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In practice, it is common for collected data to be underreported, an issue that is particularly prevalent in fields such as the social sciences, ecology and epidemiology. Drawing inferences from such data using conventional statistical methods can lead to incorrect conclusions. In this paper, we study tests for serial or cross dependence in time series data that are subject to underreporting. We introduce new test statistics, develop corresponding group-of-blocks bootstrap techniques and establish their consistency. The methods are shown via simulation studies to be efficient and are used to identify key factors responsible for the spread of dengue fever and the occurrence of cardiovascular disease. [ABSTRACT FROM AUTHOR]

Sufficient dimension reduction (SDR) has progressed steadily. However, its ability to improve general function estimation or classification has not been well received, especially for high-dimensional data. In this article, we first devise a local linear smoother for high dimensional nonparametric regression and then utilise it in the outer-product-of-gradient (OPG) approach of SDR. We call the method high-dimensional OPG (HOPG). To apply SDR to classification in high-dimensional data, we propose an ensemble classifier by aggregating results of classifiers that are built on subspaces reduced by the random projection and HOPG consecutively from the data. Asymptotic results for both HOPG and the classifier are established. Superior performance over the existing methods is demonstrated in simulations and real data analyses. for this article are available online. [ABSTRACT FROM AUTHOR]

The Gaussian radial basis function (RBF) is a widely used kernel function in kernel-based methods. The parameter in RBF, referred to as the shape parameter, plays an essential role in model fitting. In this paper, we propose a method to select the shape parameters for the general Gaussian RBF kernel. It can simultaneously serve for variable selection and regression function estimation. For the former, asymptotic consistency is established; for the latter, the estimation is as efficient as if the true or optimal shape parameters are known. Simulations and real examples are used to illustrate the method's performance of prediction by comparing it with other popular methods. [ABSTRACT FROM AUTHOR]

The existing methods for subgroup analysis can be roughly divided into two categories: finite mixture models (FMM) and regularization methods with an ℓ1‐type penalty. In this paper, by introducing the group centers and ℓ2‐type penalty in the loss function, we propose a novel center‐augmented regularization (CAR) method; this method can be regarded as a unification of the regularization method and FMM and hence exhibits higher efficiency and robustness and simpler computations than the existing methods. In particular, its computational complexity is reduced from the O(n2)$O(n^2)$ of the conventional pairwise‐penalty method to only O(nK)$O(nK)$, where n is the sample size and K is the number of subgroups. The asymptotic normality of CAR is established, and the convergence of the algorithm is proven. CAR is applied to a dataset from a multicenter clinical trial, Buprenorphine in the Treatment of Opiate Dependence; a larger R2 is produced and three additional significant variables are identified compared to those of the existing methods. [ABSTRACT FROM AUTHOR]