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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 is concerned with the estimation problem in partially linear regression models with serially correlated errors. The authors propose a semiparametric generalized least squares estimator (SGLSE) for the parametric component and show that it is asymptotically more efficient than the semiparametric ordinary least squares estimator (SOLSE) in terms of asymptotic covariance matrix. Other properties of this SGLSE including the asymptotic normality and the law of the iterated logarithm are established as well. A simulation study is conducted to examine the finite-sample properties of the proposed estimator and an empirical example is discussed.

Consider a repeated measurement partially linear regression model with an unknown vector parameter β 1, an unknown function g(·), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions.

Consider a partially linear regression model with an unknown vector parameter β, an unknown functiong(·), and unknown heteroscedastic error variances. In this paper we develop an asymptotic semiparametric generalized least squares estimation theory under some weak moment conditions. These moment conditions are satisfied by many of the error distributions encountered in practice, and our theory does not require the number of replications to go to infinity.

A least squares non-parametric discovery process model has been developed recently for assessing petroleum resources in mature plays with complex size distribution characteristics. Applications of this model to oil plays in the Colorado Group suggests that these techniques can be used to assess petroleum plays composed of a mixture of pools comprising both conventional and unconventional petroleum accumulations. We use the Cardium oil play of the Colorado Group in the Western Canada Sedimentary Basin to illustrate use of the non-parametric approach for such a mixed petroleum play. Our Colorado Group resource assessment indicates a large remaining oil resource potential in this petroleum system, largely in tight unconventional reservoirs.

When fitting, by least squares, a linear model (with an intercept term) with $p$ parameters to $n$ data points, the asymptotic behavior of the residual empirical process is shown to be the same as in the single sample problem provided $p^3 \log^2 (p) /n \to 0$ for any error density having finite variance and a bounded first derivative. No further conditions are imposed on the sequence of design matrices. The result is extended to more general estimates with the property that the average error and average squared error in the fitted values are on the same order as for least squares.

This paper is concerned with a partial linear regression model with serially correlated random errors which are unobservable and modeled by a moving-average process of infinite order. We study a class of estimators for the linear regression coefficients as well as the function characterizing the non-linear part of the model, constructed based on general kernel smoothing and least squares methods. The law of iterated logarithm and strong convergence rates of these estimator are derived by truncating the moving-average error process, a procedure widely applied in the analysis of time series. Our results can be used to establish uniform strong convergence rate of the estimators of autocovariance and autocorrelation functions of the error process.