustrated with artificial and real data sets.     

Approximate inference in multivariate nonlinear functional relationships

An estimation procedure based on estimating equations is presented for the parameters in a multivariate functional relationship model, where all observations are subject to error. The covariance matrix of the observational errors may be parametrized and is allowed to be different for different sets of observations. Estimators are defined for the unknown relation parameters and error parameters.
For linear models (i.e. where the model function is linear in the incidental parameters) the estimators are consistent and asymptotically normal. A consistent expression for the covariance matrix of the estimators is derived. The results are valid for general error distributions.
For nonlinear models the estimators are based on locally linear approximations to the model function. The afore mentioned properties of the estimators are now only approximately valid. The adequacy of the approximate inference, based on asymptotic theory for the linearized model, needs at least informal check. Some examples are given to illustrate the estimation procedure.     

Fisher information under Gaussian quadrature models

This paper develops formulae to compute the Fisher information matrix for the regression parameters of generalized linear models with Gaussian random effects. The Fisher information matrix relies on the estimation of the response variance under the model assumptions. We propose two approaches to estimate the response variance: the first is based on an analytic formula (or a Taylor expansion for cases where we cannot obtain the closed form), and the second is an empirical approximation using the model estimates via the expectation–maximization process. Further, simulations under several response distributions and a real data application involving a factorial experiment are presented and discussed. In terms of standard errors and coverage probabilities for model parameters, the proposed methods turn out to behave more reliably than does the ‘disparity rule’ or direct extraction of results from the generalized linear model fitted in the last expectation–maximization iteration.     

简析滚轮齿条在直线运动机构中的优势

滚轮齿条驱动机构是一种新型的直线驱动机构,滚轮齿条的驱动方式与传统齿轮齿条驱动方式相比,有更优越的驱动效果,滚轮齿条在轮齿双方向上保证零背隙,能实现高速的运行能力,往复定位精度将比传统齿轮齿条传定位精度更加精确。滚轮齿条驱动在自动化生产线中也更大的提高了产线往复的效率,使设备运动精度得到了进一步提高,为下一工序的顺利进行提供了重要保障。     

Asymptotic consequences of neglected dynamics in individual effects models*

We assess the asymptotic consequences of estimating static models based on cross-section or panel data, when in reality the data are generated by a dynamic relationship, involving lagged dependent and current and lagged exogenous variables as well as individual effects. If the exogenous variable follows a stationary process, then the static estimators usually underestimate its long-run effect. This inconsistency is less severe, the higher the autocorrelation of the exogenous variable. If the exogenous variable follows a random walk with or without individual-specific drift, then the estimators are found to be consistent for the long-run effect.     

Forecasting crude oil prices with DSGE models

In this study, we conducted an oil prices forecasting competition among a set of structural models, including vector autoregression and dynamic stochastic general equilibrium (DSGE) models. Our results highlight two principles. First, forecasts should exploit the fact that real oil prices are mean reverting over long horizons. Second, models should not replicate the high volatility of the oil prices observed in samples. By following these principles, we show that an oil sector DSGE model performs much better at real oil price forecasting than random walk or vector autoregression.     

Robustness of normal theory statistics in structural equation models*

A condition is given by which optimal normal theory methods, such as the maximum likelihood methods, are robust against violation of the normality assumption in a general linear structural equation model. Specifically, the estimators and the goodness of fit test are robust. The estimator is efficient within some defined class, and its standard errors can be obtained by a correction formula applied to the inverse of the information matrix. Some special models, like the factor analysis model and path models, are discussed in more detail. A method for evaluating the robustness condition is given.     

Thinning and harvesting in stochastic forest models

This paper analyzes a stochastic forest growth model in which the manager is able to first thin the forest to promote better growth before harvesting. Both Wicksell single thinning and harvesting cycle and Faustmann on-going rotation problems are considered. The Wicksell problem is analyzed by first restricting the class of decision times to (thinning, harvesting) pairs that bound the growth away from infinity and imbedding the problem in an infinite-dimensional linear program on a space of triplets of measures. These measures capture the thinning and harvesting decisions along with the behavior of the growth process prior to harvest. An auxiliary linear program then leads to a nonlinear optimization problem for which an optimal value and solution are determined. The values of all the problems are be related through a set of inequalities. The solution of the nonlinear problem determines (random) thinning and harvesting times for the single thinning and harvesting cycle which demonstrate the equality of the values of these various problems. Finally for the Wicksell problem, the unrestricted class of thinning and harvest times is shown to give the same value as the restricted class. The Faustmann on-going thinning and harvesting rotation problem is reduced to a Wicksell problem which then allows for the characterization of the value as the solution to a different nonlinear optimization problem. The effects of the opportunity to thin the forest are illustrated on a mean-reverting stochastic model.     

Logarithmic calibration for multiplicative distortion measurement errors regression models

In this article, we propose a new identifiability condition by using the logarithmic calibration for the distortion measurement error models, where neither the response variable nor the covariates can be directly observed but are measured with multiplicative measurement errors. Under the logarithmic calibration, the direct-plug-in estimators of parameters and empirical likelihood based confidence intervals are proposed, and we studied the asymptotic properties of the proposed estimators. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the restricted estimator and test statistic are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.