There are few techniques available for testing whether or not a family of parametric times series models fits a set of data reasonably well without serious restrictions on the forms of alternative models. In this paper, we consider generalised likelihood ratio tests of whether or not the spectral density function of a stationary time series admits certain parametric forms. We propose a bias correction method for the generalised likelihood ratio test of Fan et al. (2001). In particular, our methods can be applied to test whether or not a residual series is white noise. Sampling properties of the proposed tests are established. A bootstrap approach is proposed for estimating the null distribution of the test statistics. Simulation studies investigate the accuracy of the proposed bootstrap estimate and compare the power of the various ways of constructing the generalised likelihood ratio tests as well as some classic methods like

Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to capture the varying association between imaging measures in a three-dimensional volume (or two-dimensional surface) with a set of covariates. Two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unknown edges and jumps and substantial spatial correlations. To specifically account for these two features, SVCM includes a measurement model with multiple varying coefficient functions, a jumping surface model for each varying coefficient function, and a functional principal component model. We develop a three-stage estimation procedure to simultaneously estimate the varying coefficient functions and the spatial correlations. The estimation procedure includes a fast multiscale adaptive estimation and

This article deals with statistical inferences based on the varying-coefficient models proposed by Hastie and Tibshirani. Local polynomial regression techniques are used to estimate coefficient functions, and the asymptotic normality of the resulting estimators is established. The standard error formulas for estimated coefficients are derived and are empirically tested. A goodness-of-fit test technique, based on a nonparametric maximum likelihood ratio type of test, is also proposed to detect whether certain coefficient functions in a varying-coefficient model are constant or whether any covariates are statistically significant in the model. The null distribution of the test is estimated by a conditional bootstrap method. Our estimation techniques involve solving hundreds of local likelihood equations. To reduce the computational burden, a one-step Newton-Raphson estimator is proposed and implemented. The resulting one

Discrepancy is a kind of important measure used in experimental design. Recently, a so-called discrete discrepancy has been applied to evaluate the uniformity of factorial designs. In this paper, we review some recent advances on application of the discrete discrepancy to several common experimental designs and summarize some important results.

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three sparsity exploration problems under a unified framework with a general penalty function. We show that the rates of convergence for these problems under the Frobenius norm are of order (s n log p n/n) 1/2, where s n is the number of nonzero elements, p n is the size of the covariance matrix and n is the sample size. This explicitly spells out the contribution of high-dimensionality is merely of a logarithmic factor. The conditions on the rate with which