The least-mean-square (LMS) estimator is a nonlinear estimator with information dependencies spanning the entire set of data fed into it. The traditional analysis techniques used to model this estimator obscure these dependencies; to simplify the analysis they restrict the estimator to the finite set of data sufficient to span the length of its filter. Thus the finite Wiener filter is often con...

This paper considers the Wiener degradation model with random effects. Random-effect models take into account unit-to-unit variability of index. It is assumed that a parameter has truncated normal distribution. During research, expression for maximum likelihood estimates and reliability function been obtained. Two statistical tests have proposed to reveal existence effects in data corresponding...

This study focuses on the individual sedation model identification problem, and proposes a subspace-based Wiener system identification method. The traditional compartmental pharmacokinetics-pharmacodynamics hypnosis model is considered as a specific Wiener system with the Hill equation nonlinear term. To deal with the Hill nonlinear term, the proposed method employs a set of specific bases to t...

Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given.

This paper designs the recursive least-squares (RLS) Wiener finite impulse response (FIR) predictor and filter, based on the innovation approach, in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white noise and the signal process is uncorrelated with the observation noise process. This paper also presents the recursive algorithms for the estima...

Capability to manage the performance of a shared resources environment relies on the model estimation of all dynamics in the system. The main challenge is to capture the nonlinear characteristic which inherently exists in software system applications. Hammerstein-Wiener block structural model is widely regarded as a basis for description of nonlinear systems. This paper extends the existing wor...

We consider a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process (GP) model for the static nonlinearity. The GP model is a exible model that can describe di erent types of nonlinearities while avoiding making strong assumptions such as monotonicity. We derive an inferent...