Statistical Papers最新文献

The estimation of signal dimension under heavy-tailed latent variable models is studied. As a primary contribution, robust extensions of an earlier estimator based on Gaussian Stein’s unbiased risk estimation are proposed. These novel extensions are based on the framework of elliptical distributions and robust scatter matrices. Extensive simulation studies are conducted in order to compare the novel methods with several well-known competitors in both estimation accuracy and computational speed. The novel methods are applied to a financial asset return data set.

Group LASSO (gLASSO) estimator has been recently proposed to estimate thresholds for the self-exciting threshold autoregressive model, and a group least angle regression (gLAR) algorithm has been applied to obtain an approximate solution to the optimization problem. Although gLAR algorithm is computationally fast, it has been reported that the algorithm tends to estimate too many irrelevant thresholds along with the relevant ones. This paper develops an active-set based block coordinate descent (aBCD) algorithm as an exact optimization method for gLASSO to improve the performance of estimating relevant thresholds. Methods and strategy for choosing the appropriate values of shrinkage parameter for gLASSO are also discussed. To consistently estimate relevant thresholds from the threshold set obtained by the gLASSO, the backward elimination algorithm (BEA) is utilized. We evaluate numerical efficiency of the proposed algorithms, along with the Single-Line-Search (SLS) and the gLAR algorithms through simulated data and real data sets. Simulation studies show that the SLS and aBCD algorithms have similar performance in estimating thresholds although the latter method is much faster. In addition, the aBCD-BEA can sometimes outperform gLAR-BEA in terms of estimating the correct number of thresholds under certain conditions. The results from case studies have also shown that aBCD-BEA performs better in identifying important thresholds.

A new goodness-of-fit (GoF) test is proposed and investigated for the Gaussianity of the observed functional data. The test statistic is the Cramér-von Mises distance between the observed empirical characteristic functional (CF) and the theoretical CF corresponding to the null hypothesis stating that the functional observations (process paths) were generated from a specific parametric family of Gaussian processes, possibly with unknown parameters. The asymptotic null distribution of the proposed test statistic is derived also in the presence of these nuisance parameters, the consistency of the classical parametric bootstrap is established, and some particular choices of the necessary tuning parameters are discussed. The empirical level and power are investigated in a simulation study involving GoF tests of an Ornstein–Uhlenbeck process, Vašíček model, or a (fractional) Brownian motion, both with and without nuisance parameters, with suitable Gaussian and non-Gaussian alternatives.

In biomedical studies, panel count data have been extensively investigated. Such data occur if study subjects are monitored or observed only at some discrete time points during observation periods. In addition, these data may be collected from multiple centers, and study subjects from the same center might be correlated. Limited literature exists for clustered panel count data. Ignoring such cluster effects could result in biased variance estimation. In this paper, two semiparametric additive mean models are proposed for clustered panel count data. The first model contains a common baseline function across all clusters, while the second model features cluster-specific baseline functions. Some estimation equations are derived to estimate the regression parameters of interest for the proposed two models. For the common baseline model, the baseline function is also estimated. Given some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. Extensive simulation studies are carried out and indicate that the proposed approaches perform well in finite samples. An application of the China Health and Nutrition Study is also provided for illustration.

The article offers a method for estimating the volatility covariance matrix of vectors of financial time series data using a change point approach. The proposed method supersedes general varying-coefficient parametric models, such as GARCH, whose coefficients may vary with time, by a change point model. In this study, an adaptive pointwise selection of homogeneous segments with a given right-end point by a local change point analysis is introduced. Sufficient conditions are obtained under which the maximum likelihood process is adaptive against the covariance estimate to yield an optimal rate of convergence with respect to the change size. This rate is preserved while allowing the jump size to diminish. Under these circumstances, argmax results of a two-sided negative Brownian motion or a two-sided negative drift random walk under vanishing and non-vanishing jump size regimes, respectively, provide inference for the change point parameter. Theoretical results are supported by the Monte–Carlo simulation study. A bivariate data on daily log returns of two US stock market indices as well as tri-variate data on daily log returns of three banks are analyzed by constructing confidence interval estimates for multiple change points that have been identified previously for each of the two data sets.