We introduce a procedure for generalized monotonic curve fitting that is based on a Bayesian analysis of the isotonic regression model. Conventional isotonic regression fits monotonically increasing step functions to data. In our approach we treat the number and location of the steps as random. For each step level we adopt the conjugate prior to the sampling distribution of the data as if the c...

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We study additive models within the context of the parametric random field model proposed by Hamilton (2001). This is a flexible parametric approach to model nonlinearities in the context of a regression model. Though the model is parametric, it enjoys the flexibility of the nonparametric approach as it can approximate a large collection of nonlinear functions and it has the added advantage tha...

A simulation based method for the numerical solution of PDE with random coefficients is presented. By the Feynman-Kac formula, the solution can be represented as conditional expectation of a functional of a corresponding stochastic differential equation driven by independent noise. A time discretization of the SDE for a set of points in the domain and a subsequent Monte Carlo regression lead to...

Using the weighted maximum likelihood method, we propose a consistent estimation of parametric portion and nonparametric portion in exponential semiparametric regression models under random censorship. A small Monte Carlo study is carried out to examine the proposed estimation method.

A random-effects probit model is developed for the case in which the outcome of interest is a series of correlated binary responses. These responses can be obtained as the product of a longitudinal response process where an individual is repeatedly classified on a binary outcome variable (e.g., sick or well on occasion t), or in "multilevel" or "clustered" problems in which individuals within g...

We consider the regression problem and describe an algorithm approximating the regression function by estimators piecewise constant on the elements of an adaptive partition. The partitions are iteratively constructed by suitable random merges and splits, using cuts of arbitrary geometry. We give a risk bound under the assumption that a “weak learning hypothesis” holds, and characterize this hyp...

In this paper, we present an accelerated numerical method based on random projection for sparse linear regression. Previous studies have shown that under appropriate conditions, gradient-based methods enjoy a geometric convergence rate when applied to this problem. However, the time complexity of evaluating the gradient is as large as O(nd), where n is the number of data points and d is the dim...

Shape restricted regressions, including isotonic regression and concave regression as special cases, are studied using priors on Bernstein polynomials and Markov chain Monte Carlo methods. These priors have large supports, select only smooth functions, can easily incorporate geometric information into the prior, and can be generated without computational difficulty. Algorithms generating priors...

In this paper we address the problem of clustering sets of curve or trajectory data generated by groups of objects or individuals. The focus is to model curve data directly using a set of model-based curve clustering algorithms referred to as mixtures of regressions or regression mixtures. The proposed methodology is based on extension to regression mixtures that we call random effects regressi...