The Buckley-James estimator (BJE) is a widely recognized approach in dealing with right-censored linear regression models. There have been a lot of discussions in the literature on the estimation of the BJE as well as...
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The Buckley-James estimator (BJE) is a widely recognized approach in dealing with right-censored linear regression models. There have been a lot of discussions in the literature on the estimation of the BJE as well as its asymptotic distribution. So far, no simulation has been done to directly estimate the asymptotic variance of the BJE. Kong and Yu [Asymptotic distributions of the Buckley-James estimator under nonstandard conditions, Statist. Sinica 17 (2007), pp. 341-360] studied the asymptotic distribution under discontinuous assumptions. Based on their methodology, we recalculate and correct some missing terms in the expression of the asymptotic variance in Theorem 2 of their work. We propose an estimator of the standard deviation of the BJE by using plug-in estimators. The estimator is shown to be consistent. The performance of the estimator is accessed through simulation studies under discrete underline distributions. We further extend our studies to several continuous underline distributions through simulation. The estimator is also applied to a real medical data set. The simulation results suggest that our estimation is a good approximation to the true standard deviation with reference to the empirical standard deviation.
linear autoregressive (AR) model is widely used in signal processing. Usually the AR models are solved by classical least square (LS) method. An important issue with the LS solution of the AR model, which has been see...
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ISBN:
(纸本)9781457713033
linear autoregressive (AR) model is widely used in signal processing. Usually the AR models are solved by classical least square (LS) method. An important issue with the LS solution of the AR model, which has been seemingly overlooked, is its numerical stability. The issue is related to the rank condition of the design matrix. We observed, in case of natural images, that the probability of numerical rank deficiency is rather high, roughly thirty-five per cent, due to discrete nature and structures of the digital images. Without care numerical rank deficiency can adversely affect the parameter estimation of the AR model. In this paper we use the rank revealing QR (RRQR) factorization to select optimal subset from the design matrix so as to effectively lower the condition number of the system. By removing the ill conditioned part of the right orthogonal matrix of the RRQR decomposition, we obtain a robust truncated solution to the linear system. On the other hand, for natural images, the unselected data tend to highly correlate with the pixel being modeled, and their exclusion from the modeling process waste valuable information. To avoid this loss we recycle the data including those discard by the parametric AR estimator into a nonparametrgic model of nonlocal type. Interestingly, the data that cause ill condition to the parametric AR model are of high quality for the non-local nonparametric modeling. Therefore, an approach of hybrid parametric-nonparametric modeling can make the best use of data and improve the model performance. The hybrid modeling approach is applied to image resolution upconversion, and it greatly improves the performance of the state-of-the-art image interpolator, achieving a gain of 3dB or more in PSNR in some cases.
In recent year, the rise of economic growth and technology advance leads to improve the quality of service of traditional transport system. Intelligent Transportation System (ITS) has become more and more popular. At ...
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ISBN:
(纸本)9783037850176
In recent year, the rise of economic growth and technology advance leads to improve the quality of service of traditional transport system. Intelligent Transportation System (ITS) has become more and more popular. At present, the collection of real-time traffic information is executed in two ways: (1) Stationary Vehicle Detectors (VD) and (2) Global Position System (GPS)-based probe cars reporting. However, VD devices need a large sum of money to build and maintain. Therefore, we propose the linear regression model to infer the equation between vehicle speed and traffic flow. The traffic flow can be estimated from the speed which is obtained from GPS-based probe cars. In experiments, the Speed Error Ratio (SER) and Flow Error Ratio (FER) of linear regression model are 4.60% and 24.63% respectively. The estimated speed and traffic flow by using linear regression model is better than by using linearmodel, power law model, exponential model, and normal distribution model. Therefore, the linear regression model can be used to estimate traffic information for ITS.
Being noninvasive, low-risk and inexpensive, EEG is a promising methodology in the application of human Brain Computer Interface (BCI) to help those with motor dysfunctions. Here we employed a center-out task paradigm...
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ISBN:
(纸本)9781424441228
Being noninvasive, low-risk and inexpensive, EEG is a promising methodology in the application of human Brain Computer Interface (BCI) to help those with motor dysfunctions. Here we employed a center-out task paradigm to study the decoding of hand velocity in the EEG recording. We tested the hypothesis using a linear regression model and found a significant correlation between velocity and the low-pass filtered EEG signal (<2 Hz). The low-pass filtered EEG was not only tuned to the direction but also phase-locked to the amplitude of velocity. This suggests an EEG form of the neuronal population vector theory, which is considered to encode limb kinematic information, and provides a new method of BCI implementation.
Trajectory modeling of moving objects is one of the key problems in spatio-tempo-ral databases research. In a series of moves spatio-temporal database information and finding time to update in actual application space...
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ISBN:
(纸本)9783037850152
Trajectory modeling of moving objects is one of the key problems in spatio-tempo-ral databases research. In a series of moves spatio-temporal database information and finding time to update in actual application space and threshold distance threshold, this paper combines the ideas of the linear regression model in mathematics to propose the trajectory model, which is on the basis of the Moving Objects Spatio-Temporal model and supports the past, present and future information processing. It effectively predicts the moving objects of movement trend and scope at any time within the threshold.
Classical spatial autoregressive models share the same weakness as the classical linear regression models, namely it is not possible to estimate non-linear relationships between the dependent and independent variables...
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ISBN:
(纸本)9781424496365
Classical spatial autoregressive models share the same weakness as the classical linear regression models, namely it is not possible to estimate non-linear relationships between the dependent and independent variables. In the case of classical linearregression a semi-parametric approach can be used to address this issue. Therefore an advanced semi-parametric modelling approach for spatial autoregressive models is introduced. Advanced semi-parametric modelling requires determining the best configuration of independent variable vectors, number of spline-knots and their positions. To solve this combinatorial optimization problem an asynchronous multi-agent system based on genetic-algorithms is utilized. Three teams of agents work each on a subset of the problem and cooperate through sharing their most optimal solutions. Through this system more complex relationships between the dependent and independent variables can be derived. These could be better suited for the possibly non-linear real-world problems faced by applied spatial econometricians.
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