Alternative posterior consistency results in nonparametric binary regression using Gaussian process priors

We establish consistency of posterior distribution when a Gaussian process prior is used as a prior distribution for the unknown binary regression function. Specifically, we take the work of Ghosal and Roy [2006. Posterior consistency of Gaussian process prior for nonparametric binary regression. Ann. Statist. 34, 2413–2429] as our starting point, and then weaken their assumptions on the smoothness of the Gaussian process kernel while retaining a stronger yet applicable condition about design points. Furthermore, we extend their results to multi-dimensional covariates under a weaker smoothness condition on the Gaussian process. Finally, we study the extent to which posterior consistency can be achieved under a general model where, when additional hyperparameters in the covariance function of a Gaussian process are involved.     

Non-ergodic martingale estimating functions and related asymptotics

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.     

Testing non-nested log-linear models with pseudo estimator

As the number of random variables for the categorical data increases, the possible number of log-linear models which can be fitted to the data increases rapidly, so that various model selection methods are developed. However, we often found that some models chosen by different selection criteria do not coincide. In this paper, we propose a comparison method to test the final models which are non-nested. The statistic of Cox (1961, 1962) is applied to log-linear models for testing non-nested models, and the Kullback-Leibler measure of closeness (Pesaran 1987) is explored. In log-linear models, pseudo estimators for the expectation and the variance of Cox's statistic are not only derived but also shown to be consistent estimators.     

Bootstrap confidence regions computed from autoregressions of arbitrary order

Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second-order properties then it may be used in a double-bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second-order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the 'raw' estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct.     

Predictive factors of acculturation attitudes and social support among Asian immigrants in the USA

This study examines acculturation attitude and its relation to social support among Asian immigrants. The data were collected from 242 Korean, Indian and Filipino immigrants in the USA using the Acculturation Attitude Scale and the Social Support Index. Findings showed that Koreans had a less positive attitude toward acculturation than did Indian and Filipino participants. Acculturation attitude was positively correlated with educational level and English fluency. This study also found a negative correlation between acculturation attitude and social support. Social support from friends and English fluency were identified as significant predictor variables in determining the level of acculturation attitude. These findings not only contribute to social work education and practice, but also increase cultural sensitivity and awareness in working with these populations.     

Bayesian variable selection approach to a Bernstein polynomial regression model with stochastic constraints

This paper provides a Bayesian estimation procedure for monotone regression models incorporating the monotone trend constraint subject to uncertainty. For monotone regression modeling with stochastic restrictions, we propose a Bayesian Bernstein polynomial regression model using two-stage hierarchical prior distributions based on a family of rectangle-screened multivariate Gaussian distributions extended from the work of Gurtis and Ghosh [7 S.M. Curtis and S.K. Ghosh, A variable selection approach to monotonic regression with Bernstein polynomials, J. Appl. Stat. 38 (2011), pp. 961–976. doi: 10.1080/02664761003692423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. This approach reflects the uncertainty about the prior constraint, and thus proposes a regression model subject to monotone restriction with uncertainty. Based on the proposed model, we derive the posterior distributions for unknown parameters and present numerical schemes to generate posterior samples. We show the empirical performance of the proposed model based on synthetic data and real data applications and compare the performance to the Bernstein polynomial regression model of Curtis and Ghosh [7 S.M. Curtis and S.K. Ghosh, A variable selection approach to monotonic regression with Bernstein polynomials, J. Appl. Stat. 38 (2011), pp. 961–976. doi: 10.1080/02664761003692423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] for the shape restriction with certainty. We illustrate the effectiveness of our proposed method that incorporates the uncertainty of the monotone trend and automatically adapts the regression function to the monotonicity, through empirical analysis with synthetic data and real data applications.     

We Don’t Belong Here: Adolescents of North Korean Refugee Families and Their Suicidal Behaviors

Despite the increasing number of studies that examine the link between immigration and suicide in Korean youths, most have focused on self-harming behaviours among adolescents in multicultural families, while much less attention has been directed towards those in North Korean (NK) refugee families. This paper addresses this gap by comparing three determinants of suicidal behaviours across three groups of Korean adolescents. Data are drawn from the KYRBS, a nationally representative sample of students in middle and high schools, and the results indicate that NK youths were 87.2 per cent more likely to have suicidal ideation than their South Korean peers, that they are 3.7 times more likely to experience suicidal plans and 4.1 times more likely to attempt suicide. These results clearly suggest that immigrant youths, including NK refugees, are confronting significant difficulties with assimilation, and those disadvantages lead to a higher propensity of self-threatening behaviours.     

INVESTMENT SHOCKS,CONSUMPTION PUZZLE,AND BUSINESS CYCLES

A mass of recent research shows that investment shocks are primary driving forces of business cycles. A thorny issue, however, arises due to countercyclical consumption behavior following the investment shocks. This article contributes to the literature by resolving this anomalous issue in a model that features time inconsistency, modeled as naïve hyperbolic discounting. The proposed model delivers positive responses of consumption to an investment shock and thus produces comovement of key macroaggregates, which is in line with the observed U.S. business cycles. Furthermore, this article also substantiates the validity of the proposed model by producing comovement following an investment news (or anticipated investment) shock. Additional analyses on changes in model structure and parameter value do not reverse the main finding. (JEL E3, E7)