A fuzzy clustering approach is studied for optimal pole selection of Orthonormal Basis Functions (OBFs) used for the identification of Linear Parameter Varying (LPV) systems. The identification approach is based on interpolation of locally identified Linear Time Invariant (LTI) models, using globally fixed OBFs. The selection of the optimal OBF structure, that guarantees the least worstcase loc...

Let g be a function which assigns to each stationary process (Xn) ∞ n=1 and to each sample X1 . . . Xn of the process a real number g(X1, . . . , Xn), which may also depend on the distribution of (Xn). We obtain effective bounds on the probability that the sequence (g(X1, . . . , Xn)) ∞ n=1 crosses a fixed interval some number of times in terms of a quantity measuring the “average sub-additivit...

In the common nonparametric regression model the problem of testing for a specific parametric form of the variance function is considered. Recently Dette and Hetzler (2008) proposed a test statistic, which is based on an empirical process of pseudo residuals. The process converges weakly to a Gaussian process with a complicated covariance kernel depending on the data generating process. In the ...