Han Xiao

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SUMMARY In this paper, we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons. These quadratures have desirable properties such as positivity of weights and interiority of nodes and can readily be used as software libraries where(More)
We consider small factor analysis models with one or two factors. Fixing the number of factors, we prove a finiteness result about the covariance matrix parameter space when the size of the covariance matrix increases. According to this result, there exists a distinguished matrix size starting at which one can determine whether a given covariance matrix(More)
Electric vehicle (EV) industry gets into fast growth period in China, so that charging of large scale of EV will pose inevitable impacts on power grid in the future. In this article, the main factors and modeling methods of EV charging load are analyzed; The literature reviews are carried out on EV integration and impacts on power grids, including grid(More)
Traditional kernel spectral density estimators are linear as a function of the sample autocovariance sequence. The purpose of the present paper is to propose and analyze two new spectral estimation methods that are based on the sample autocovariances in a nonlinear way. The rate of convergence of the new estimators is quantified, and practical issues such(More)
We establish Nagaev and Rosenthal-type inequalities for dependent random variables. The imposed dependence conditions, which are expressed in terms of functional dependence measures, are directly related to the physical mechanisms of the underlying processes and are easy to work with. Our results are applied to nonlinear time series and kernel density(More)
We propose a single-pass algorithm for estimating spectral densities of stationary processes. Our algorithm is computationally fast in the sense that, when a new observation arrives, it can provide a real-time update within <i>O</i>(1) computation. The proposed algorithm is probabilistically fast in that, for stationary processes whose auto-covariances(More)
We consider the maximum deviations of the sample covariances under the contexts of high dimensional data analysis and time series analysis. In the large n (number of observations) and large m (data dimension) paradigm, we show that the maximum deviation of the sample covariances converges in distribution to the extreme value distribution of type I. The(More)
Automatic frequency tuning circuit of on-chip Gm-C filter has so many problems such as complex structure, high power consumption and low precision. In order to solve these problems, an improved constant-Gm bias circuit was designed in this paper. The circuit has been analyzed theoretically in detail. Simulation results show that the circuit simplified the(More)
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