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Nonparametric regression methods are used as exploratory tools for formulating, identifying and estimating non-linear models for the Canadian lynx data, which have attained benchmark status in the time series literature since the work of Moran in 1953. To avoid the curse of dimensionality in the nonparametric analysis of this short series with 114 observations, we con®ne attention to the restricted class of additive and projection pursuit regression (PPR) models and rely on the estimated prediction error variance to compare the predictive performance of various (non-) linear models. A PPR model is found to have the smallest (in-sample) estimated prediction error variance of all the models ®tted to these data in the literature. We use a data perturbation procedure to assess and adjust for the effect of data mining on the estimated prediction error variances; this renders most models ®tted to the lynx data comparable and nearly equivalent. However, on the basis of the mean-squared error of out-of-sample prediction error, the semiparametric model X t 1X08 1X37X tÀ1 f (X tÀ2 ) e t and Tong's self-exciting threshold autoregressive model perform much better than the PPR and other models known for the lynx data.

This study proposes the first estimator in the open literature (to the present authors' best knowledge) to nonparametrically estimate a Hammerstein system's nonlinear static subsystem when excited by an input that is temporally self-correlated with an unknown spectrum, an unknown variance and an unknown mean (instead of the input as commonly presumed to be white and zero-mean). This proposed nonparametric estimator is analytically proved here to be asymptotically unbiased and pointwise consistent. The proposed estimate's associated finite-sample convergence rate is also derived analytically. | INTRODUCTIONA Hammerstein system comprises two subsystems in series: (i) a nonlinear, static (memoryless) subsystem, trailed by (ii) a linear, dynamic, time-invariant, asymptotically stable subsystem. Please see Figure 1 for a schematic showing these two subsystems and their associated signals, which are described in great details in Section 1.This study proposes a new estimate for the nonlinear static subsystem's input-output nonlinearity m(⋅). This estimator relies on observations of only the input and the output of the overall Hammerstein system (i.e. {(U n , Y n ), ∀n}), but not on any observation of any intrasystem signal/noise (e.g. {W n , Z n , V n , X n , P n , ∀n}).This proposed estimator also does not require any prior/simultaneous identification of the nonlinear static subsystem.This is an open access article under the terms of the Creative Commons Attribution-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited and no modifications or adaptations are made.

Cardioid microphones/hydrophones are highly directional acoustical sensors, which enjoy easy availability via numerous commercial vendors for professional use. Collocating three such cardioids in orthogonal orientation to each other, the resulting triad would be sharply directional yet physically compact, while decoupling the incident signal's time-frequency dimensions from its azimuth-elevation directional dimensions, thereby simplifying signal-processing computations. This paper studies such a cardioid triad's azimuth-elevation direction-of-arrival estimation accuracy, which is characterized here by the hybrid Cramér-Rao bound. This analysis allows the cardioidicity index (α) to be stochastically uncertain, applies to any cardioidic order (k), and is valid for any real-valued incident signal regardless of the signal's time-frequency structure.