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作者： Wang, Shuang Boston University

学位级别：Ph.D., Doctor of Philosophy

My dissertation consists of three chapters that evaluate the social welfare effect of either antitrust policy or industrial transition, all using discrete choice model estimation as the front end for counterfactual analysis. In the first chapter, I investigate the economic impact of the merger that created the world's largest hotel chain, Marriott's acquisition of Starwood, thereby shedding light on the antitrust authorities' performance in protecting competitive markets for the benefit of consumers. Different from traditional merger analysis that focuses on the tradeoff between the upward pricing pressure and the cost synergy among the merging parties while fixing the market structure, I endogenize firms’ entry decisions into an oligopoly price competition model. To tackle the associated multiple equilibria issue, I use moment inequality estimation and propose a novel lower probability bound that reduces the computational burden from being exponential to being linear in the number of players. It also adds to the scant empirical evidence on post-merger cost synergy by showing that every one more affiliated hotel in the local market reduces a hotel's marginal cost by up to 2.3%. Then a comparison between the simulated with-merger and without-merger equilibria indicates that this merger enhances social welfare. In particular, for those markets that are previously not profitable for any firm to enter, because of the post-merger cost saving, Marriott or Starwood would enter 6% - 24% of them, which provides a new perspective for merger reviews. The second chapter, joint with Mingli Chen, Marc Rysman and Krzysztof Wozniak, studies the determinants of the US payment system's shift from paper payment instruments, namely cash and check, to digital instruments, such as debit cards and credit cards. With a 5-year transaction-level panel data, for the first time in the literature, we can distinguish the short-term effects of transaction size from the long-term changes in househ

关键词： Cloud computing Demand estimation Entry game Merger simulation minorization-maximization algorithm Moment inequality

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The fully visible Boltzmann machine and the Senate of the 45th Australian Parliament in 2016

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JOURNAL OF COMPUTATIONAL SOCIAL SCIENCE 2020年第1期3卷 55-81页

作者： Bagnall, Jessica J. Jones, Andrew T. Karavarsamis, Natalie Nguyen, Hien D. La Trobe Univ Dept Math & Stat Melbourne Vic 3086 Australia Univ Queensland Sch Math & Phys Brisbane Qld 4072 Australia

After the 2016 double dissolution election, the 45th Australian Parliament was formed. At the time of its swearing in, the Senate of the 45th Australian Parliament consisted of nine political parties, the largest number in the history of the Australian Parliament. Due to the breadth of the political spectrum that the Senate represented, the situation presented an interesting opportunity for the study of political interactions in the Australian context. Using publicly available Senate voting data in 2016, we quantitatively analyzed two aspects of the Senate. First, we analyzed the degree to which each of the non-government parties of the Senate is pro- or anti-government. Second, we analyzed the degree to which the votes of each of the non-government Senate parties are in concordance or discordance with one another. We utilized the fully visible Boltzmann machine (FVBM) model to conduct these analyses. The FVBM is an artificial neural network that can be viewed as a multivariate generalization of the Bernoulli distribution. Via a maximum pseudolikelihood estimation approach, we conducted parameter estimation and constructed hypothesis tests that revealed the interaction structures within the Australian Senate. The conclusions that we drew are well supported by external sources of information.

关键词： Australian Parliament Bernoulli distribution Maximum pseudolikelihood estimation minorization-maximization algorithm Neural networks Parametric model

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Statistical inference for generalized case-cohort design under the proportional hazards model with parameter constraints

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2019年第8期48卷 2467-2486页

作者： Pan, Yingli Ding, Jieli Liu, Yanyan Huazhong Univ Sci & Technol Sch Math & Stat Wuhan Hubei Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China

The generalized case-cohort design is widely used in large cohort studies to reduce the cost and improve the efficiency. Taking prior information of parameters into consideration in modeling process can further raise the inference efficiency. In this paper, we consider fitting proportional hazards model with constraints for generalized case-cohort studies. We establish a working likelihood function for the estimation of model parameters. The asymptotic properties of the proposed estimator are derived via the Karush-Kuhn-Tucker conditions, and their finite properties are assessed by simulation studies. A modified minorization-maximization algorithm is developed for the numerical calculation of the constrained estimator. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice.

关键词： Constrained estimation Generalized case-cohort design Karush-Kuhn-Tucker conditions minorization-maximization algorithm Proportional hazards model

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A novel MM algorithm and the mode-sharing method in Bayesian computation for the analysis of general incomplete categorical data

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 140卷 122-143页

作者： Tian, Guo-Liang Liu, Yin Tang, Man-Lai Li, Tao Southern Univ Sci & Technol Dept Math Shenzhen 518055 Guangdong Peoples R China Zhongnan Univ Econ & Law Sch Math & Stat Wuhan 430073 Hubei Peoples R China Hang Seng Univ Hong Kong Sch Decis Sci Dept Math & Stat Siu Lek YuenShatin Hong Kong Peoples R China

Incomplete categorical data often occur in the fields such as biomedicine, epidemiology, psychology, sports and so on. In this paper, we first introduce a novel minorization-maximization (MM) algorithm to calculate the maximum likelihood estimates (MLEs) of parameters and the posterior modes for the analysis of general incomplete categorical data. Although the data augmentation (DA) algorithm and Gibbs sampling as the corresponding stochastic counterparts of the expectation-maximization (EM) and ECM algorithms are developed very well, up to now, little work has been done on creating stochastic versions to the existing MM algorithms. This is the first paper to propose a mode-sharing method in Bayesian computation for general incomplete categorical data by developing a new acceptance-rejection (AR) algorithm aided with the proposed MM algorithm. The key idea is to construct a class of envelope densities indexed by a working parameter and to identify a specific envelope density which can overcome the four drawbacks associated with the traditional AR algorithm. The proposed mode-sharing based AR algorithm has three significant characteristics: (I) it can automatically establish a family of envelope densities {g(lambda)(.): lambda is an element of S-lambda} indexed by a working parameter lambda, where each member in the family shares mode with the posterior density;(II) with the onedimensional grid method searching over the finite interval S-lambda,S- it can identify an optimal working parameter lambda(opt) by maximizing the theoretical acceptance probability, yielding a best easy-sampling envelope density g lambda(opt) (.), which is more dispersive than the posterior density;(III) it can obtain the optimal envelope constant c(opt) by using the mode-sharing theorem (indicating that the high-dimensional optimization can be completely avoided) or by using the proposed MM algorithm again. Finally, a toy model and three real data sets are used to illustrate the proposed meth

关键词： Acceptance-rejection algorithm Bayesian analysis General incomplete categorical data minorization-maximization algorithm Mode-sharing method

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A robust and efficient estimation method for partially nonlinear models via a new MM algorithm

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STATISTICAL PAPERS 2019年第6期60卷 2063-2085页

作者： Jiang, Yunlu Tian, Guo-Liang Fei, Yu Jinan Univ Dept Stat Coll Econ Guangzhou 510632 Guangdong Peoples R China Southern Univ Sci & Technol Dept Math Shenzhen 518055 Peoples R China Yunnan Univ Finance & Econ Sch Math & Stat Kunming 650221 Yunnan Peoples R China

When the observed data set contains outliers, it is well known that the classical least squares method is not robust. To overcome this difficulty, Wang et al. (J Am Stat Assoc 108(502): 632-643, 2013) proposed a robust variable selection method by using the exponential squared loss (ESL) function with a tuning parameter. Although many important statistical models are investigated, to date, in the presence of outliers there is no paper to study the partially nonlinear model by using the ESL function. To fill in this gap, in this paper, we propose a robust and efficient estimation method for the partially nonlinear model based on the ESL function. Under certain conditions, we have shown that the proposed estimators can achieve the best convergence rates. Next, the asymptotic normality of the proposed estimators is established. In addition, we develop a new minorization-maximization algorithm to calculate the estimates for both non-parametric and parametric parts and present a procedure for deriving initial values. Finally, we provide a data-driven approach to select the tuning parameters. Numerical simulations and a real data analysis are used to illustrate that when there are outliers, the proposed ESL method is more robust and efficient for partially nonlinear models than the existing linear approximation method and the composite quantile regression method.

关键词： Exponential squared loss function minorization-maximization algorithm Partially nonlinear model Robustness

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Regression analysis for the proportional hazards model with parameter constraints under case-cohort design

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2018年 117卷 194-206页

作者： Deng, Lifeng Ding, Jieli Liu, Yanyan Wei, Chengdong Huazhong Univ Sci & Technol Sch Math & Stat Wuhan 430074 Hubei Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China Guangxi Teachers Educ Univ Sch Math & Stat Nanning 530023 Guangxi Peoples R China

To reduce the cost and improve the efficiency of cohort studies, case-cohort design is a widely used biased-sampling scheme for time-to-event data. In modeling process, case cohort studies can benefit further from taking parameters' prior information, such as the histological type and disease stage of the cancer in medical, the liquidity and market demand of the enterprise in finance. Regression analysis of the proportional hazards model with parameter constraints under case-cohort design is studied. Asymptotic properties are derived by applying the Lagrangian method based on Karush-Kuhn-Tucker conditions. The consistency and asymptotic normality of the constrained estimator are established. A modified minorization-maximization algorithm is developed for the calculation of the constrained estimator. Simulation studies are conducted to assess the finite-sample performance of the proposed method. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice. (C) 2017 Published by Elsevier B.V.

关键词： Case-cohort design Proportional hazards model Constrained estimation Karush-Kuhn-Tucker conditions minorization-maximization algorithm

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Laplace mixture of linear experts

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2016年 93卷 177-191页

作者： Nguyen, Hien D. McLachlan, Geoffrey J. Univ Queensland Sch Math & Phys St Lucia Qld 4072 Australia

Mixture of Linear Experts (MoLE) models provide a popular framework for modeling nonlinear regression data. The majority of applications of MoLE models utilizes a Gaussian distribution for regression error. Such assumptions are known to be sensitive to outliers. The use of a Laplace distributed error is investigated. This model is named the Laplace MoLE (LMoLE). Links are drawn between the Laplace error model and the least absolute deviations regression criterion, which is known to be robust among a wide class of criteria. Through application of the minorization maximization algorithm framework, an algorithm is derived that monotonically increases the likelihood in the estimation of the LMoLE model parameters. It is proven that the maximum likelihood estimator (MLE) for the parameter vector of the LMoLE is consistent. Through simulation studies, the robustness of the LMoLE model over the Gaussian MOLE model is demonstrated, and support for the consistency of the MLE is provided. An application of the LMoLE model to the analysis of a climate science data set is described. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Laplace distribution minorization-maximization algorithm Mixture of experts Robust regression

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Mixture of Time-Dependent Growth Models with an Application to Blue Swimmer Crab Length-Frequency Data

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BIOMETRICS 2016年第4期72卷 1255-1265页

作者： Lloyd-Jones, Luke R. Nguyen, Hien D. McLachlan, Geoffrey J. Sumpton, Wayne Wang, You-Gan Univ Queensland Queensland Brain Inst Ctr Neurogenet & Stat Genom Brisbane Qld 4072 Australia Univ Queensland Sch Math & Phys Brisbane Qld 4072 Australia Ecosci Precinct Queensland Dept Agr & Fisheries Joe Baker StDutton Pk Brisbane Qld 4102 Australia Queensland Univ Technol Sch Math Sci Brisbane Qld 4000 Australia

Understanding how aquatic species grow is fundamental in fisheries because stock assessment often relies on growth dependent statistical models. Length-frequency-based methods become important when more applicable data for growth model estimation are either not available or very expensive. In this article, we develop a new framework for growth estimation from length-frequency data using a generalized von Bertalanffy growth model (VBGM) framework that allows for time-dependent covariates to be incorporated. A finite mixture of normal distributions is used to model the length-frequency cohorts of each month with the means constrained to follow a VBGM. The variances of the finite mixture components are constrained to be a function of mean length, reducing the number of parameters and allowing for an estimate of the variance at any length. To optimize the likelihood, we use a minorization-maximization (MM) algorithm with a Nelder-Mead sub-step. This work was motivated by the decline in catches of the blue swimmer crab (BSC) (Portunus armatus) off the east coast of Queensland, Australia. We test the method with a simulation study and then apply it to the BSC fishery data.

关键词： Blue swimmer crab Growth model estimation Length-frequency data minorization-maximization algorithm Mixture modeling

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Laplace mixture autoregressive models

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STATISTICS & PROBABILITY LETTERS 2016年 110卷 18-24页

作者： Nguyen, Hien D. McLachlan, Geoffrey J. Ullmann, Jeremy F. P. Janke, Andrew L. Univ Queensland Sch Math & Phys St Lucia Qld Australia Univ Queensland Ctr Adv Imaging St Lucia Qld Australia

Autoregressive (AR) models are an important tool in the study of time series data. However, the standard AR model only allows for unimodal marginal and conditional densities, and cannot capture conditional heteroscedasticity. Previously, the Gaussian mixture AR (GMAR) model was considered to remedy these shortcomings by using a Gaussian mixture conditional model. We introduce the Laplace mixture (LMAR) model that utilizes a Laplace mixture conditional model, as an alternative to the GMAR model. We characterize the LMAR model and provide conditions for stationarity. An MM (minorization-maximization) algorithm is then proposed for maximum pseudolikelihood (MPL) estimation of an LMAR model. Conditions for asymptotic inference and a rule for model selection for the MPL estimator are considered. An example analysis of data arising from the calcium imaging of a zebrafish brain is performed. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Laplace distribution Mixture model Autoregressive model minorization-maximization algorithm Calcium imaging Zebrafish brain

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Maximum likelihood estimation of Gaussian mixture models without matrix operations

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2015年第4期9卷 371-394页

作者： Nguyen, Hien D. McLachlan, Geoffrey J. Univ Queensland Dept Math Sch Math & Phys Brisbane Qld 4072 Australia

The Gaussian mixture model (GMM) is a popular tool for multivariate analysis, in particular, cluster analysis. The expectation-maximization (EM) algorithm is generally used to perform maximum likelihood (ML) estimation for GMMs due to the M-step existing in closed form and its desirable numerical properties, such as monotonicity. However, the EM algorithm has been criticized as being slow to converge and thus computationally expensive in some situations. In this article, we introduce the linear regression characterization (LRC) of the GMM. We show that the parameters of an LRC of the GMM can be mapped back to the natural parameters, and that a minorization-maximization (MM) algorithm can be constructed, which retains the desirable numerical properties of the EM algorithm, without the use of matrix operations. We prove that the ML estimators of the LRC parameters are consistent and asymptotically normal, like their natural counterparts. Furthermore, we show that the LRC allows for simple handling of singularities in the ML estimation of GMMs. Using numerical simulations in the R programming environment, we then demonstrate that the MM algorithm can be faster than the EM algorithm in various large data situations, where sample sizes range in the tens to hundreds of thousands and for estimating models with up to 16 mixture components on multivariate data with up to 16 variables.

关键词： Gaussian mixture model minorization-maximization algorithm matrix operation-free Linear Regression

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