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We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a given proportion of variance. The computation of these solutions is very efficient. The proposed method compares well with the optimal least squares sparse components. We show that other SPCA methods fail to identify the best sparse approximations of the principal components and explain less variance than our solutions. We illustrate and compare our method with others with extensive simulations and with the analysis of the computational results for nine datasets of increasing dimensions up to 16,000 variables.

This paper obtains some specific density functions for aggregated discounted claims where the claim amounts are dependent, or the inter-claim times are dependent, or the claim amounts and the claim arrival process are both dependent. The dependence is structured through mixing, and the claim arrival process studied is either an ordinary Poisson process or a mixed Poisson process. Closed form densities are obtained for gamma, generalized exponential, generalized Pareto and beta mixing, and an important use of them is illustrated.

Generalized method of moment (GMM) is an important estimation method for econometric models. However, it is highly sensitive to the outliers and influential observations. This paper studies the detection of influential observations using GMM estimation and establishes some useful diagnostic tools, such as residual and leverage measures. The case deletion technique is employed to derive diagnostic measures. Under linear moment conditions, an exact deletion formula is derived, and under nonlinear moment condition an approximate formula is suggested. The results are applied to efficient instrumental variable estimation and dynamic panel data models. In addition, generalized residuals and leverage measure for GMM estimator are defined and discussed. Two real data sets are used for illustration and a simulation study is conducted to confirm the usefulness of the proposed methodology.

This paper studies the estimation and inference for a class of varying-coefficient regression models with error-prone covariates. The authors focus on the situation where the covariates are unobserved, there are no repeated measurements, and the covariance matrix of the measurement errors is unknown, but some auxiliary information is available. The authors propose an instrumental variable type local polynomial estimator for the unknown varying-coefficient functions, and show that the estimator achieves the optimal nonparametric convergence rate, is asymptotically normal, and avoids using undersmoothing to allow the bandwidths to be selected using data-driven methods. A simulation is carried out to study the finite sample performance of the proposed estimator, and a real date set is analyzed to illustrate the usefulness of the developed methodology.

The generalized Pareto distribution (GPD) is important in the analysis of extreme values, especially in modeling exceedances over thresholds. Most of the existing methods for estimating the scale and shape parameters of the GPD suffer from theoretical and/or computational problems. A new hybrid estimation method is proposed in this article, which minimizes a goodness-of-fit measure and incorporates some useful likelihood information. Compared with the maximum likelihood method and other leading methods, our new hybrid estimation method retains high efficiency, reduces the estimation bias, and is computation friendly.