Partial Least Squares (PLS) is a standard statistical method in chemometrics. It can be considered as an incomplete, or “partial”, version of the Least Squares estimator of regression, applicable when high or perfect multicollinearity is present in the predictor variables. The Least Squares estimator is well-known to be an optimal estimator for regression, but only when the error terms are norm...

state estimation is the foundation of any control and decision making in power networks. the first requirement for a secure network is a precise and safe state estimator in order to make decisions based on accurate knowledge of the network status. this paper introduces a new estimator which is able to detect bad data with few calculations without need for repetitions and estimation residual cal...

The exponential series density estimator is advantageous to the copula density estimation as it is strictly positive, explicitly defined on a bounded support, and largely mitigates the boundary bias problem. However, the selection of basis functions is challenging and can cause numerical difficulties, especially for high dimensional density estimations. To avoid the issues associated with basis...

In this paper, we present an M-estimator based robust radial basis function (RBF) learning algorithm with growing and pruning techniques. The Welsch M-estimator and median scale estimator are employed to avoid the influence from outliers. The concept of neuron significance is adopted to implement the growing and pruning techniques of network nodes. The proposed method not only eliminates the in...

Gaussian kernel regularization is widely used in the machine learning literature and has proved successful in many empirical experiments. The periodic version of Gaussian kernel regularization has been shown to be minimax rate optimal in estimating functions in any finite order Sobolev space. However, for a data set with n points, the computation complexity of the Gaussian kernel regularization...

A crucial ingredient of the Neyman (1937) “smooth type” tests for goodness-of-fit is the selection of the smoothing parameter, which is influenced dramatically by one’s notion of optimality. This is illustrated with the test based on the L1 difference between the histogram estimator and its expectation under the null hypothesis. We determine asymptotically the minimum power β(n,m, δ) as a funct...

This paper intends to improve the accuracy of power system State Estimation (SE) by introducing a hybrid linear robust state estimator. To this end, automatic bad data rejection is accomplished through an M-estimator, i.e. Schweppe-type estimator with Huber loss function. The method Iteratively Reweighted Least Squares (IRLS) used maximize likelihood function in M-estimator. Leverage measuremen...