Chun Yip Yau

Inequality in obesigenic environments : Fast food density in New York City

The high prevalence of obesity in African American populations may be due to the food environment in residential communities, and the density of fast food restaurants is an important aspect of the restaurant landscape in US cities. This study investigated racial and socioeconomic correlates of fast food density in New York City. We found that predominantly Black areas had higher densities of fast food than predominantly White areas; high-income Black areas had similar exposure as low-income Black areas; and national chains were most dense in commercial areas. The results highlight the importance of policy level interventions to address disparities in food environments as a key goal in obesity prevention efforts.

Group LASSO for Structural Break Time Series

Consider a structural break autoregressive (SBAR) process where j = 1, …, m + 1, {t1, …, tm} are change-points, 1 = t0 < t1 < ⋅⋅⋅ < tm + 1 = n + 1, σ( · ) is a measurable function on , and {ϵt} are white noise with unit variance. In practice, the number of change-points m is usually assumed to be known and small, because a large m would involve a huge amount of computational burden for parameters estimation. By reformulating the problem in a variable selection context, the group least absolute shrinkage and selection operator (LASSO) is proposed to estimate an SBAR model when m is unknown. It is shown that both m and the locations of the change-points {t1, …, tm} can be consistently estimated from the data, and the computation can be efficiently performed. An improved practical version that incorporates group LASSO and the stepwise regression variable selection technique are discussed. Simulation studies are conducted to assess the finite sample performance. Supplementary materials for this article are available online.

Likelihood inference for discriminating between long-memory and change-point models

We develop a likelihood ratio (LR) test procedure for discriminating between a short‐memory time series with a change‐point (CP) and a long‐memory (LM) time series. Under the null hypothesis, the time series consists of two segments of short‐memory time series with different means and possibly different covariance functions. The location of the shift in the mean is unknown. Under the alternative, the time series has no shift in mean but rather is LM. The LR statistic is defined as the normalized log‐ratio of the Whittle likelihood between the CP model and the LM model, which is asymptotically normally distributed under the null. The LR test provides a parametric alternative to the CUSUM test proposed by Berkes et al. (2006). Moreover, the LR test is more general than the CUSUM test in the sense that it is applicable to changes in other marginal or dependence features other than a change‐in‐mean. We show its good performance in simulations and apply it to two data examples.

Empirical Likelihood in Long‐Memory Time Series Models

This article studies the empirical likelihood method for long‐memory time series models. By virtue of the Whittle likelihood, one obtains a score function that can be viewed as an estimating equation of the parameters of a fractional integrated autoregressive moving average (ARFIMA) model. This score function is used to obtain an empirical likelihood ratio which is shown to be asymptotically chi‐square distributed. Confidence regions for the parameters are constructed based on the asymptotic distribution of the empirical likelihood ratio. Bartlett correction and finite sample properties of the empirical likelihood confidence regions are examined.

LARS-type algorithm for group lasso

The least absolute shrinkage and selection operator (lasso) has been widely used in regression analysis. Based on the piecewise linear property of the solution path, least angle regression provides an efficient algorithm for computing the solution paths of lasso. Group lasso is an important generalization of lasso that can be applied to regression with grouped variables. However, the solution path of group lasso is not piecewise linear and hence cannot be obtained by least angle regression. By transforming the problem into a system of differential equations, we develop an algorithm for efficient computation of group lasso solution paths. Simulation studies are conducted for comparing the proposed algorithm to the best existing algorithm: the groupwise-majorization-descent algorithm.

Estimation of Multiple-Regime Threshold Autoregressive Models With Structural Breaks

The threshold autoregressive (TAR) model is a class of nonlinear time series models that have been widely used in many areas. Due to its nonlinear nature, one major difficulty in fitting a TAR model is the estimation of the thresholds. As a first contribution, this article develops an automatic procedure to estimate the number and values of the thresholds, as well as the corresponding AR order and parameter values in each regime. These parameter estimates are defined as the minimizers of an objective function derived from the minimum description length (MDL) principle. A genetic algorithm (GA) is constructed to efficiently solve the associated minimization problem. The second contribution of this article is the extension of this framework to piecewise TAR modeling; that is, the time series is partitioned into different segments for which each segment can be adequately modeled by a TAR model, while models from adjacent segments are different. For such piecewise TAR modeling, a procedure is developed to estimate the number and locations of the breakpoints, together with all other parameters in each segment. Desirable theoretical results are derived to lend support to the proposed methodology. Simulation experiments and an application to an U.S. GNP data are used to illustrate the empirical performances of the methodology. Supplementary materials for this article are available online.

A hidden Markov model for earthquake prediction

Earthquake occurrence is well-known to be associated with structural changes in underground dynamics, such as stress level and strength of electromagnetic signals. While the causation between earthquake occurrence and underground dynamics remains elusive, the modeling of changes in underground dynamics can provide insights on earthquake occurrence. However, underground dynamics are usually difficult to measure accurately or even unobservable. In order to model and examine the effect of the changes in unobservable underground dynamics on earthquake occurrence, we propose a novel model for earthquake prediction by introducing a latent Markov process to describe the underground dynamics. In particular, the model is capable of predicting the change-in-state of the hidden Markov chain, and thus can predict the time and magnitude of future earthquake occurrences simultaneously. Simulation studies and applications on a real earthquake dataset indicate that the proposed model successfully predicts future earthquake occurrences. Theoretical results, including the stationarity and ergodicity of the proposed model, as well as consistency and asymptotic normality of model parameter estimation, are provided.

Threshold Estimation via Group Orthogonal Greedy Algorithm

A threshold autoregressive (TAR) model is an important class of nonlinear time series models that possess many desirable features such as asymmetric limit cycles and amplitude-dependent frequencies. Statistical inference for the TAR model encounters a major difficulty in the estimation of thresholds, however. This article develops an efficient procedure to estimate the thresholds. The procedure first transforms multiple-threshold detection to a regression variable selection problem, and then employs a group orthogonal greedy algorithm to obtain the threshold estimates. Desirable theoretical results are derived to lend support to the proposed methodology. Simulation experiments are conducted to illustrate the empirical performances of the method. Applications to U.S. GNP data are investigated.

New recursive estimators of the time-average variance constant

Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC with