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参数维度增长下的简约模型平均AI 解读

Model averaging generally provides better predictions than model selection, but the existing model averaging methods cannot lead to parsimonious models. Parsimony is an especially important property when the number of parameters is large. To achieve a parsimonious model averaging coefficient estimator, we suggest a novel criterion for choosing weights. Asymptotic properties are derived in two practical scenarios: (i) one or more correct models exist in the candidate model…

MALMEM：线性测量误差模型中的模型平均AI 解读

Summary We develop model averaging estimation in the linear regression model where some covariates are subject to measurement error. The absence of the true covariates in this framework makes the calculation of the standard residual-based loss function impossible. We take advantage of the explicit form of the parameter estimators and construct a weight choice criterion. It is asymptotically equivalent to the unknown model average estimator minimizing the loss function. When…

通过混合 Copula 平均估计金融数据依赖结构AI 解读

A mixture copula is a linear combination of several individual copulas that can be used to generate dependence structures not belonging to existing copula families. Because different pairs of markets may exhibit quite different dependence structures in empirical studies, mixture copulas are useful in modeling the dependence in financial data. Therefore, rather than selecting a single copula based on certain criteria, we propose using a model averaging approach to estimate…

线性回归模型平均后的推断AI 解读

This article considers the problem of inference for nested least squares averaging estimators. We study the asymptotic behavior of the Mallows model averaging estimator (MMA; Hansen, 2007) and the jackknife model averaging estimator (JMA; Hansen and Racine, 2012) under the standard asymptotics with fixed parameters setup. We find that both MMA and JMA estimators asymptotically assign zero weight to the under-fitted models, and MMA and JMA weights of just-fitted and…

合并还是不合并：面板回归参数估计与预测的策略AI 解读

Summary This paper considers estimating the slope parameters and forecasting in potentially heterogeneous panel data regressions with a long time dimension. We propose a novel optimal pooling averaging estimator that makes an explicit trade‐off between efficiency gains from pooling and bias due to heterogeneity. By theoretically and numerically comparing various estimators, we find that a uniformly best estimator does not exist and that our new estimator is superior in…

变系数部分线性模型的Mallows型模型平均估计AI 解读

In the last decade, significant theoretical advances have been made in the area of frequentist model averaging (FMA); however, the majority of this work has emphasized parametric model setups. This article considers FMA for the semiparametric varying-coefficient partially linear model (VCPLM), which has gained prominence to become an extensively used modeling tool in recent years. Within this context, we develop a Mallows-type criterion for assigning model weights and prove…

基于留主体交叉验证的向量自回归模型平均AI 解读

The vector autoregressive (VAR) model is a useful tool for economic evaluation and prediction. This paper develops a leave-subject-out cross-validation model averaging (LsoMA) method to average predictions from VAR models. The approximate unbiasedness of LsoMA and its asymptotic optimality in terms of obtaining the lowest possible quadratic errors are established. The rate of the LsoMA based weights converging to the optimal weights minimizing the expected quadratic errors…

通过函数型线性回归模型平均进行函数预测AI 解读

Prediction is often the primary goal of data analysis. In this work, we propose a novel model averaging approach to the prediction of a functional response variable. We develop a crossvalidation model averaging estimator based on functional linear regression models in which the response and the covariate are both treated as random functions. We show that the weights chosen by the method are asymptotically optimal in the sense that the squared error loss of the predicted…

误设广义线性混合模型的渐近性质与信息准则AI 解读

Summary The problem of misspecification poses challenges in model selection. The paper studies the asymptotic properties of estimators for generalized linear mixed models with misspecification under the framework of conditional Kullback–Leibler divergence. A conditional generalized information criterion is introduced, and a model selection procedure is proposed by minimizing the criterion. We prove that the model selection procedure proposed is asymptotically loss efficient…

空间自回归模型的权重矩阵选择与模型平均AI 解读

Spatial econometrics relies on the spatial weights matrix to specify the cross-sectional dependence; however, the candidate spatial weights matrices might not be unique. This paper proposes a model selection procedure to choose a weights matrix from several candidates by using a Mallows type criterion. We prove that when the true weights matrix is not in the candidates, the procedure is asymptotically optimal in the sense of minimizing the squared loss; otherwise, the…

协变量含测量误差时的线性模型选择AI 解读

Prediction precision is arguably the most relevant criterion of a model in practice and is often a sought after property. A common difficulty with covariates measured with errors is the impossibility of performing prediction evaluation on the data even if a model is completely given without any unknown parameters. We bypass this inherent difficulty by using special properties on moment relations in linear regression models with measurement errors. The end product is a model…

广义线性模型与广义线性混合效应模型的最优模型平均估计AI 解读

Considering model averaging estimation in generalized linear models, we propose a weight choice criterion based on the Kullback–Leibler (KL) loss with a penalty term. This criterion is different from that for continuous observations in principle, but reduces to the Mallows criterion in the situation. We prove that the corresponding model averaging estimator is asymptotically optimal under certain assumptions. We further extend our concern to the generalized linear…

基于留一受试者交叉验证的模型平均AI 解读

This paper develops a frequentist model averaging method based on the leave-subject-out cross-validation. This method is applicable not only to averaging longitudinal data models, but also to averaging time series models which can have heteroscedastic errors. The resulting model averaging estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors. Both simulation study and empirical example show the superiority of the…

用验证信息准则确定降维模型的结构维数AI 解读

A crucial component of performing sufficient dimension reduction is to determine the structural dimension of the reduction model. We propose a novel information criterion-based method for this purpose, a special feature of which is that when examining the goodness-of-fit of the current model, one needs to perform model evaluation by using an enlarged candidate model. Although the procedure does not require estimation under the enlarged model of dimension k+1, the decision as…

离散响应时间序列的自适应组合预测AI 解读

Adaptive combining is generally a desirable approach for forecasting, which, however, has rarely been explored for discrete response time series. In this paper, we propose an adaptively combined forecasting method for such discrete response data. We demonstrate in theory that the proposed forecast is of the desired adaptation with respect to the widely used squared risk and other significant risk functions under mild conditions. Furthermore, we study the issue of adaptation…

依赖数据模型中基于刀切准则的模型平均AI 解读

The past decade witnessed a literature on model averaging by frequentist methods. For the most part, the asymptotic optimality of various existing frequentist model averaging estimators has been established under i.i.d. errors. Recently, Hansen and Racine [Hansen, B.E., Racine, J., 2012. Jackknife model averaging. Journal of Econometrics 167, 38–46] developed a jackknife model averaging (JMA) estimator, which has an important advantage over its competitors in that it…

非零阈值 Tobit 模型中的聚焦信息准则、模型选择与模型平均AI 解读

Claeskens and Hjort (2003) have developed a focused information criterion (FIC) for model selection that selects different models based on different focused functions with those functions tailored to the parameters singled out for interest. Hjort and Claeskens (2003) also have presented model averaging as an alternative to model selection, and suggested a local misspecification framework for studying the limiting distributions and asymptotic risk properties of post-model…

频率学派模型平均估计量的最优权重选择AI 解读

There has been increasing interest recently in model averaging within the frequentist paradigm. The main benefit of model averaging over model selection is that it incorporates rather than ignores the uncertainty inherent in the model selection process. One of the most important, yet challenging, aspects of model averaging is how to optimally combine estimates from different models. In this work, we suggest a procedure of weight choice for frequentist model average…

广义可加部分线性模型的聚焦信息准则与模型平均AI 解读

We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major…

基于 Mallows 准则的最小二乘模型平均AI 解读

This paper is in response to a recent paper by Hansen (2007) who proposed an optimal model average estimator with weights selected by minimizing a Mallows criterion. The main contribution of Hansen's paper is a demonstration that the Mallows criterion is asymptotically equivalent to the squared error, so the model average estimator that minimizes the Mallows criterion also minimizes the squared error in large samples. We are concerned with two assumptions that accompany…