Let (X; Y) be a pair of random variables with supp(X) 0; 1] and EY 2 < 1. Let m be the corresponding regression function. Estimation of m from i.i.d. data is considered. The L 2 error with integration with respect to the design measure (i.e., the distribution of X) is used as an error criterion. Estimates are constructed by estimating the coeecients of an orthonormal expansion of the regression...

A multi-step Expectation Maximization based (EM-based) algorithm is proposed to solve piecewise surface regression problem which has typical applications in market segmentation research, identification of consumer behavior patterns, weather patterns in meteorological research, and so on. The multiple steps involved are local regression on each data point of the training data set and a small set...

We propose enhancing the tting of linear regression models to massive multidimensional data by partitioning the data using a DataSphere (proposed in our previous work) and tting piecewise linear regression models to each class in the representation. Nonlinear models typically involve several iterations through the data and require the knowledge of every data point. Linear regression models, on ...

We consider the generic regularized optimization problem β̂(λ) = arg minβ L(y,Xβ) + λJ (β). Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407–499] have shown that for the LASSO—that is, if L is squared error loss and J (β)= ‖β‖1 is the 1 norm of β—the optimal coefficient path is piecewise linear, that is, ∂β̂(λ)/∂λ is piecewise constant. We derive a general characterization of ...

The goal of regression analysis is to describe the stochastic relationship between an input vector x and a scalar output y. This can be achieved by estimating the entire conditional density p(y / x). In this letter, we present a new approach for nonparametric conditional density estimation. We develop a piecewise-linear path-following method for kernel-based quantile regression. It enables us t...

We prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression mdoel where the break-point is unknown. The non-differentiability of the likelihood of the model with regard to the break-point parameter induces technical difficulties that we overcome by creating a regularised version of the problem at hand. We first recover ...

To detect the small island effect (SIE) and nestedness patterns of herpetofauna of the West Indies, we derived and updated data on the presence/absence of herpetofauna in this region from recently published reviews. We applied regression-based analyses, including linear regression and piecewise regressions with two and three segments, to detect the SIE and then used the Akaike's information cri...

We investigate the problem of sequential piecewise linear regression from a competitive framework. For an arbitrary and unknown data length n, we first introduce a method to partition the regressor space. Particularly, we present a recursive method that divides the regressor space into O(n) disjoint regions (partitions) that can result in approximately 1.5 different piecewise linear models on t...