Nonparametric estimation of cumulative distribution function and probability densityfunction of continuous random variables is a basic and central problem in probability theory and statistics. Although many methods s...
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Nonparametric estimation of cumulative distribution function and probability densityfunction of continuous random variables is a basic and central problem in probability theory and statistics. Although many methods such as kernel densityestimation have been presented, it is still quite a challenging problem to be addressed to researchers. In this paper, we proposed a new method of spline regression, in which the spline function could consist of totally different types of functions for each segment with the result of Monte Carlo simulation. Based on the new spline regression, a new method to estimate the distribution and densityfunction was provided, which showed significant advantages over the existing methods in the numerical experiments. Finally, the density function estimation of high dimensional random variables was discussed. It has shown the potential to apply the method in classification and regression models.
In this paper, distributed coverage optimization and control problem with collision avoidance and parameter estimation are studied. First, we consider the case that the densityfunction phi(q) is known by all the robo...
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ISBN:
(纸本)9789881563958
In this paper, distributed coverage optimization and control problem with collision avoidance and parameter estimation are studied. First, we consider the case that the densityfunction phi(q) is known by all the robots in the network. By using the interaction term of Voronoi neighbour, coverage optimization and control protocols are designed in a distributed way such that the best position of each robot can be determined and all the robots can move to the best positions without collision. Then, we consider the case that the densityfunction phi(q) is not known by the robots. By using the adaptive technique, the densityfunction phi(q) can be estimated in a fast and distributed way. Finally, the proposed coverage control scheme are applied to remote sensing for precision farming and the effectiveness of the strategy is validated through some simulation results.
In this paper, distributed coverage optimization and control problem with collision avoidance and parameter estimation are studied. First, we consider the case that the densityfunction φ(q) is known by all the robot...
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In this paper, distributed coverage optimization and control problem with collision avoidance and parameter estimation are studied. First, we consider the case that the densityfunction φ(q) is known by all the robots in the network. By using the interaction term of Voronoi neighbour, coverage optimization and control protocols are designed in a distributed way such that the best position of each robot can be determined and all the robots can move to the best positions without collision. Then, we consider the case that the densityfunction φ(q) is not known by the robots. By using the adaptive technique, the densityfunctionφ(q) can be estimated in a fast and distributed way. Finally, the proposed coverage control scheme are applied to remote sensing for precision farming and the effectiveness of the strategy is validated through some simulation results.
Background: Magnetic resonance imaging reveals macro- and microstructural correlates of neurodegeneration, which are often assessed using voxel-by-voxel t-tests for comparing mean image intensities measured by fractio...
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Background: Magnetic resonance imaging reveals macro- and microstructural correlates of neurodegeneration, which are often assessed using voxel-by-voxel t-tests for comparing mean image intensities measured by fractional anisotropy (FA) between cases and controls or regression analysis for associating mean intensity with putative risk factors. This analytic strategy focusing on mean intensity in individual voxels, however, fails to account for change in distribution of image intensities due to disease. New method: We propose a method that aims to facilitate simple and clear characterization of underlying distribution. Our method consists of two steps: subject-level (Step 1) and group-level or a specific risk level density function estimation across subjects (Step 2). Results: The proposed method was demonstrated with a simulated data set and real FA data sets from two white matter tracts, where the proposed method successfully detected any departure of the FA distribution from the normal state by disease: p < 0.001 for simulated data;p = 0.047 for the posterior limb of internal capsule;p = 0.06 for the posterior thalamic radiation. Comparison with existing method(s): The proposed method found significant disease effect (p <0.001) while conventional 2-group t-test focused only on mean intensity did not (p = 0.61) in a simulation study. While significant age effects were found for each white matter tract from conventional linear model analysis with real FA data, the proposed method further confirmed that aging also triggers distribution wide change. Conclusion: Our proposed method is powerful for detection of risk factors associated with any type of microstructural neurodegenerations with brain imaging data. (C) 2016 Elsevier B.V. All rights reserved.
Two classes of unbiased estimators of the densityfunction of ergodic distribution for the diffusion process of observations are proposed. The estimators are square-root consistent and asymptotically normal. This curi...
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Two classes of unbiased estimators of the densityfunction of ergodic distribution for the diffusion process of observations are proposed. The estimators are square-root consistent and asymptotically normal. This curious situation is entirely different from the case of discrete-time models (Davis 1977) where the unbiased estimator rarely exists and usually the estimators are not square-root consistent.
In the first part of this paper a new on-line Fully Self-Organizing artificial Neural Network model (FSONN), pursuing dynamic generation and removal of neurons and synaptic links, is proposed. The model combines prope...
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ISBN:
(纸本)0819425877
In the first part of this paper a new on-line Fully Self-Organizing artificial Neural Network model (FSONN), pursuing dynamic generation and removal of neurons and synaptic links, is proposed. The model combines properties of the Self-Organizing Map (SOM), Fuzzy c-Means (FCM), Growing Neural Gas (GNG) and Fuzzy Simplified Adaptive Resonance Theory (Fuzzy SART) algorithms. In the second part of the paper experimental results are provided and discussed. Our conclusion is that the proposed connectionist model features several interesting properties, such as the following: i) the system requires no a priori knowledge of the dimension, size and/or adjacency structure of the network;ii) with respect to other connectionist models found in the literature, the system can be employed successfully in: a) vector quantization;b) density function estimation;and c) structure detection in input data to be mapped topologically correctly onto an output lattice pursuing dimensionality reduction;and iii) the system is computationally efficient, its processing time increasing linearly with the number of neurons and synaptic links.
In this note we consider the problem of fitting a general functional relationship between two variables. We require only that the function to be fitted is, in some sense, “smooth”, and do not assume that it has a kn...
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In this note we consider the problem of fitting a general functional relationship between two variables. We require only that the function to be fitted is, in some sense, “smooth”, and do not assume that it has a known mathematical form involving only a finite number of unknown parameters.
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