The empirical best linear unbiased predictor (EBLUP) or the empirical Bayes estimator (EB) in the linear mixed model is recognized as being useful for small area estimation, because it can increase the estimation precision by using information from the related areas. Two of the measures of uncertainty of the EBLUP are the estimation of the mean squared error (MSE) and the confidence interval, which have been studied under second-order accuracy in the literature. This paper provides general and advanced analytical results for these two measures in the unified framework. Namely, we derive the conditions on the general consistent estimators of the variance components so as to establish third-order accuracy in the estimation of the MSE and confidence interval in the general linear mixed normal models. Those conditions are shown to be satisfied by not only the maximum likelihood (ML) and restricted maximum likelihood (REML), but also other estimators including the Prasad-Rao and Fay-Herriot estimators in specific models.
Zografos et al. (1990) introduced the φ-divergence family of statistics Cφ to the goodness-of-fit test. The φ-divergence family of statistics Cφ includes the power divergence family of statistics proposed by Cressie and Read (Cressie and Read (1984) and Read and Cressie (1988)) as a special case. Sekiya and Taneichi (2004) derived the multivariate Edgeworth expansion assuming a continuous distribution for the distributions of power divergence statistics under a nonlocal alternative hypothesis. In this paper, we consider an expansion for the family of general φ-divergence statistics Cφ. We derive the multivariate Edgeworth expansion assuming a continuous distribution for the distribution of Cφ under a nonlocal alternative hypothesis. By using the expansion, we propose a new approximation for the power of the statistic Cφ. We numerically investigate the accuracy of the approximation when two types of concrete φ-divergence statistics are applied. By the numerical investigation, we show that the present approximation is a good approximation especially when alternative hypotheses are distant from the null hypothesis.
The paper develops a new Dynamic Conditional Correlation (DCC) model, namely the Wishart DCC (wDCC) model. The paper applies the wDCC approach to the exponential GARCH (EGARCH) and GJR models to propose asymmetric DCC models. We use the standardized multivariate t-distribution to accommodate heavy-tailed errors. The paper presents an empirical example using the trivariate data of the Nikkei 225, Hang Seng and Straits Times Indices for estimating and forecasting the wDCC-EGARCH and wDCC-GJR models, and compares the performance with the asymmetric BEKK model. The empirical results show that AIC and BIC favour the wDCC-EGARCH model to the wDCC-GJR, asymmetric BEKK and alternative conventional DCC models. Moreover, the empirical results indicate that the wDCC-EGARCH-t model produces reasonable VaR threshold forecasts, which are very close to the nominal 1% to 3% values.
Nonparametric additive modeling is a fundamental tool for statistical data analysis which allows flexible functional forms for conditional mean or quantile functions but avoids the curse of dimensionality for fully nonparametric methods induced by high-dimensional covariates. This paper proposes empirical likelihood-based inference methods for unknown functions in three types of nonparametric additive models: (i) additive mean regression with the identity link function, (ii) generalized additive mean regression with a known non-identity link function, and (iii) additive quantile regression. The proposed empirical likelihood ratio statistics for the unknown functions are asymptotically pivotal and converge to chi-square distributions, and their associated confidence intervals possess several attractive features compared to the conventional Wald-type confidence intervals.
Computationally efficient methods for Bayesian analysis of Seemingly Unrelated Regression (SUR) models with a large number of predictors are developed. One of the most crucial problems in Bayesian modeling of SUR models is how to determine the optimal combination of predictors. In this paper, under a Bayesian hierarchical framework where each regression function is represented as a linear combination of a large number of basis functions, the regression coefficients, the variance matrix of the errors, and a set of predictors to be included in the model are estimated simultaneously. Usually the Bayesian model estimation problem is solved using Markov Chain Monte Carlo (MCMC) techniques. Herein we show how a direct Monte Carlo (DMC) technique can be employed to solve the variable selection and model parameter estimation problems more efficiently.
We propose semiparametric estimation of the memory parameter that controls persistence of autocorrelation in stationary long-memory signal plus white noise processes, including an important extension to long-memory stochastic volatility (LMSV) models. The proposed estimation is constructed from the Whittle likelihood based on fractional exponential (FEXP) models, which is called a global or broadband semiparametric estimation. We establish that the estimators are consistent without Gaussianity. A numerical examination reveals that the proposed estimation works well in finite samples. Finally, we provide an illustrative example of volatility analysis by using the LMSV model.