Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

Direct Adaptive Fuzzy Tracking Control of Marine Vehicles With Fully Unknown Parametric Dynamics and Uncertainties

Abstract: In this brief, a novel direct adaptive fuzzy tracking control (DAFTC) scheme for marine vehicles with fully unknown parametric dynamics and uncertainties is proposed. The significant contributions of the DAFTC approach are as follows. First, in the backstepping framework, fully unknown parametric dynamics and uncertainties are encapsulated into a lumped nonlinearity function encompassing system states and virtual control signals. Second, the integrated nonlinearity function is further identified online by an adaptive fuzzy approximator that synthesizes a model-free control scheme (termed DAFTC) without requiring any a priori knowledge of the model. Third, tracking errors are proven to be uniformly ultimately bounded (UUB) and can converge to an arbitrarily small neighborhood of zero in a finite time. Simulation studies and comprehensive comparisons demonstrate that the proposed DAFTC scheme has remarkable performance and is superior in both tracking accuracy and unknown parametric dynamics compensation.

Fast nonparametric matrix factorization for large-scale collaborative filtering

Abstract: With the sheer growth of online user data, it becomes challenging to develop preference learning algorithms that are sufficiently flexible in modeling but also affordable in computation. In this paper we develop nonparametric matrix factorization methods by allowing the latent factors of two low-rank matrix factorization methods, the singular value decomposition (SVD) and probabilistic principal component analysis (pPCA), to be data-driven, with the dimensionality increasing with data size. We show that the formulations of the two nonparametric models are very similar, and their optimizations share similar procedures. Compared to traditional parametric low-rank methods, nonparametric models are appealing for their flexibility in modeling complex data dependencies. However, this modeling advantage comes at a computational price--it is highly challenging to scale them to large-scale problems, hampering their application to applications such as collaborative filtering. In this paper we introduce novel optimization algorithms, which are simple to implement, which allow learning both nonparametric matrix factorization models to be highly efficient on large-scale problems. Our experiments on EachMovie and Netflix, the two largest public benchmarks to date, demonstrate that the nonparametric models make more accurate predictions of user ratings, and are computationally comparable or sometimes even faster in training, in comparison with previous state-of-the-art parametric matrix factorization models.

Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion

Abstract: We study the spatial correlations of quantum fluctuations that can be observed in multimode parametric down-conversion in the regime of high gain. We investigate both a type-I and a type-II phase-matching configuration: in the latter case spatial correlations at the quantum level are shown to exist both in the near-field and in the far-field zones of the down-converted light. In the stationary and plane-wave approximation we treat the problem analytically. A stochastic model is solved numerically to obtain quantitative results beyond this approximation. The finite transverse size and pulse duration of the pump beam and other features of the system, such as spatial walk-off and diffraction are taken into account, and we show that correlations beyond the standard quantum limit exist for values of parameters consistent with realistic experiments.

The Quantitative Modeling of Operational Risk: Between g-and-h and EVT

Abstract: Operational risk has become an important risk component in the banking and insurance world. The availability of (few) reasonable data sets has given some authors the opportunity to analyze operational risk data and to propose different models for quantification. As proposed in Dutta and Perry [12], the parametric g-and-h distribution has recently emerged as an interesting candidate. In our paper, we discuss some fundamental properties of the g-and-h distribution and their link to extreme value theory (EVT). We show that for the g-and-h distribution, convergence of the excess distribution to the generalized Pareto distribution (GPD) is extremely slow and therefore quantile estimation using EVT may lead to inaccurate results if data are well modeled by a g-andh distribution. We further discuss the subadditivity property of Value-at-Risk (VaR) for g-and-h random variables and show that for reasonable g and h parameter values, superadditivity may appear when estimating high quantiles. Finally, we look at the g-and-h distribution in the one-claim-causes-ruin paradigm.