The paper examines an economic growth problem how social planners reasonably open up and retain natural resources. The objective is to maximize the total expected discounted utility of comsumption. Social planners' o...The paper examines an economic growth problem how social planners reasonably open up and retain natural resources. The objective is to maximize the total expected discounted utility of comsumption. Social planners' optimal decision and optimal expected rates at the steady state are derived. At last, how productivity and productivity shock affect on the expected growth rate, consumption-resources ratio and the fraction of exploited resources, are analyzed.展开更多
We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classi...We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.展开更多
Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the s...Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.展开更多
A complex product subjects to multiple failure modes such as minor and catastrophic failure with some probability.This paper investigates the effects of minor failure and catastrophic failure on the periodic replaceme...A complex product subjects to multiple failure modes such as minor and catastrophic failure with some probability.This paper investigates the effects of minor failure and catastrophic failure on the periodic replacement policy for a complex product supported by a warranty period.Cost models are developed and the expected optimal replacement policies are developed analytically such that long run expected life-cycle cost rate is minimized.Structural properties of the optimal replacement policies are derived for a product which fails with multiple failure modes and the failure rate is an increasing function of time.Finally,a numerical experiment is performed to show the important features of our study.展开更多
This study considers an age replacement policy(ARP) for a repairable product with an increasing failure rate with and without a product warranty. As for the warranty policy to consider in association with such an age ...This study considers an age replacement policy(ARP) for a repairable product with an increasing failure rate with and without a product warranty. As for the warranty policy to consider in association with such an age replacement policy, we adapt a renewable minimal repair-replacement warrant(MRRW) policy with 2D factors of failure time of the product and its corresponding repair time. The expected cost rate during the life cycle of the product is utilized as a criterion to find the optimal policies for both with and without the product warranty. We determine the optimal replacement age that minimizes the objective function which evaluates the expected cost rate during the product cycle and investigate the impact of several factors on the optimal replacement age. The main objective of this study lies on the generalization of the classical age replacement policy to the situation where a renewable warranty depending on 2D factors is in effect. We present some interesting observations regarding the effect of relevant factors based on numerical analysis.展开更多
基金Supported by the National Natural Science Foun-dation of China(10401027)
文摘The paper examines an economic growth problem how social planners reasonably open up and retain natural resources. The objective is to maximize the total expected discounted utility of comsumption. Social planners' optimal decision and optimal expected rates at the steady state are derived. At last, how productivity and productivity shock affect on the expected growth rate, consumption-resources ratio and the fraction of exploited resources, are analyzed.
文摘We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.
基金Supported by National Natural Science Foundation of China (61662036)。
文摘Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.
基金This work was supported by the National Natural Science Foundation of China under grant numbers 71531010 and 71831006.
文摘A complex product subjects to multiple failure modes such as minor and catastrophic failure with some probability.This paper investigates the effects of minor failure and catastrophic failure on the periodic replacement policy for a complex product supported by a warranty period.Cost models are developed and the expected optimal replacement policies are developed analytically such that long run expected life-cycle cost rate is minimized.Structural properties of the optimal replacement policies are derived for a product which fails with multiple failure modes and the failure rate is an increasing function of time.Finally,a numerical experiment is performed to show the important features of our study.
基金the National Research Foundation of Korea Grant(NRF-2014S1A5A8012594)the 2014Hongik University Research Fund,the Basic Science Research Program Through the National Research Foundation of Korea(Nos.2013-2058436 and 2011-0022397)the Basic Science Research Program Through the National Research Foundation of Korea
文摘This study considers an age replacement policy(ARP) for a repairable product with an increasing failure rate with and without a product warranty. As for the warranty policy to consider in association with such an age replacement policy, we adapt a renewable minimal repair-replacement warrant(MRRW) policy with 2D factors of failure time of the product and its corresponding repair time. The expected cost rate during the life cycle of the product is utilized as a criterion to find the optimal policies for both with and without the product warranty. We determine the optimal replacement age that minimizes the objective function which evaluates the expected cost rate during the product cycle and investigate the impact of several factors on the optimal replacement age. The main objective of this study lies on the generalization of the classical age replacement policy to the situation where a renewable warranty depending on 2D factors is in effect. We present some interesting observations regarding the effect of relevant factors based on numerical analysis.