Empirical information criteria for time series forecasting model selection

In this article, we propose a new empirical information criterion (EIC) for model selection which penalizes the likelihood of the data by a non-linear function of the number of parameters in the model. It is designed to be used where there are a large number of time series to be forecast. However, a bootstrap version of the EIC can be used where there is a single time series to be forecast. The EIC provides a data-driven model selection tool that can be tuned to the particular forecasting task.

We compare the EIC with other model selection criteria including Akaike’s information criterion (AIC) and Schwarz’s Bayesian information criterion (BIC). The comparisons show that for the M3 forecasting competition data, the EIC outperforms both the AIC and BIC, particularly for longer forecast horizons. We also compare the criteria on simulated data and find that the EIC does better than existing criteria in that case also.     

Weighted bivariate logarithmic series distributions

In this paper, we are interested in the weighted distributions of a bivariate three parameter logarithmic series distribution studied by Kocherlakota and Kocherlakota (1990). The weighted versions of the model are derived with weight W(x,y) = x^[r] y^[s]. Explicit expressions for the probability mass function and probability generating functions are derived in the case r = s = l. The marginal and conditional distributions are derived in the general case. The maximum likelihood estimation of the parameters, in both two parameter and three parameter cases, is studied. A procedure for computer generation of bivariate data from a discrete distribution is described. This enables us to present two examples, in order to illustrate the methods developed, for finding the maximum likelihood estimates.     

Adaptive weights smoothing with applications to image restoration

We propose a new method of nonparametric estimation which is based on locally constant smoothing with an adaptive choice of weights for every pair of data points. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on some simulated univariate and bivariate examples and compare it with other nonparametric methods. Finally we discuss applications of this procedure to magnetic resonance and satellite imaging.     

Smoothing a Time Series by Segments of the Data Range

We consider the problem of estimating a trend with different amounts of smoothness for segments of a time series subjected to different variability regimes. We propose using an unobserved components model to consider the existence of at least two data segments. We first fix some desired percentages of smoothness for the trend segments and deduce the corresponding smoothing parameters involved. Once the size of each segment is chosen, the smoothing formulas here derived produce trend estimates for all segments with the desired smoothness as well as their corresponding estimated variances. Empirical examples from demography and economics illustrate our proposal.     

On Locating and Characterizing Parameter Variation by the Mosumsq Test Statistic

In modelling a system structure it is often important to test the constancy of the structural parameters. If the hypothesis of constant parameters is rejected we wish to characterize the parameter variation. In this paper we examine the usefulness of the MOSUMSQ test statistics for locating and characterizing the parameter variation in linear regression models. The means and the variances of the test statistics are given for non-random parameter variation. The observed path of the MOSUMSQ test statistics provides valuable knowledge about the time of the onset of the parameter change and whether it is instantaneous or gradual.     

A cubic smoothing spline based lack of fit test for nonlinear regression models

The use of a statistic based on cubic spline smoothing is considered for testing nonlinear regression models for lack of fit. The statistic is defined to be the Euclidean squared norm of the smoothed residual vector obtained from fitting the nonlinear model, The asymptotic distribution of the statistic is derived under suitable smooth local alternatives and a numerical example is presented.     

Bayesian estimation of multidimensional item response theory model using gibbs sampling

We propose Bayesian parameter estimation in a multidimensional item response theory model using the Gibbs sampling algorithm. We apply this approach to dichotomous responses to a questionnaire on sleep quality. The analysis helps determine the underlying dimensions.     

Improved likelihood-based inference for the stationary AR(2) model

An improved likelihood-based method based on Fraser et al. (1999) is proposed in this paper to test the significance of the second lag of the stationary AR(2) model. Compared with the test proposed by Fan and Yao (2003) and the signed log-likelihood ratio test, the proposed method has remarkable accuracy. Simulation studies are performed to illustrate the accuracy of the proposed method. Application of the proposed method on historical data is presented to demonstrate the implementation of this method. Furthermore, the method can be extended to the general AR(p) model.     

Flexible regression modeling

The author proposes a new method for flexible regression modeling of multi‐dimensional data, where the regression function is approximated by a linear combination of logistic basis functions. The method is adaptive, selecting simple or more complex models as appropriate. The number, location, and (to some extent) shape of the basis functions are automatically determined from the data. The method is also affine invariant, so accuracy of the fit is not affected by rotation or scaling of the covariates. Squared error and absolute error criteria are both available for estimation. The latter provides a robust estimator of the conditional median function. Computation is relatively fast, particularly for large data sets, so the method is well suited for data mining applications.     

饱和粘土蠕变特性研究及参数确定

将两种弹 粘弹性模型（Burgers和H 2K模型）的一维蠕变方程，转换成三维状态下的应力 应变 时间关系，分别推导出常应力下两种模型的轴向应变随时间变化的方程。采用分级加载法进行室内长期单轴压缩蠕变试验，结合两种模型三维应力状态的轴向应变表达式，对试验结果进行拟合，得出相应模型的本构参数。试验结果表明：饱和粘土在新增荷载作用下2~3　d变形趋于稳定，Burgers模型和H 2K模型均能较好地模拟饱和粘土的衰减蠕变过程；而H 2K模型能更好地模拟土样在常应力作用下的蠕变特性。