Approximate Studentization with marginal and conditional inference

Many inference problems lead naturally to a marginal or conditional measure of departure that depends on a nuisance parameter. As a device for first-order elimination of the nuisance parameter, we suggest averaging with respect to an exact or approximate confidence distribution function. It is shown that for many standard problems where an exact answer is available by other methods, the averaging method reproduces the exact answer. Moreover, for the gamma-mean problem, where the exact answer is not explicitly available, the averaging method gives results that agree closely with those obtained from higher-order asymptotic methods. Examples are discussed; detailed asymptotic calculations will be examined elsewhere.     

Bayesian Model Averaging in Proportional Hazard Models: Assessing the Risk of a Stroke

In the context of the Cardiovascular Health Study, a comprehensive investigation into the risk factors for strokes, we apply Bayesian model averaging to the selection of variables in Cox proportional hazard models. We use an extension of the leaps-and-bounds algorithm for locating the models that are to be averaged over and make available S-PLUS software to implement the methods. Bayesian model averaging provides a posterior probability that each variable belongs in the model, a more directly interpretable measure of variable importance than a P -value. P -values from models preferred by stepwise methods tend to overstate the evidence for the predictive value of a variable and do not account for model uncertainty. We introduce the partial predictive score to evaluate predictive performance. For the Cardiovascular Health Study, Bayesian model averaging predictively outperforms standard model selection and does a better job of assessing who is at high risk for a stroke.     

我国猪肉价格的影响因素是时变的吗？——基于动态模型平均的分析与预测

猪肉价格的超常波动给人民生活与相关产业发展均带来了不利影响。为有效识别猪肉价格影响因素并对猪肉价格进行科学的预测,从猪肉价格影响因素的时变特征入手,提出一套基于动态模型平均理论的猪肉价格影响因素与预测分析框架。 检测猪肉供给、猪肉需求、我国经济环境和国际市场等四个方面11个价格影响因素,研究并识别猪肉价格影响因素的时变特征,进而构建猪肉价格预测模型,并通过预测误差指标和Diebold Mariano检验比较其与基准模型的预测能力。研究发现：我国猪肉价格影响因素存在显著的时变特征,且因素间差异明显;自2009年以来,猪肉价格的决定机制更为复杂,影响因素更为多元;基于动态模型平均的猪肉价格预测模型的预测表现明显优于基准模型。政府部门在制定生猪市场调控政策时,需充分考虑到供给、需求、我国经济环境、国际贸易对猪肉价格的影响,并且可以借助准确的猪肉价格预测信息以增强调控政策的主动性、前瞻性和科学性。     

A model averaging approach for the ordered probit and nested logit models with applications

This paper considers model averaging for the ordered probit and nested logit models, which are widely used in empirical research. Within the frameworks of these models, we examine a range of model averaging methods, including the jackknife method, which is proved to have an optimal asymptotic property in this paper. We conduct a large-scale simulation study to examine the behaviour of these model averaging estimators in finite samples, and draw comparisons with model selection estimators. Our results show that while neither averaging nor selection is a consistently better strategy, model selection results in the poorest estimates far more frequently than averaging, and more often than not, averaging yields superior estimates. Among the averaging methods considered, the one based on a smoothed version of the Bayesian Information criterion frequently produces the most accurate estimates. In three real data applications, we demonstrate the usefulness of model averaging in mitigating problems associated with the ‘replication crisis’ that commonly arises with model selection.     

Critical appraisal of jointness concepts in Bayesian model averaging: evidence from life sciences,sociology, and other scientific fields

Jointness is a Bayesian approach to capturing dependence among regressors in multivariate data. It addresses the general issue of whether explanatory factors for a given empirical phenomenon are complements or substitutes. I ask a number of questions about existing jointness concepts: Are the patterns revealed stable across datasets? Are results robust to prior choice and do data characteristics affect results? And importantly: What do the answers imply from a practical vista? The present study takes an applied, interdisciplinary and comparative perspective, validating jointness concepts on datasets across scientific fields with focus on life sciences (Parkinson's disease) and sociology. Simulations complement the study of real-world data. My findings suggest that results depend on which jointness concept is used: Some concepts deliver jointness patterns remarkably uniform across datasets, while all concepts are fairly robust to the choice of prior structure. This can be interpreted as critique of jointness from a practical perspective, given that the patterns revealed are at times very different and no concept emerges as overall advantageous. The composite indicators approach to combining information across jointness concepts is also explored, suggesting an avenue to facilitate the application of the concepts in future research.     

Constructing Optimal Instruments by First‐Stage Prediction Averaging

This paper considers model averaging as a way to construct optimal instruments for the two‐stage least squares (2SLS), limited information maximum likelihood (LIML), and Fuller estimators in the presence of many instruments. We propose averaging across least squares predictions of the endogenous variables obtained from many different choices of instruments and then use the average predicted value of the endogenous variables in the estimation stage. The weights for averaging are chosen to minimize the asymptotic mean squared error of the model averaging version of the 2SLS, LIML, or Fuller estimator. This can be done by solving a standard quadratic programming problem.     

Forecasting comparisons using a hybrid ARFIMA and LRNN models

In this article, an autoregressive fractionally integrated moving average model (ARFIMA) and a layer recurrent neural network (LRNN) were combined to form a hybrid forecasting model. The hybrid model was applied on the daily crude oil production data of the Nigerian National Petroleum Corporation (NNPC) to forecast the daily crude oil production of the NNPC. The Bayesian model averaging technique was used to obtain a combined forecast from the two separate methods. A comparison was made between the hybrid model with standalone ARFIMA and LRNN methods in which the hybrid model produced better forecasting performance than the standalone methods.     

Model averaging for multivariate multiple regression models

The theories and applications of model averaging have been developed comprehensively in the past two decades. In this paper, we consider model averaging for multivariate multiple regression models. In order to make use of the correlation information of the dependent variables sufficiently, we propose a model averaging method based on Mahalanobis distance which is related to the correlation of the dependent variables. We prove the asymptotic optimality of the resulting Mahalanobis Mallows model averaging (MMMA) estimators under certain assumptions. In the simulation study, we show that the proposed MMMA estimators compare favourably with model averaging estimators based on AIC and BIC weights and the Mallows model averaging estimators from the single dependent variable regression models. We further apply our method to the real data on urbanization rate and the proportion of non-agricultural population in ethnic minority areas of China.     

Can Long-Term Exposure Distributions Be Predicted from Short-Term Measurements?

A method for estimating long-term distributions of exposure based on repeated short-term measurements within the same population is developed. If the short-term measurements span seasonal variation, and if the distributions are log-normal or nearly so, then long-term distributions can be estimated from as few as two visits to the same population. The method is illustrated using examples drawn from EPA's TEAM Study of exposures to volatile organic compounds.     

Bayesian neural networks for nonlinear time series forecasting

In this article, we apply Bayesian neural networks (BNNs) to time series analysis, and propose a Monte Carlo algorithm for BNN training. In addition, we go a step further in BNN model selection by putting a prior on network connections instead of hidden units as done by other authors. This allows us to treat the selection of hidden units and the selection of input variables uniformly. The BNN model is compared to a number of competitors, such as the Box-Jenkins model, bilinear model, threshold autoregressive model, and traditional neural network model, on a number of popular and challenging data sets. Numerical results show that the BNN model has achieved a consistent improvement over the competitors in forecasting future values. Insights on how to improve the generalization ability of BNNs are revealed in many respects of our implementation, such as the selection of input variables, the specification of prior distributions, and the treatment of outliers.