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Simulation from the truncated multivariate normal distribution in high dimensions is a recurrent problem in statistical computing and is typically only feasible by using approximate Markov chain Monte Carlo sampling. We propose a minimax tilting method for exact independently and identically distributed data simulation from the truncated multivariate normal distribution. The new methodology provides both a method for simulation and an efficient estimator to hitherto intractable Gaussian integrals. We prove that the estimator has a rare vanishing relative error asymptotic property. Numerical experiments suggest that the scheme proposed is accurate in a wide range of set-ups for which competing estimation schemes fail. We give an application to exact independently and identically distributed data simulation from the Bayesian posterior of the probit regression model.

Regression discontinuity models are commonly used to nonparametrically identify and estimate a local average treatment effect (LATE). We show that the derivative of the treatment effect with respect to the running variable at the cutoff, referred to as the treatment effect derivative (TED), is nonparametrically identified, easily estimated, and has implications for testing external validity and extrapolating the estimated LATE away from the cutoff. Given a local policy invariance assumption, we further show this TED equals the change in the treatment effect that would result from a marginal change in the threshold, which we call the marginal threshold treatment effect (MTTE). We apply these results to Goodman (2008), who estimates the effect of a scholarship program on college choice. MTTE in this case identifies how this treatment effect would change if the test score threshold to qualify for a scholarship were changed, even though no such change in threshold is actually observed.

We propose a novel sparse tensor decomposition method, namely the tensor truncated power method, that incorporates variable selection in the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family of high dimensional latent variable models, including high dimensional Gaussian mixtures and mixtures of sparse regressions. A thorough theoretical investigation is further conducted. In particular, we show that the final decomposition estimator is guaranteed to achieve a local statistical rate, and we further strengthen it to the global statistical rate by introducing a proper initialization procedure. In high dimensional regimes, the statistical rate obtained significantly improves those shown in the existing nonsparse decomposition methods. The empirical advantages of tensor truncated power are confirmed in extensive simulation results and two real applications of click-through rate prediction and high dimensional gene clustering.

Interval-censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis. However, most of the existing methods are for univariate data and there exists only limited research on bivariate data, especially on regression analysis of bivariate interval-censored data. We present a class of semiparametric transformation models for the problem and for inference, a sieve maximum likelihood approach is developed. The model provides a great flexibility, in particular including the commonly used proportional hazards model as a special case, and in the approach, Bernstein polynomials are employed. The strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore, the estimators are shown to be asymptotically efficient. Extensive simulation studies are conducted and indicate that the proposed method works well for practical situations. Supplementary materials for this article are available online.

As the global climate problem becomes increasingly serious, the green technology innovation to achieve “carbon peak and carbon neutral” has gradually become the global consensus of major countries, and how the rapid development of artificial intelligence (AI) technology affects green technology innovation (GTI) has received a great deal of attention in the field of economics. Therefore, based on China’s inter-provincial panel data from 2006 to 2019, the system GMM, dynamic panel threshold model, and quantile regression model were constructed to examine various influences of AI development on GTI under different environmental regulation intensity, research and development (R&D) investment, and institutional environmental threshold conditions. The findings presented that AI development significantly contributes to GTI and GTFP, with an impact coefficient of 0.0122 and 0.0084, and this influence is mainly reflected in the western region of China and is more obvious in the 2006–2012 period. AI development mainly enhances green technological efficiency, and it has dampening effects on green technological progress during the period 2013–2019. Additionally, there are non-linear threshold effects in the relationship between the level of AI development and GTI when environmental regulatory intensity, R&D investment, and institutional environment are in different level intervals. AI development will boost GTI only when the intensity of environmental regulation and institutional environment is above a certain threshold value. However, the AI development represented by industrial robot applications still has no obvious effect on GTI even when the R&D investment exceeds a certain threshold. Furthermore, the growth effect of AI development on GTI indicates a decreasing nonlinear pattern as the GTI’s quantile rises under the condition that R&D investment and institutional environment intensity cross the threshold, while this growth effect increases gradually with the rise of GTI’s quantile when the environmental regulation is above the threshold.

A comprehensive, unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly used semiparametric models: proportional hazards, proportional odds, and accelerated failure time. Unlike many other approaches, all manner of censored survival times are simultaneously accommodated including uncensored, interval censored, current-status, left and right censored, and mixtures of these. Left-truncated data are also accommodated leading to models for time-dependent covariates. Both georeferenced (location exactly observed) and areally observed (location known up to a geographic unit such as a county) spatial locations are handled; formal variable selection makes model selection especially easy. Model fit is assessed with conditional Cox-Snell residual plots, and model choice is carried out via log pseudo marginal likelihood (LPML) and deviance information criterion (DIC). Baseline survival is modeled with a novel transformed Bernstein polynomial prior. All models are fit via a new function which calls efficient compiled C++ in the R package spBayesSurv . The methodology is broadly illustrated with simulations and real data applications. An important finding is that proportional odds and accelerated failure time models often fit significantly better than the commonly used proportional hazards model. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation. Existing modelling solutions to this problem are either applicable only on subdomains or appeal to multiple limit theories. We introduce a unified representation for bivariate extremes that encompasses a wide variety of dependence scenarios and applies when at least one variable is large. Our representation motivates a parametric model that encompasses both dependence classes. We implement a simple version of this model and show that it performs well in a range of settings.

This paper introduces the structural threshold regression (STR) model that allows for an endogenous threshold variable as well as for endogenous regressors. This model provides a parsimonious way of modeling nonlinearities and has many potential applications in economics and finance. Our framework can be viewed as a generalization of the simple threshold regression framework of Hansen (2000, Econometrica 68, 575–603) and Caner and Hansen (2004, Econometric Theory 20, 813–843) to allow for the endogeneity of the threshold variable and regime-specific heteroskedasticity. Our estimation of the threshold parameter is based on a two-stage concentrated least squares method that involves an inverse Mills ratio bias correction term in each regime. We derive its asymptotic distribution and propose a method to construct confidence intervals. We also provide inference for the slope parameters based on a generalized method of moments. Finally, we investigate the performance of the asymptotic approximations using a Monte Carlo simulation, which shows the applicability of the method in finite samples.

Achieving carbon peak and carbon neutrality is an inherent requirement for countries to promote green recovery and transformation of the global economy after the COVID-19 pandemic. As “a smoke-free industry,” producer services agglomeration (PSA) may have significant impacts on CO 2 emission reduction. Therefore, based on the nightlight data to calculate the CO 2 emissions of 268 cities in China from 2005 to 2017, this study deeply explores the impact and transmission mechanism of PSA on CO 2 emissions by constructing dynamic spatial Durbin model and intermediary effect model. Furthermore, the dynamic threshold model is used to analyze the nonlinear characteristics between PSA and CO 2 emissions under different degrees of government intervention. The results reveal that: (1) Generally, China’s CO 2 emissions are path-dependent in the time dimension, showing a “snowball effect.” PSA significantly inhibits CO 2 emissions, but heterogeneous influences exist in different regions, time nodes, and sub-industries; (2) PSA can indirectly curb CO 2 emissions through economies of scale, technological innovation, and industrial structure upgrading. (3) The impact of PSA on China’s CO 2 emissions has an obvious double threshold effect under different degree of government intervention. Accordingly, the Chinese government should increase the support for producer services, dynamically adjust industrial policies, take a moderate intervention, and strengthen market-oriented reform to reduce CO 2 emissions. This study opens up a new path for the low-carbon economic development and environmental sustainability, and also fills in the theoretical gaps on these issues. The findings and implications will offer instructive guideline for early achieving carbon peak and carbon neutrality.

Surfacing the stress of global CO 2 emission reduction and the change into a low-emission economy has become one of the prominent economic concerns in the twenty-first century. The essence of evolving a low-emission economy is to raise carbon productivity that can be estimated as the cost-effective paybacks of CO 2 emissions. A panel threshold model was applied to approximate the threshold effect of globalization on carbon productivity under the development of human capital by using the panel data of thirty provinces of China from 2009 to 2017. The empirical findings demonstrate that China’s carbon productivity increases, while economic growth shape moves towards sustainable development with low-carbon emission. Moreover, the driving force of globalization on carbon productivity is not tediously decreasing/increasing, but it has a double threshold effect of human capital. In line with this, this study finding found a single and double threshold of 9.3478 and 10.8800, respectively, as a benchmark where the relationship turns positive. The empirical findings have suggested several policy implications for the Chinese Government, policymakers, and regulatory authorities regarding this critical issue.