Recent work by Reiss and Ogden (2009) provides a theoretical basis for sometimes preferring restricted maximum likelihood (REML) to generalized cross validation (GCV) for smoothing parameter selection in semiparametric regression. However, existing REML or marginal likelihood (ML) based methods for semiparametric GLMs use iterative REML/ML estimation of the smoothing parameters of working linea...

In bioluminescence tomography (BLT), reconstruction of internal bioluminescent source distribution from the surface optical signals is an ill-posed inverse problem. In real BLT experiment, apart from the measurement noise, the system errors caused by geometry mismatch, numerical discretization, and optical modeling approximations are also inevitable, which may lead to large errors in the recons...

Nonparametric regression makes it possible to visualize and describe spatial trends without requiring the specification of a parametric model, but appropriate choice of smoothing parameters is important to avoid misinterpreting the nonparametric fits. Because spatial data are often correlated, currently available data-driven smoothing parameter selection methods often fail to provide useful res...

Segmented line regression has been used in many applications, and the problem of estimating the number of change-points in segmented line regression has been discussed in Kim et al. (2000). This paper studies asymptotic properties of the number of change-points selected by the permutation procedure of Kim et al. (2000). This procedure is based on a sequential application of likelihood ratio typ...

To my mom, Mei, my wife, Nan and in memory of my grandma, Yanqing for all of your love iii ACKNOWLEDGEMENTS I would like to thank Prof. Stanley Reeves of Auburn university who provided help with the implementation of Generalized Cross Validation (GCV). There are many helpful feedbacks from the readers of our papers. For example, Lalaké Apoyan pointed out the scintillation effects of turbulence....

Speckle noise usually occurs in Synthetic Aperture Radar (SAR) images due to coherent radiation. Speckle reduction is a mandatory step prior to the processing of SAR images. Here a novel de-speckling scheme is presented which is in line with the wavelet transform based schemes with several modifications due to the implementation of directionlet transform. As in any transform based de-speckling ...

Prenatal exposure to carcinogenic polycyclic aromatic hydrocarbons (c-PAHs) through maternal inhalation induces higher risk for a wide range of fetotoxic effects. However, the most health-relevant dose function from chronic gestational exposure remains unclear. Whether there is a gestational window during which the human embryo/fetus is particularly vulnerable to PAHs has not been examined thor...

PURPOSE Developing a computationally efficient automated method for the optimal choice of regularization parameter in diffuse optical tomography. METHODS The least-squares QR (LSQR)-type method that uses Lanczos bidiagonalization is known to be computationally efficient in performing the reconstruction procedure in diffuse optical tomography. The same is effectively deployed via an optimizati...

Abstract: A popular approach in the investigation of the short-term behavior of a non-stationary time series is to assume that the time series decomposes additively into a long-term trend and short-term fluctuations. A first step towards investigating the short-term behavior requires estimation of the trend, typically via smoothing in the time domain. We propose a method for time-domain smoothi...