Tractable Consideration Set Structures for Assortment Optimization and Network Revenue Management

Discrete‐choice models are widely used to model consumer purchase behavior in assortment optimization and revenue management. In many applications, each customer segment is associated with a consideration set that represents the set of products that customers in this segment consider for purchase. The firm has to make a decision on what assortment to offer at each point in time without the ability to identify the customer's segment. A linear program called the Choice‐based Deterministic Linear Program (CDLP) has been proposed to determine these offer sets. Unfortunately, its size grows exponentially in the number of products and it is NP‐hard to solve when the consideration sets of the segments overlap. The Segment‐based Deterministic Concave Program with some additional consistency equalities (SDCP+) is an approximation of CDLP that provides an upper bound on CDLP's optimal objective value. SDCP+ can be solved in a fraction of the time required to solve CDLP and often achieves the same optimal objective value. This raises the question under what conditions can one guarantee equivalence of CDLP and SDCP+. In this study, we obtain a structural result to this end, namely that if the segment consideration sets overlap with a certain tree structure or if they are fully nested, CDLP can be equivalently replaced with SDCP+. We give a number of examples from the literature where this tree structure arises naturally in modeling customer behavior.     

环境管制、知识产权保护与区域创新能力——基于我国省际面板数据的实证研究

文章基于政府主导视角,利用2006—2015年我国30个省级面板数据,构建多元回归模型,分析变量之间的关系.其结果显示,环境管制、知识产权保护与区域创新能力之间呈非线性关系,环境管制与知识产权保护同时实施对区域创新能力有显著的促进作用,且具有区域异质性.从企业生存角度出发,提出门槛效应假说,采用Hansen面板门槛回归模型进行检验.结果表明,在环境管制与知识产权保护共同发挥作用时,环境管制必须控制在合理的范围内.最后采用门槛效应回归方法找到了环境管制与知识产权保护对区域创新能力影响的门槛值,并提出相应的政策建议.     

A new test for multivariate normality by combining extreme and nonextreme BHEP tests

In this article, we propose a new multiple test procedure for assessing multivariate normality, which combines BHEP (Baringhaus–Henze–Epps–Pulley) tests by considering extreme and nonextreme choices of the tuning parameter in the definition of the BHEP test statistic. Monte Carlo power comparisons indicate that the new test presents a reasonable power against a wide range of alternative distributions, showing itself to be competitive against the most recommended procedures for testing a multivariate hypothesis of normality. We further illustrate the use of the new test for the Fisher Iris dataset.     

An algorithm for maximum likelihood estimation in incomplete block variance component models

In the recovery of interblock information to improve the treatment differences estimates in incomplete block designs, the parameter p is usually unknown. Many authors have worked on the problem of estimating it and of studying its properties together with the properties of the treatment differences estimates. In this paper a numerically efficient algorithm is developed which yields the maximum likelihood estimates (MLE) of all the parameters in the mixed incomplete block design model (treatment effects, ρ and variance)     

An Extended Single‐index Model with Missing Response at Random

An extended single‐index model is considered when responses are missing at random. A three‐step estimation procedure is developed to define an estimator for the single‐index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An algorithm for computing this estimator is proposed. This algorithm only involves one‐dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation studies are conducted to investigate the finite sample performances of the proposed estimators.     

Estimation of nonseparable models with censored dependent variables and endogenous regressors

In this article we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalize the identification argument put forward in Altonji, Ichimura, and Otsu (2012 Altonji, J. G., Ichimura, H., Otsu, T. (2012). Estimating derivatives in nonseparable models with limited dependent variables. Econometrica 80:1701–1719.[Crossref], [Web of Science ®] , [Google Scholar]), construct a nonparametric estimator, characterize its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. Identification is constructive and is achieved through a control function approach. We show that the estimator is consistent and asymptotically normally distributed. The Monte Carlo results are encouraging.     

A goodness of fit test for the multilevel proportional odds model

It is essential to test the goodness of fit of the model before making inferences based on it. Multilevel modeling of ordinal categorical responses is not as developed as for continuous responses. Assessing model adequacy in terms of the goodness of fit with ordinal categorical responses is still being developed and no satisfactory tests are available so far. As a consequence of that, this study concentrates on developing such a goodness of fit test for Multilevel Proportional Odds models and to study the properties of the test.     

Computation of an efficient and robust estimator in a semiparametric mixture model

In this article, we propose an efficient and robust estimation for the semiparametric mixture model that is a mixture of unknown location-shifted symmetric distributions. Our estimation is derived by minimizing the profile Hellinger distance (MPHD) between the model and a nonparametric density estimate. We propose a simple and efficient algorithm to find the proposed MPHD estimation. Monte Carlo simulation study is conducted to examine the finite sample performance of the proposed procedure and to compare it with other existing methods. Based on our empirical studies, the newly proposed procedure works very competitively compared to the existing methods for normal component cases and much better for non-normal component cases. More importantly, the proposed procedure is robust when the data are contaminated with outlying observations. A real data application is also provided to illustrate the proposed estimation procedure.     

Correlated random effects regression analysis for a log-normally distributed variable

In regression analysis, it is assumed that the response (or dependent variable) distribution is Normal, and errors are homoscedastic and uncorrelated. However, in practice, these assumptions are rarely satisfied by a real data set. To stabilize the heteroscedastic response variance, generally, log-transformation is suggested. Consequently, the response variable distribution approaches nearer to the Normal distribution. As a result, the model fit of the data is improved. Practically, a proper (seems to be suitable) transformation may not always stabilize the variance, and the response distribution may not reduce to Normal distribution. The present article assumes that the response distribution is log-normal with compound autocorrelated errors. Under these situations, estimation and testing of hypotheses regarding regression parameters have been derived. From a set of reduced data, we have derived the best linear unbiased estimators of all the regression coefficients, except the intercept which is often unimportant in practice. Unknown correlation parameters have been estimated. In this connection, we have derived a test rule for testing any set of linear hypotheses of the unknown regression coefficients. In addition, we have developed the confidence ellipsoids of a set of estimable functions of regression coefficients. For the fitted regression equation, an index of fit has been proposed. A simulated study illustrates the results derived in this report.     

Hazard rate ordering of the second-order statistics from multiple-outlier PHR samples

In this paper, we compare the hazard rate functions of the second-order statistics arising from two sets of independent multiple-outlier proportional hazard rates (PHR) samples. It is proved that the submajorization order between the sample size vectors together with the supermajorization order between the hazard rate vectors imply the hazard rate ordering between the corresponding second-order statistics from multiple-outlier PHR random variables. The results established here provide theoretical guidance both for the winner's price for the bid in the second-price reverse auction in auction theory and fail-safe system design in reliability. Some numerical examples are also provided for illustration.