This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual com...This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone.We show that the ERM model has bounded level sets under the stochastic weak R0-property.We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications.Then,we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis.Furthermore,we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks.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
This paper sheds light on all open problem put forward by Cochran[1]. The comparison between two commonly used variance estimators v1(^R) and v2(^R) of the ratio estimator R for population ratio R from small sample se...This paper sheds light on all open problem put forward by Cochran[1]. The comparison between two commonly used variance estimators v1(^R) and v2(^R) of the ratio estimator R for population ratio R from small sample selected by simple random sampling is made following the idea of the estimated loss approach (See [2]). Considering the superpopulation model under which the ratio estimator ^-YR for population mean -Y is the best linear unbiased one, the necessary and sufficient conditions for v1(^R) v2(^R) and v2(^R) v1(^R) are obtained with ignored the sampling fraction f. For a substantial f, several rigorous sufficient conditions for v2(^R) v1(^R) are derived.展开更多
Built upon an iterative process of resampling without replacement and out-of-sample prediction, the delete-d cross validation statistic CV(d) provides a robust estimate of forecast error variance. To compute CV(d), a ...Built upon an iterative process of resampling without replacement and out-of-sample prediction, the delete-d cross validation statistic CV(d) provides a robust estimate of forecast error variance. To compute CV(d), a dataset consisting of n observations of predictor and response values is systematically and repeatedly partitioned (split) into subsets of size n – d (used for model training) and d (used for model testing). Two aspects of CV(d) are explored in this paper. First, estimates for the unknown expected value E[CV(d)] are simulated in an OLS linear regression setting. Results suggest general formulas for E[CV(d)] dependent on σ2 (“true” model error variance), n – d (training set size), and p (number of predictors in the model). The conjectured E[CV(d)] formulas are connected back to theory and generalized. The formulas break down at the two largest allowable d values (d = n – p – 1 and d = n – p, the 1 and 0 degrees of freedom cases), and numerical instabilities are observed at these points. An explanation for this distinct behavior remains an open question. For the second analysis, simulation is used to demonstrate how the previously established asymptotic conditions {d/n → 1 and n – d → ∞ as n → ∞} required for optimal linear model selection using CV(d) for model ranking are manifested in the smallest sample setting, using either independent or correlated candidate predictors.展开更多
基金This work was supported in part by the National Natural Science Foundation of China(Nos.71831008,11671250,11431004 and 11601458)Humanity and Social Science Foundation of Ministry of Education of China(No.15YJA630034)+2 种基金Shandong Province Natural Science Fund(No.ZR2014AM012)Higher Educational Science and Technology Program of Shandong Province(No.J13LI09)Scientific Research of Young Scholar of Qufu Normal University(No.XKJ201315).
文摘This paper considers the so-called expected residual minimization(ERM)formulation for stochastic second-order cone complementarity problems,which is based on a new complementarity function called termwise residual complementarity function associated with second-order cone.We show that the ERM model has bounded level sets under the stochastic weak R0-property.We further derive some error bound results under either the strong monotonicity or some kind of constraint qualifications.Then,we apply the Monte Carlo approximation techniques to solve the ERM model and establish a comprehensive convergence analysis.Furthermore,we report some numerical results on a stochastic second-order cone model for optimal power flow in radial networks.
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the National Natural Science Foundation of China (No.10071091)
文摘This paper sheds light on all open problem put forward by Cochran[1]. The comparison between two commonly used variance estimators v1(^R) and v2(^R) of the ratio estimator R for population ratio R from small sample selected by simple random sampling is made following the idea of the estimated loss approach (See [2]). Considering the superpopulation model under which the ratio estimator ^-YR for population mean -Y is the best linear unbiased one, the necessary and sufficient conditions for v1(^R) v2(^R) and v2(^R) v1(^R) are obtained with ignored the sampling fraction f. For a substantial f, several rigorous sufficient conditions for v2(^R) v1(^R) are derived.
文摘Built upon an iterative process of resampling without replacement and out-of-sample prediction, the delete-d cross validation statistic CV(d) provides a robust estimate of forecast error variance. To compute CV(d), a dataset consisting of n observations of predictor and response values is systematically and repeatedly partitioned (split) into subsets of size n – d (used for model training) and d (used for model testing). Two aspects of CV(d) are explored in this paper. First, estimates for the unknown expected value E[CV(d)] are simulated in an OLS linear regression setting. Results suggest general formulas for E[CV(d)] dependent on σ2 (“true” model error variance), n – d (training set size), and p (number of predictors in the model). The conjectured E[CV(d)] formulas are connected back to theory and generalized. The formulas break down at the two largest allowable d values (d = n – p – 1 and d = n – p, the 1 and 0 degrees of freedom cases), and numerical instabilities are observed at these points. An explanation for this distinct behavior remains an open question. For the second analysis, simulation is used to demonstrate how the previously established asymptotic conditions {d/n → 1 and n – d → ∞ as n → ∞} required for optimal linear model selection using CV(d) for model ranking are manifested in the smallest sample setting, using either independent or correlated candidate predictors.
