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Register a new userOn the asymptotic distribution of model averaging based on information criterion
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Added by
Miaomiao Wang
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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Smoothed AIC (S-AIC) and Smoothed BIC (S-BIC) are very widely used in model averaging and are very easily to implement. Especially, the optimal model averaging method MMA and JMA have only been well developed in linear models. Only by modifying, they can be applied to other models. But S-AIC and S-BIC can be used in all situations where AIC and BIC can be calculated. In this paper, we study the asymptotic behavior of two commonly used model averaging estimators, the S-AIC and S-BIC estimators, under the standard asymptotic with general fixed parameter setup. In addition, the resulting coverage probability in Buckland et al. (1997) is not studied accurately, but it is claimed that it will be close to the intended. Our derivation make it possible to study accurately. Besides, we also prove that the confidence interval construction method in Hjort and Claeskens (2003) still works in linear regression with normal distribution error. Both the simulation and applied example support our theory conclusion.
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Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function, which could be very sensitive to the presence of outliers in the data. In this paper, we propose an outlier-robust model averaging approach by Mallows-type criterion. The key idea is to develop weight choice criteria by minimising an estimator of the expected prediction error for the function being convex with an unique minimum, and twice differentiable in expectation, rather than the expected squared error. The robust loss functions, such as least absolute deviation and Hubers function, reduce the effects of large residuals and poor samples. Simulation study and real data analysis are conducted to demonstrate the finite-sample performance of our estimators and compare them with other model selection and averaging methods.
We introduce an information criterion, PCIC, for predictive evaluation based on quasi-posterior distributions. It is regarded as a natural generalisation of the widely applicable information criterion (WAIC) and can be computed via a single Markov chain Monte Carlo run. PCIC is useful in a variety of predictive settings that are not well dealt with in WAIC, including weighted likelihood inference and quasi-Bayesian prediction
Large, non-Gaussian spatial datasets pose a considerable modeling challenge as the dependence structure implied by the model needs to be captured at different scales, while retaining feasible inference. Skew-normal and skew-t distributions have only recently begun to appear in the spatial statistics literature, without much consideration, however, for the ability to capture dependence at multiple resolutions, and simultaneously achieve feasible inference for increasingly large data sets. This article presents the first multi-resolution spatial model inspired by the skew-t distribution, where a large-scale effect follows a multivariate normal distribution and the fine-scale effects follow a multivariate skew-normal distributions. The resulting marginal distribution for each region is skew-t, thereby allowing for greater flexibility in capturing skewness and heavy tails characterizing many environmental datasets. Likelihood-based inference is performed using a Monte Carlo EM algorithm. The model is applied as a stochastic generator of daily wind speeds over Saudi Arabia.
The analysis of record-breaking events is of interest in fields such as climatology, hydrology, economy or sports. In connection with the record occurrence, we propose three distribution-free statistics for the changepoint detection problem. They are CUSUM-type statistics based on the upper and/or lower record indicators which occur in a series. Using a version of the functional central limit theorem, we show that the CUSUM-type statistics are asymptotically Kolmogorov distributed. The main results under the null hypothesis are based on series of independent and identically distributed random variables, but a statistic to deal with series with seasonal component and serial correlation is also proposed. A Monte Carlo study of size, power and changepoint estimate has been performed. Finally, the methods are illustrated by analyzing the time series of temperatures at Madrid, Spain. The $textsf{R}$ package $texttt{RecordTest}$ publicly available on CRAN implements the proposed methods.
Contributed discussion to the paper of Drton and Plummer (2017), presented before the Royal Statistical Society on 5th October 2016.
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