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Estimation of a function, or its derivatives via nonparametric regression requires selection of one or more tuning parameters. In the present work, we propose a tuning parameter selection criterion called DCp for nonparametric derivative estimation in random design. Our criterion is general in that it can be applied with any nonparametric estimation method which is linear in the observed outcomes. Charnigo et al. [A generalized $ C_p $ C p criterion for derivative estimation. Technometrics. 2011;53(3):238–253] had proposed a GCp criterion for a similar purpose, assuming values of the covariate to be fixed and constant error variance. Here we consider the setting with random design and non-constant error variance since the covariate values will not generally be fixed and equally spaced in real data applications. We justify DCp in this setting both theoretically and by simulation. We also illustrate use of DCp with two economics data sets. [ABSTRACT FROM AUTHOR]

This article studies the generalized method of moment estimation of semiparametric varying coefficient partially linear spatial autoregressive model. The technique of profile least squares is employed and all estimators have explicit formulas which are computationally convenient. We derive the limiting distributions of the proposed estimators for both parametric and non parametric components. Variable selection procedures based on smooth-threshold estimating equations are proposed to automatically eliminate irrelevant parameters and zero varying coefficient functions. Compared to the alternative approaches based on shrinkage penalty, the new method is easily implemented. Oracle properties of the resulting estimators are established. Large amounts of Monte Carlo simulations confirm our theories and demonstrate that the estimators perform reasonably well in finite samples. We also apply the novel methods to an empirical data analysis. [ABSTRACT FROM AUTHOR]

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy‐tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large‐scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among older women. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the secondary control problems of AC microgrids with physical states (i.e., voltage, frequency and power, etc.) constrained in the process of actual control, namely, under the condition of state constraint. On the basis of the primary control (i.e., droop control), the control signals generated by distributed secondary control algorithm are used to solve the problems of voltage and frequency recovery and power allocation for each distributed generators (DGs). Therefore, the model predictive control (MPC) with the mechanism of rolling optimization is adopted in the second control layer to achieve the above control objectives and solve the physical state constraint problem at the same time. Meanwhile, in order to reduce the communication cost, we designed the self-triggered control based on the prediction mechanism of MPC. In addition, the proposed algorithm of self-triggered MPC does not need sampling and detection at any time, thus avoiding the design of observer and reducing the control complexity. In addition, the Zeno behavior is excluded through detailed analysis. Furthermore, the stability of the algorithm is verified by theoretical derivation of Lyapunov. Finally, the effectiveness of the algorithm is proved by simulation. [ABSTRACT FROM AUTHOR]