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Full-Text Articles in Physical Sciences and Mathematics

Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu Aug 2021

Glivenko-Cantelli Theorems For Integrated Functionals Of Stochastic Processes, Jia Li, Congshan Zhang, Yunxiao Liu

Research Collection School Of Economics

We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Hölder classes as special cases. The general Glivenko-Cantelli theorem is then applied in more concrete high-frequency statistical settings to establish uniform convergence results for general integrated functionals of the volatility of efficient price and local moments of microstructure noise.


Determining The Number Of Communities In Degree-Corrected Stochastic Block Models, Shujie Ma, Liangjun Su, Yichong Zhang Apr 2021

Determining The Number Of Communities In Degree-Corrected Stochastic Block Models, Shujie Ma, Liangjun Su, Yichong Zhang

Research Collection School Of Economics

We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio. For estimation, we consider a spectral clustering together with binary segmentation method. This approach guarantees an upper bound for the pseudo likelihood ratio statistic when the model is over-fitted. We also derive its limiting distribution when the model is under-fitted. Based on these properties, we establish the consistency of our estimator for the true number of communities. Developing these theoretical properties require a mild condition on the average degree: growing at a rate faster than log(n), where n is the number …


Activation Of Trpa1 Nociceptor Promotes Systemic Adult Mammalian Skin Regeneration, Jenny J. Wei, Hali S. Kim, Casey A. Spencer, Donna Brennan-Crispi, Ying Zheng, Nicolette M. Johnson, Misha Rosenbach, Christopher Miller, Denis H. Y. Leung, George Cotsarelis, Thomas H. Leung Aug 2020

Activation Of Trpa1 Nociceptor Promotes Systemic Adult Mammalian Skin Regeneration, Jenny J. Wei, Hali S. Kim, Casey A. Spencer, Donna Brennan-Crispi, Ying Zheng, Nicolette M. Johnson, Misha Rosenbach, Christopher Miller, Denis H. Y. Leung, George Cotsarelis, Thomas H. Leung

Research Collection School Of Economics

Adult mammalian wounds, with rare exception, heal with fibrotic scars that severely disrupt tissue architecture and function. Regenerative medicine seeks methods to avoid scar formation and restore the original tissue structures. We show in three adult mouse models that pharmacologic activation of the nociceptor TRPA1 on cutaneous sensory neurons reduces scar formation and can also promote tissue regeneration. Local activation of TRPA1 induces tissue regeneration on distant untreated areas of injury, demonstrating a systemic effect. Activated TRPA1 stimulates local production of interleukin-23 (IL-23) by dermal dendritic cells, leading to activation of circulating dermal IL-17–producing γδ T cells. Genetic ablation of …


Disentangling Greenhouse Warming And Aerosol Cooling To Reveal Earth's Climate Sensitivity, T. Storelvmo, T. Leirvik, U. Lohmann, Peter C. B. Phillips, M. Wild Apr 2016

Disentangling Greenhouse Warming And Aerosol Cooling To Reveal Earth's Climate Sensitivity, T. Storelvmo, T. Leirvik, U. Lohmann, Peter C. B. Phillips, M. Wild

Research Collection School Of Economics

Earth's climate sensitivity has long been subject to heated debate and has spurred renewed interest after the latest IPCC assessment report suggested a downward adjustment of its most likely range(1). Recent observational studies have produced estimates of transient climate sensitivity, that is, the global mean surface temperature increase at the time of CO2 doubling, as low as 1.3 K (refs 2,3), well below the best estimate produced by global climate models (1.8 K). Here, we present an observation-based study of the time period 1964 to 2010, which does not rely on climate models. The method incorporates observations of greenhouse gas …


Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang Jan 2013

Variable Selection In Nonparametric And Semiparametric Regression Models, Liangjun Su, Yonghui Zhang

Research Collection School Of Economics

This chapter reviews the literature on variable selection in nonparametric and semiparametric regression models via shrinkage. We highlight recent developments on simultaneous variable selection and estimation through the methods of least absolute shrinkage and selection operator (Lasso), smoothly clipped absolute deviation (SCAD) or their variants, but restrict our attention to nonparametric and semiparametric regression models. In particular, we consider variable selection in additive models, partially linear models, functional/varying coefficient models, single index models, general nonparametric regression models, and semiparametric/nonparametric quantile regression models.


Estimation And Forecasting Of Dynamic Conditional Covariance: A Semiparametric Multivariate Model, Xiangdong Long, Liangjun Su, Aman Ullah Jan 2011

Estimation And Forecasting Of Dynamic Conditional Covariance: A Semiparametric Multivariate Model, Xiangdong Long, Liangjun Su, Aman Ullah

Research Collection School Of Economics

We propose a semiparametric conditional covariance (SCC) estimator that combines the first-stage parametric conditional covariance (PCC) estimator with the second-stage nonparametric correction estimator in a multiplicative way. We prove the asymptotic normality of our SCC estimator, propose a nonparametric test for the correct specification of PCC models, and study its asymptotic properties. We evaluate the finite sample performance of our test and SCC estimator and compare the latter with that of PCC estimator, purely nonparametric estimator, and Hafner, Dijk, and Franses’s (2006) estimator in terms of mean squared error and Value-at-Risk losses via simulations and real data analyses.


Model Selection In Validation Sampling Data: An Asymptotic Likelihood-Based Lasso Approach, Chenlei Leng, Denis H. Y. Leung Jan 2011

Model Selection In Validation Sampling Data: An Asymptotic Likelihood-Based Lasso Approach, Chenlei Leng, Denis H. Y. Leung

Research Collection School Of Economics

We propose an asymptotic likelihood-based LASSO approach for model selection in regression analysis when data are subject to validation sampling. The method makes use of an initial estimator of the regression coefficients and their asymptotic covariance matrix to form an asymptotic likelihood. This ``working'' objective function facilitates the formulation of the LASSO and the implementation of a fast algorithm. Our method circumvents the need to use a likelihood set-up that requires full distributional assumptions about the data. We show that the resulting estimator is consistent in model selection and that the method has lower prediction errors than a model that …


Nonparametric Testing For Asymmetric Information, Liangjun Su, Martin Spindler Jul 2010

Nonparametric Testing For Asymmetric Information, Liangjun Su, Martin Spindler

Research Collection School Of Economics

Asymmetric information is an important phenomenon in many markets and in particular in insurance markets. Testing for asymmetric information has become a very important issue in the literature in the last two decades. Almost all testing procedures that are used in empirical studies are parametric, which may yield misleading conclusions in the case of misspecification of either functional or distributional relationships among the variables of interest. Motivated by the literature on testing conditional independence, we propose a new nonparametric test for asymmetric information which is applicable in a variety of situations. We demonstrate the test works reasonably well through Monte …


Numerical Analysis Of Non-Constant Pure Rate Of Time Preference: A Model Of Climate Policy, Tomoki Fujii, Larry Karp Jan 2010

Numerical Analysis Of Non-Constant Pure Rate Of Time Preference: A Model Of Climate Policy, Tomoki Fujii, Larry Karp

Research Collection School Of Economics

When current decisions affect welfare in the far-distant future, as with climate change, the use of a declining pure rate of time preference (PRTP) provides potentially important modeling flexibility. The difficulty of analyzing models with non-constant PRTP limits their application. We describe and provide software (available online) to implement an algorithm to numerically obtain a Markov perfect equilibrium for an optimal control problem with non-constant PRTP. We apply this software to a simplified version of the numerical climate change model used in the Stern Review. For our calibration, the policy recommendations are less sensitive to the PRTP than widely believed.


Bayesian Analysis Of Structural Credit Risk Models With Microstructure Noises, Shirley J. Huang, Jun Yu Nov 2009

Bayesian Analysis Of Structural Credit Risk Models With Microstructure Noises, Shirley J. Huang, Jun Yu

Research Collection School Of Economics

In this paper a Markov chain Monte Carlo (MCMC) technique is developed for the Bayesian analysis of structural credit risk models with microstructure noises. The technique is based on the general Bayesian approach with posterior computations performed by Gibbs sampling. Simulations from the Markov chain, whose stationary distribution converges to the posterior distribution, enable exact ¯nite sample inferences of model parameters. The exact inferences can easily be extended to latent state variables and any nonlinear transformation of state variables and parameters, facilitating practical credit risk applications. In addition, the comparison of alternative models can be based on deviance information criterion …


A Semiparametric Stochastic Volatility Model, Jun Yu Jul 2008

A Semiparametric Stochastic Volatility Model, Jun Yu

Research Collection School Of Economics

This paper examines how volatility responds to return news in the context of stochastic volatility (SV) using a nonparametric method. The correlation structure in the classical leverage SV model is generalized based on a linear spline. In the new model the correlation between the return innovation and volatility innovation is dependent on the type of news arrived to the market. Theoretical properties of the proposed model are examined. A simulation-based maximum likelihood method is developed to estimate the new model. Simulations show that the estimation method provides reliable parameter estimates. The new model is fitted to daily and weekly data …


Profile Likelihood Estimation Of Partially Linear Panel Data Models With Fixed Effects, Liangjun Su, Aman Ullah May 2006

Profile Likelihood Estimation Of Partially Linear Panel Data Models With Fixed Effects, Liangjun Su, Aman Ullah

Research Collection School Of Economics

We consider consistent estimation of partially linear panel data models with fixed effects. We propose profile-likelihood-based estimators for both the parametric and nonparametric components in the models and establish convergence rates and asymptotic normality for both estimators.


A Class Of Nonlinear Stochastic Volatility Models, Jun Yu, Zhenlin Yang Jan 2006

A Class Of Nonlinear Stochastic Volatility Models, Jun Yu, Zhenlin Yang

Research Collection School Of Economics

This paper proposes a class of nonlinear stochastic volatility models based on the Box-Cox transformation which offers an alternative to the one introduced in Andersen (1994). The proposed class encompasses many parametric stochastic volatility models that have appeared in the literature, including the well known lognormal stochastic volatility model, and has an advantage in the ease with which different specifications on stochastic volatility can be tested. In addition, the functional form of transformation which induces marginal normality of volatility is obtained as a byproduct of this general way of modeling stochastic volatility. The efficient method of moments approach is used …


Multivariate Stochastic Volatility Models: Bayesian Estimation And Model Comparison, Jun Yu, Renate Meyer Nov 2004

Multivariate Stochastic Volatility Models: Bayesian Estimation And Model Comparison, Jun Yu, Renate Meyer

Research Collection School Of Economics

In this paper we show that fully likelihood-based estimation and comparison of multivariate stochastic volatility (SV) models can be easily performed via a freely available Bayesian software called WinBUGS. Moreover, we introduce to the literature several new specifications which are natural extensions to certain existing models, one of which allows for time varying correlation coefficients. Ideas are illustrated by fitting, to a bivariate time series data of weekly exchange rates, nine multivariate SV models, including the specifications with Granger causality in volatility, time varying correlations, heavy-tailed error distributions, additive factor structure, and multiplicative factor structure. Empirical results suggest that the …


On Leverage In A Stochastic Volatility Model, Jun Yu Apr 2004

On Leverage In A Stochastic Volatility Model, Jun Yu

Research Collection School Of Economics

This paper is concerned with specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications co-exist in the literature. One is the Euler approximation to the well known continuous time SV model with leverage effect and the other is the discrete time SV model of Jacquier, Polson and Rossi (2004, Journal of Econometrics, forthcoming). Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage effect in the conventional model whereas it is not clear how to obtain the leverage effect …


Deviance Information Criterion For Comparing Stochastic Volatility Models, Andreas Berg, Renate Meyer, Jun Yu Jan 2004

Deviance Information Criterion For Comparing Stochastic Volatility Models, Andreas Berg, Renate Meyer, Jun Yu

Research Collection School Of Economics

Bayesian methods have been efficient in estimating parameters of stochastic volatility models for analyzing financial time series. Recent advances made it possible to fit stochastic volatility models of increasing complexity, including covariates, leverage effects, jump components, and heavy-tailed distributions. However, a formal model comparison via Bayes factors remains difficult. The main objective of this article is to demonstrate that model selection is more easily performed using the deviance information criterion (DIC). It combines a Bayesian measure of fit with a measure of model complexity. We illustrate the performance of DIC in discriminating between various different stochastic volatility models using simulated …


The Kpss Test With Seasonal Dummies, Sainan Jin, Sainan Jin Oct 2002

The Kpss Test With Seasonal Dummies, Sainan Jin, Sainan Jin

Research Collection School Of Economics

It is shown that the KPSS test for stationarity may be applied without change to regressions with seasonal dummies. In particular, the limit distribution of the KPSS statistic is the same under both the null and alternative hypotheses whether or not seasonal dummies are used.