2-D threshold function f is a function defined on the integer interior of a rectangular area [0, m] × [0, n] on a plane and takes values from the set {0, 1} such that there is a straight line separating the pre-images f −1 (0) and f −1 (1). For the number of such functions only asymptotic bounds were known. We give an exact formula for the number of 2-D threshold functions and derive an asympto...

We consider the estimation of parameters in a particular segmented generalized linear model with additive measurement error in predictors, with a focus on linear and logistic regression. In epidemiologic studies segmented regression models often occur as threshold models, where it is assumed that the exposure has no influence on the response up to a possibly unknown threshold. Furthermore, in o...

In this study, we employ a recently developed econometric technique of the threshold model with the GJR-GARCH process on error terms to investigate the relationships between weather factors and stock market returns in Taiwan using daily data for the period of 1 July 1997–22 October 2003. The major weather factors studied include temperature, humidity, and cloud cover. Our empirical evidence sho...

Recently, Starns et al. (2008) collected source judgments for old items, which participants had claimed to be new, and found residual source discriminability depending on the old-new response bias. The finding was interpreted as evidence in favor of the multivariate signal-detection model but against the high-threshold model of source memory. According to the latter, “new” responses only follow...

In this paper, we develop a Bayesian approach to estimate a Cox proportional hazards model that allows a threshold in the regression coefficient, when some fraction of subjects are not susceptible to the event of interest. A data augmentation scheme with latent binary cure indicators is adopted to simplify the Markov chain Monte Carlo implementation. Given the binary cure indicators, the Cox cu...

Cox proportional hazards (PH) regression is a well-known model for analyzing survival data and its strengths are widely recognized. Threshold regression (TR) is a relatively new methodology but one that is receiving greater attention and being used successfully by researchers in different fields, including biopharmaceutical statistics. In threshold regression, event times are modeled by a stoch...