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Bootstrap 模型平均AI 解读

Model averaging has garnered significant attention in recent years for its ability to combine information from multiple models. A critical challenge in frequentist model averaging is determining the appropriate weight vector. The bootstrap method, well-known for its desirable properties, offers a promising solution. In this article, we propose a bootstrap model averaging approach that selects weights by minimizing a bootstrap-based criterion. Notably, our weight selection…

核平均估计量AI 解读

The issue of bandwidth selection is a fundamental model selection problem stemming from the uncertainty about the smoothness of the regression. In this article, we advocate a model averaging approach to circumvent the problem caused by this uncertainty. Our new approach involves averaging across a series of Nadaraya-Watson kernel estimators each under a different bandwidth, with weights for these different estimators chosen such that a least-squares cross-validation…

参数维数增长的时间序列模型平均预测AI 解读

An important problem with the model averaging approach is the choice of weights. In this paper, a generalized Mallows model averaging (GMMA) criterion for choosing weights is developed in the context of an infinite order autoregressive (AR(∞)) process. The GMMA method adapts to the circumstances in which the dimensions of candidate models can be large and increase with the sample size. The GMMA method is shown to be asymptotically optimal in the sense of achieving the lowest…

具有网络结构的高维协方差矩阵的模型平均估计AI 解读

Summary In this paper, we develop a model averaging method to estimate a high-dimensional covariance matrix, where the candidate models are constructed by different orders of polynomial functions. We propose a Mallows-type model averaging criterion and select the weights by minimizing this criterion, which is an unbiased estimator of the expected in-sample squared error plus a constant. Then, we prove the asymptotic optimality of the resulting model average covariance…

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…

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…

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…

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…

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…

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…

受限最小二乘估计量对协方差误设的敏感性AI 解读

Traditional econometrics has long stressed the serious consequences of non-spherical disturbances for the estimation and testing procedures under the spherical disturbance setting, that is, the procedures become invalid and can give rise to misleading results. In practice, it is not unusual, however, to find that the parameter estimates do not change much after fitting the more general structure. This suggests that the usual procedures may well be robust to covariance…

回归误差方差估计中预检验最优临界值的进一步结果AI 解读

This paper enlarges on results of Wan and Zou (Journal of Econometrics 114 (2003), 165--96) on the choice of critical values for pre-test procedures based on the minimum risk criterion. We consider a modification of the general theorem given in Wan and Zou (2003) to obtain the optimal critical value that minimizes the risks of various inequality pre-test estimators of the regression error variance under a general class of first-order differentiable loss functions.…

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