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Articles 1 - 5 of 5
Full-Text Articles in Statistics and Probability
Derivative Estimation With Local Polynomial Fitting, Kris De Brabanter, Jos De Brabanter, Bart De Moor, Irene Gijbels
Derivative Estimation With Local Polynomial Fitting, Kris De Brabanter, Jos De Brabanter, Bart De Moor, Irene Gijbels
Kris De Brabanter
We present a fully automated framework to estimate derivatives nonparametrically without estimating the regression function. Derivative estimation plays an important role in the exploration of structures in curves (jump detection and discontinuities), comparison of regression curves, analysis of human growth data, etc. Hence, the study of estimating derivatives is equally important as regression estimation itself. Via empirical derivatives we approximate the qth order derivative and create a new data set which can be smoothed by any nonparametric regression estimator. We derive L1 and L2 rates and establish consistency of the estimator. The new data sets created by this technique are …
Kernel Regression In The Presence Of Correlated Errors, Kris De Brabanter, Jos De Brabanter, Johan A.K. Suykens, Bart De Moor
Kernel Regression In The Presence Of Correlated Errors, Kris De Brabanter, Jos De Brabanter, Johan A.K. Suykens, Bart De Moor
Kris De Brabanter
It is a well-known problem that obtaining a correct bandwidth and/or smoothing parameter in nonparametric regression is difficult in the presence of correlated errors. There exist a wide variety of methods coping with this problem, but they all critically depend on a tuning procedure which requires accurate information about the correlation structure. We propose a bandwidth selection procedure based on bimodal kernels which successfully removes the correlation without requiring any prior knowledge about its structure and its parameters. Further, we show that the form of the kernel is very important when errors are correlated which is in contrast to the …
Optimal Dynamic Policies For Influenza Management, Michael Ludkovski, Jarad Niemi
Optimal Dynamic Policies For Influenza Management, Michael Ludkovski, Jarad Niemi
Jarad Niemi
Management policies for influenza outbreaks balance the expected morbidity and mortality costs versus the cost of intervention policies. We present a methodology for dynamic determination of optimal policies in a completely observed stochastic compartmental model with parameter uncertainty. Our approach is simulation-based and searches the full set of sequential control strategies. For each time point, it generates a policy map describing the optimal intervention to implement as a function of outbreak state and Bayesian parameter posteriors. As a running example, we study a stochastic SIR model with isolation and vaccination as two possible interventions. Numerical simulations based on a classic …
Markov Chain Monte Carlo Defect Identification In Nde Images, Aleksandar Dogandžić, Benhong Zhang
Markov Chain Monte Carlo Defect Identification In Nde Images, Aleksandar Dogandžić, Benhong Zhang
Aleksandar Dogandžić
We derive a hierarchical Bayesian method for identifying elliptically‐shaped regions with elevated signal levels in NDE images. We adopt a simple elliptical parametric model for the shape of the defect region and assume that the defect signals within this region are random following a truncated Gaussian distribution. Our truncated‐Gaussian model ensures that the signals within the defect region are higher than the baseline level corresponding to the noise‐only case. We derive a closed‐form expression for the kernel of the posterior probability distribution of the location, shape, and defect‐signal distribution parameters (model parameters). This result is then used to develop Markov …
Admissible Solutions Of Finite State Sequence Compound Decision Problems, Stephen B. Vardeman
Admissible Solutions Of Finite State Sequence Compound Decision Problems, Stephen B. Vardeman
Stephen B. Vardeman
A general method of constructing procedures which are both admissible and asymptotically optimal in finite state sequence compound decision problems is suggested and applied to the situation of a two state classification component. When used in an empirical Bayes setting, procedures so constructed are seen to be both admissible and asymptotically optimal.