A Gaussian pseudolikelihood approach for quantile regression with repeated measurements

To enhance the efficiency of regression parameter estimation by modeling the correlation structure of correlated binary error terms in quantile regression with repeated measurements, we propose a Gaussian pseudolikelihood approach for estimating correlation parameters and selecting the most appropriate working correlation matrix simultaneously. The induced smoothing method is applied to estimate the covariance of the regression parameter estimates, which can bypass density estimation of the errors. Extensive numerical studies indicate that the proposed method performs well in selecting an accurate correlation structure and improving regression parameter estimation efficiency. The proposed method is further illustrated by analyzing a dental dataset.     

Comparison of approaches for estimating reliability of individual regression predictions

The paper compares different approaches to estimate the reliability of individual predictions in regression. We compare the sensitivity-based reliability estimates developed in our previous work with four approaches found in the literature: variance of bagged models, local cross-validation, density estimation, and local modeling. By combining pairs of individual estimates, we compose a combined estimate that performs better than the individual estimates. We tested the estimates by running data from 28 domains through eight regression models: regression trees, linear regression, neural networks, bagging, support vector machines, locally weighted regression, random forests, and generalized additive model. The results demonstrate the potential of a sensitivity-based estimate, as well as the local modeling of prediction error with regression trees. Among the tested approaches, the best average performance was achieved by estimation using the bagging variance approach, which achieved the best performance with neural networks, bagging and locally weighted regression.     

Asymptotically optimal smoothing of averaged LMS estimates for regression parameter tracking

The sequence of estimates formed by the LMS algorithm for a standard linear regression estimation problem is considered. It is known since earlier that smoothing these estimates by simple averaging will lead to, asymptotically, the recursive least-squares algorithm. In this paper, it is first shown that smoothing the LMS estimates using a matrix updating will lead to smoothed estimates with optimal tracking properties, also in case the true parameters are slowly changing as a random walk. The choice of smoothing matrix should be tailored to the properties of the random walk. Second, it is shown that the same accuracy can be obtained also for a modified algorithm, SLAMS, which is based on averages and requires much less computations.     

Nonparametric interpolation of the Markov sequence

Consideration was given to the problem of interpolation (smoothing) of the nonobservable component of the composite Markov process within the framework of the conditional Markov scheme. In the case of the dynamic observation models such as autoregression, equations were derived for the a posteriori interpolation density of the probability of the state of the nonobservable component. The aim of the present paper was to construct a smoothing algorithm for an unknown family of the distributions of the nonobservable component of the partially observable random Markov sequence. The result was obtained for the strictly stationary random Markov processes with mixing and for the conditional densities in the observation model from the exponential family of distributions. Computer-aided modeling within the framework of the Kalman scheme demonstrated that the sampled root-mean-square error of the nonparametric smoothing algorithm constructed for an unknown state equation was situated between the errors of the optimal linear filtration and the optimal linear interpolation.     

Period analysis of variable stars: Temporal dependence and local optima

A number of methods have been proposed to estimate the period of a variable star; e.g., a recent approach uses smoothing spline regression to fit tentative periodic functions (light curves) and selects the period minimizing a robust goodness-of-fit criterion. These methods assume that measurement errors vary independently over time. Empirical evidence, however, indicates substantial temporal dependence, possibly related to changes in observing conditions. Dependence complicates the period analysis in several respects: selection of a “best” period among several local optima, estimation of the light curve, and evaluation of uncertainty about period and light curve estimates. This article presents methods designed to accommodate dependent errors. An analysis of several data sets shows that the proposed approach can produce substantially different and arguably better results compared with other methods.     

Generalized profiling estimation for global and adaptive penalized spline smoothing

We propose the generalized profiling method to estimate the multiple regression functions in the framework of penalized spline smoothing, where the regression functions and the smoothing parameter are estimated in two nested levels of optimization. The corresponding gradients and Hessian matrices are worked out analytically, using the Implicit Function Theorem if necessary, which leads to fast and stable computation. Our main contribution is developing the modified delta method to estimate the variances of the regression functions, which include the uncertainty of the smoothing parameter estimates. We further develop adaptive penalized spline smoothing to estimate spatially heterogeneous regression functions, where the smoothing parameter is a function that changes along with the curvature of regression functions. The simulations and application show that the generalized profiling method leads to good estimates for the regression functions and their variances.     

Period analysis of variable stars: Temporal dependence and local optima

A number of methods have been proposed to estimate the period of a variable star; e.g., a recent approach uses smoothing spline regression to fit tentative periodic functions (light curves) and selects the period minimizing a robust goodness-of-fit criterion. These methods assume that measurement errors vary independently over time. Empirical evidence, however, indicates substantial temporal dependence, possibly related to changes in observing conditions. Dependence complicates the period analysis in several respects: selection of a “best” period among several local optima, estimation of the light curve, and evaluation of uncertainty about period and light curve estimates. This article presents methods designed to accommodate dependent errors. An analysis of several data sets shows that the proposed approach can produce substantially different and arguably better results compared with other methods.     

Continuous-time decentralized smoothers based on two-filter form: identical local and global models

This paper proposes some decentralized smoothing algorithms for a continuous-time linear estimation structure consisting of a central processor and of two local processors, in which the local models are assumed to be identical to the global model. The philosophy of the paper is to solve the problem in terms of the local forward and backward information (or Kalman) filters. The resulting algorithms are somewhat different from those based on the local smoothing estimates which have been studied by some other authors. Smoothing update and real-time smoothing algorithms are also presented, ft is shown that the present algorithms have some advantages: the global filtered estimates can be obtained in the course of computing the decentralized smoothing estimates and the central and local processors can be derived in a completely parallel fashion     

Bias reduction in kernel binary regression

We consider Nadaraya-Watson type estimators for binary regression functions. We propose a method for improving the performance of such estimators by employing bias reduction techniques when estimating the constituent probability densities. Direct substitution of separately optimized density estimates into the regression function formula generates disappointing results in practice. However, adjusting the global smoothing parameter to optimize a performance criterion for the binary regression function itself is more promising. We focus on an implementation of this approach which uses a variable kernel technique to provide reduced bias density estimates, and where the global bandwidth is selected by an appropriately tailored leave-one-out (cross-validation) method. Theory and numerical experiments show that this form of bias reduction improves performance substantially when the underlying regression function is highly non-linear but is not beneficial when the underlying regression function is almost linear in form.     

A semiparametric Bayesian approach for joint-quantile regression with clustered data

Based on a semiparametric Bayesian framework, a joint-quantile regression method is developed for analyzing clustered data, where random effects are included to accommodate the intra-cluster dependence. Instead of posing any parametric distributional assumptions on the random errors, the proposed method approximates the central density by linearly interpolating the conditional quantile functions of the response at multiple quantiles and estimates the tail densities by adopting extreme value theory. Through joint-quantile modeling, the proposed algorithm can yield the joint posterior distribution of quantile coefficients at multiple quantiles and meanwhile avoid the quantile crossing issue. The finite sample performance of the proposed method is assessed through a simulation study and the analysis of an apnea duration data.     

目标跟踪系统自校正解耦融合Wiener平滑器

针对带未知模型参数和噪声的多传感器目标跟踪系统,为了解决信号的平滑问题,分别利用系统辨识及相关方法得到未知模型参数和噪声方差的局部估值,并对这些局部估值求平均值作为它们的融合估值。然后将具有高可靠性的在线融合估值代入到基于现代时间序列的最优解耦融合Wiener平滑器中即可得自校正解耦融合,使自校正融合Wiener平滑器收敛于相应的最优融合Wiener平滑器,并具有渐近最优性。从而证明自校正平滑器能够很好地解决未知模型参数和噪声统计系统的平滑问题。最后利用Matlab软件仿真验证了该自校正解耦融合Wiener平滑器算法的有效性。     

Integration of IKONOS imagery for geostatistical mapping of sediment grain size at Baramarae beach,Korea

We describe the potential of high-resolution remote sensing imagery in the geostatistical mapping of sediment grain size distribution in order to supplement sparsely sampled ground observations. Within a multi-Gaussian framework, the IKONOS imagery is used as local means both to estimate the grain size values and to model local uncertainty at unsampled locations. Multiple regression and generalized additive models are applied to compute local mean values. From a case study of Baramarae beach, Korea, all imagery bands showed a reasonable linear relationship with grain size values in phi units, having a correlation coefficient of more than –0.80. Accounting for the IKONOS imagery via simple kriging with local means could reflect detailed surface characteristics with less smoothing effects. Cross validation results showed that the mean square errors from simple kriging with local means via the generalized additive model provided a relative improvement of about 60% over univariate multi-Gaussian kriging and a superior predictive capability when compared with simple kriging with local means via the traditional multiple regression model.     

Gradient Estimation in Volume Data using 4D Linear Regression

In this paper a new gradient estimation method is presented which is based on linear regression. Previous contextual shading techniques try to fit an approximate function to a set of surface points in the neighborhood of a given voxel. Therefore a system of linear equations has to be solved using the computationally expensive Gaussian elimination. In contrast, our method approximates the density function itself in a local neighborhood with a 3D regression hyperplane. This approach also leads to a system of linear equations but we will show that it can be solved with an efficient convolution. Our method provides at each voxel location the normal vector and the translation of the regression hyperplane which are considered as a gradient and a filtered density value respectively. Therefore this technique can be used for surface smoothing and gradient estimation at the same time.     

Linear instrumental variables model averaging estimation

Model averaging (MA) estimators in the linear instrumental variables regression framework are considered. The obtaining of weights for averaging across individual estimates by direct smoothing of selection criteria arising from the estimation stage is proposed. This is particularly relevant in applications in which there is a large number of candidate instruments and, therefore, a considerable number of instrument sets arising from different combinations of the available instruments. The asymptotic properties of the estimator are derived under homoskedastic and heteroskedastic errors. A simple Monte Carlo study contrasts the performance of MA procedures with existing instrument selection procedures, showing that MA estimators compare very favorably in many relevant setups. Finally, this method is illustrated with an empirical application to returns to education.     

Inventory model with two rates of production for deteriorating items with permissible delay in payments

Some decentralized smoothing problems are solved by applying a forward-pass fixed-interval smoother formula in discrete-time systems. It is assumed that a simple estimation structure consists of a global processor and of two local processors. Two cases are considered for the problems of decentralized smoothing and smoothing update: when the local backward-pass information filtered estimates are available, and when the local-smoothed estimates are available. Some features of present algorithms are discussed from the point of view of data transmissions and numerical computations, etc.     

Numerical differentiation of experimental data: local versus global methods

In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial or ordinary differential equations. Usually, one does not take care for accuracy of the resulting estimates of derivatives because modern computers are assumed to be accurate to many digits. But measurements yield intrinsic errors, which are often much less accurate than the limit of the machine used, and there exists the effect of “loss of significance”, well known in numerical mathematics and computational physics. The problem occurs primarily in numerical subtraction, and clearly, the estimation of derivatives involves the approximation of differences. In this article, we discuss several techniques for the estimation of derivatives. As a novel aspect, we divide into local and global methods, and explain the respective shortcomings. We have developed a general scheme for global methods, and illustrate our ideas by spline smoothing and spectral smoothing. The results from these less known techniques are confronted with the ones from local methods. As typical for the latter, we chose Savitzky-Golay-filtering and finite differences. Two basic quantities are used for characterization of results: The variance of the difference of the true derivative and its estimate, and as important new characteristic, the smoothness of the estimate. We apply the different techniques to numerically produced data and demonstrate the application to data from an aeroacoustic experiment. As a result, we find that global methods are generally preferable if a smooth process is considered. For rough estimates local methods work acceptably well.     

Fully spatially adaptive smoothing parameter estimation for Markov random field super-resolution mapping of remotely sensed images

This article presents a fully spatially adaptive Markov random field (MRF)-based super-resolution mapping (SRM) technique to produce land-cover maps at a finer spatial resolution than the original coarse-resolution image. MRF combines the spectral and spatial energies; hence, an MRF-SRM technique requires a smoothing parameter to manage the contributions of these energies. The main aim of this article is to introduce a new method called fully spatially adaptive MRF-SRM to automatically determine the smoothing parameter, overcoming limitations of the previously proposed approaches. This method estimates the number of endmembers in each image and uses them to assess the proportions of classes within each coarse pixel by a linear spectral unmixing method. Then, the real pixel intensity vectors and the local properties of each coarse pixel are used to compute the local spectral energy change matrix and the local spatial energy change matrix for each coarse pixel. Each pair of matrices represents all possible situations in spatial and spectral energy change for each coarse pixel and can be used to examine the balance between spatial and spectral energies, and hence to estimate a smoothing parameter for each coarse pixel. Thus, the estimated smoothing parameter is fully spatially adaptive with respect to real pixel spectral vectors and their local properties. The performance of this method is evaluated using two synthetic images and an EO1-ALI (The Advanced Land Imager instrument on Earth Observing-1 satellite) multispectral remotely sensed image. Our experiments show that the proposed method outperforms the state-of-the-art techniques.     

高斯混合概率假设密度无序估计分布式融合

针对分布式传感器网络中多目标随机集状态混合无序估计问题,本文提出了一种基于高斯混合概率假设密度无序估计分布式融合算法.在高斯混合概率假设密度滤波器的框架下,首先基于概率假设密度递推滤波特性,建立适用于多目标随机集状态混合无序估计的最新可利用估计判别机制,然后利用扩展协方差交叉融合算法对经过最新可利用估计判别机制获得的无序概率假设密度强度估计进行融合处理,针对融合过程中高斯分量快速增长的问题,在保证信息损失最小的前提下,对融合过程的不同环节实施高斯混合分量裁剪操作,给出了一种多级分层分量裁剪算法.最后,仿真实验验证了文中所提的算法的有效性和可行性.     

Smoothing methodology for predicting regional averages in multi-source forest inventory

The paper examines alternative non-parametric estimation methods or smoothing methods in the context of the Finnish multi-source forest inventory. It uses satellite images in addition to field data to produce forest variable predictions for regions ranging from the single pixel level up to the national level. With the help of the bias-variance decomposition, the influence of the smoothing parameters on prediction accuracy is considered when the smoother's pixel-level predictions are averaged in order to produce predictions for larger areas. A novel variation of cross-validation, called region-wise cross-validation, is proposed for selecting the smoothing parameters. Experimental results are presented using local linear ridge regression (LLRR), which is a variant of the better known local linear regression method.     

Bayesian analysis of semiparametric reproductive dispersion mixed-effects models

Semiparametric reproductive dispersion mixed-effects model (SPRDMM) is an extension of the reproductive dispersion model and the semiparametric mixed model, and it includes many commonly encountered models as its special cases. A Bayesian procedure is developed for analyzing SPRDMMs on the basis of P-spline estimates of nonparametric components. A hybrid algorithm combining the Gibbs sampler and the Metropolis-Hastings algorithm is used to simultaneously obtain the Bayesian estimates of unknown parameters, smoothing function and random effects, as well as their standard error estimates. The Bayes factor for model comparison is employed to select better approximation of the smoothing function via path sampling. Several simulation studies and a real example are used to illustrate the proposed methodologies.