Introducing COZIGAM: An R Package for Unconstrained and Constrained Zero-Inflated Generalized Additive Model Analysis

Zero-inflation problem is very common in ecological studies as well as other areas. Nonparametric regression with zero-inflated data may be studied via the zero-inflated generalized additive model (ZIGAM), which assumes that the zero-inflated responses come from a probabilistic mixture of zero and a regular component whose distribution belongs to the 1-parameter exponential family. With the further assumption that the probability of non-zero-inflation is some monotonic function of the mean of the regular component, we propose the constrained zero-inflated generalized additive model (COZIGAM) for analyzingzero-inflated data. When the hypothesized constraint obtains, the new approach provides a unified framework for modeling zero-inflated data, which is more parsimonious and efficient than the unconstrained ZIGAM. We have developed an R package COZIGAM which contains functions that implement an iterative algorithm for fitting ZIGAMs and COZIGAMs to zero-inflated data basedon the penalized likelihood approach. Other functions included in the packageare useful for model prediction and model selection. We demonstrate the use ofthe COZIGAM package via some simulation studies and a real application.

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H. Tong

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H. Tong [arXiv:1104.3073]Comment: Published in at http://dx.doi.org/10.1214/11-STS345B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Introducing COZIGAM: An R Package for Unconstrained and Constrained Zero-Inflated Generalized Additive Model Analysis

Zero-inflation problem is very common in ecological studies as well as other areas. Nonparametric regression with zero-inflated data may be studied via the zero-inflated generalized additive model (ZIGAM), which assumes that the zero-inflated responses come from a probabilistic mixture of zero and a regular component whose distribution belongs to the 1-parameter exponential family. With the further assumption that the probability of non-zero-inflation is some monotonic function of the mean of the regular component, we propose the constrained zero-inflated generalized additive model (COZIGAM) for analyzingzero-inflated data. When the hypothesized constraint obtains, the new approach provides a unified framework for modeling zero-inflated data, which is more parsimonious and efficient than the unconstrained ZIGAM. We have developed an R package COZIGAM which contains functions that implement an iterative algorithm for fitting ZIGAMs and COZIGAMs to zero-inflated data basedon the penalized likelihood approach. Other functions included in the packageare useful for model prediction and model selection. We demonstrate the use ofthe COZIGAM package via some simulation studies and a real application

A Note on Inequality Constraints in the GARCH Model (SHORT RUNNING TITLE: GARCH Inequality Constraints)

Abstract: We consider the parameter restrictions that need to be imposed in order to ensure that the conditional variance process of a GARCH(p, q) model remains non-negative. Previously, We also point out the linkage between the absolute monotonicity of the GARCH 1 2 generating function and the non-negativity of the GARCH kernel, and use it to provide examples of sufficient conditions for this non-negativity property to hold

Stochastic Constrained DRO with a Complexity Independent of Sample Size

Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze stochastic algorithms that apply to both non-convex and convex losses for solving Kullback Leibler divergence constrained DRO problem. Compared with existing methods solving this problem, our stochastic algorithms not only enjoy competitive if not better complexity independent of sample size but also just require a constant batch size at every iteration, which is more practical for broad applications. We establish a nearly optimal complexity bound for finding an $\epsilon$ stationary solution for non-convex losses and an optimal complexity for finding an $\epsilon$ optimal solution for convex losses. Empirical studies demonstrate the effectiveness of the proposed algorithms for solving non-convex and convex constrained DRO problems.Comment: 37 pages, 16 figure