Reconfigured Piecewise Linear Regression Tree for Multistage Manufacturing Process Control Ran Jin and Jianjun Shi H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive NW, Atlanta, GA 30332, USA, E-mail: [email protected] Abstract In a multistage manufacturing process, massive observational data are obtained from the measurem...

A regression spline is a piecewise polynomial function whose highest order nonzero derivative takes jumps at xed \knots." Usually regression splines are smoothed by deleting nonessential knots, or equivalently setting the jumps at those knots to zero. A method that is simpler to implement and has lower computational cost is to shrink the jumps at all knots towards zero by using a penalty functi...

A method of generalized regression that blends tree-structured nonparametric regression and adaptive recursive partitioning with maximum likelihood estimation is studied. The function estimate is a piecewise polynomial, with the pieces determined by the terminal nodes of a binary decision tree. The decision tree is constructed by recursively partitioning the data according to the signs of the r...

Driver’s visual attention provides important clues about his/ her activities and awareness. To monitor driver’s awareness, this paper proposes a real-time person-independent head tracking and pose estimation system using a monochromatic camera. The tracking and head-pose estimation tasks are formulated as regression problems. Three regression methods are proposed: (i) individual mapping on imag...

This paper is concerned with regression under a “sum” of partial order constraints. Examples include locally monotonic, piecewise monotonic, runlength constrained, and unimodal and oligomodal regression. These are of interest not only in nonlinear filtering but also in density estimation and chromatographic analysis. It is shown that under a least absolute error criterion, these problems can be...

Many applications in the areas of production, signal processing, economics, bioinformatics, and statistical learning involve a given partial order on certain parameters and a set of noisy observations of the parameters. The goal is to derive estimated values of the parameters that satisfy the partial order that minimize the loss of deviations from the given observed values. A prominent applicat...

| This paper is concerned with regression under a \sum" of partial order constraints. Examples include locally monotonic, piecewise monotonic, runlength constrained, and uni-and oligo-modal regression. These are of interest in nonlinear ltering, but also in density estimation and chromatographic analysis. It is shown that, under a least absolute error criterion, these problems can be transforme...

We consider the nonparametric regression model with long memory data that are not necessarily Gaussian and provide an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet-based mean regression function estimators. We show this MISE expansion, when the underlying mean regression function is only piecewise smooth, is the same as analogous expansion for the kernel...

Amethod of generalized regression that blends tree-structured nonparametric regression and adaptive recursive partitioning with maximum likelihood estimation is studied. The function estimate is a piecewise polynomial, with the pieces determined by the terminal nodes of a binary decision tree. The decision tree is constructed by recursively partitioning the data according to the signs of the re...