Information Matrices for Non Full Rank Subsystems

Consider the standard linear model Y=X θ + ε. If the parameter of interest is a full rank subsystem K′θ of mean parameters, the associated information matrix can be defined via an extremal representation. For rank deficient subsystems, Pukelsheim (1993) introduced the notion of generalized information matrices that inherit many properties of the information matrices. However, this notion is not a direct extension of the full rank case in the sense that the definition of the generalized information matrix applied to full rank subsystems does not lead to the usual information matrix. In this paper, we propose a definition of the information matrix via an extremal representation that encompasses the full rank and the non-full rank cases. We also study its properties and show its links with the generalized information matrices.     

The structure of US food demand

An exactly aggregable system of Gorman Engel curves for US food consumption is developed and implemented. Box-Cox transformations on prices and income nest functional form. The model nests rank up to rank three. The model is estimated by nonlinear three-stage least squares with annual time series data on 21 foods, 17 nutrients, age and race demographics, and the distribution of income for 1919–1941 and 1947–2000. Results are consistent with full rank three. Point estimates for the Box-Cox parameters on income and prices are 0.86 and 1.09, respectively, strongly rejecting zero and one in both cases. No statistical evidence of serial correlation, specification errors, or parameter instability is found.     

Work–life policies and female faculty representation in US doctoral‐granting economics departments

This article examines the relationships between work–life policies and female faculty representation and promotion at US doctoral‐granting economics departments. The data were collected in 2012 on tenure‐track and tenured full‐time faculty from 125 departments and updated in 2018 to include promotion status. Variables include individuals and their educational backgrounds, professional experience and publications. Only publications and experience are statistically significant for predicting academic rank for the female subsample, and the impact of publications is much larger for women compared with men. Work–life policies differ in explaining the representation of women across academic ranks. Dual‐career policies have a positive effect on female representation at the assistant and associate levels but do not have a statistically significant impact at the full professor level. National Science Foundation ADVANCE grantee universities have increased female representation across all ranks, but the effect is the smallest at the full professor level. Work–life policies are insignificant in predicting promotion.     

Weak identification robust tests in an instrumental quantile model

We develop a testing procedure that is robust to identification quality in an instrumental quantile model. In order to reduce the computational burden, a multi-step approach is taken, and a two-step Anderson–Rubin (AR) statistic is considered. We then propose an orthogonal decomposition of the AR statistic, where the null distribution of each component does not depend on the assumption of a full rank of the Jacobian. Power experiments are conducted, and inferences on returns to schooling using the Angrist and Krueger data are considered as an empirical example.     

Improved likelihood ratio tests for cointegration rank in the VAR model

We suggest improved tests for cointegration rank in the vector autoregressive (VAR) model and develop asymptotic distribution theory and local power results. The tests are (quasi-)likelihood ratio tests based on a Gaussian likelihood, but as usual the asymptotic results do not require normally distributed innovations. Our tests differ from existing tests in two respects. First, instead of basing our tests on the conditional (with respect to the initial observations) likelihood, we follow the recent unit root literature and base our tests on the full likelihood as in, e.g., Elliott et al. (1996). Second, our tests incorporate a “sign” restriction which generalizes the one-sided unit root test. We show that the asymptotic local power of the proposed tests dominates that of existing cointegration rank tests.     

Computations for constrained linear models

The article presents an algorithm for linear regression computations subject to linear parametric equality constraints, linear parametric inequality constraints, or a mixture of the two. No rank conditions are imposed on the regression specification or the constraint specification. The algorithm requires a full Moore-Penrose g-inverse which entails extra computational effort relative to other orthonormalization type algorithms. In exchange, auxiliary statistical information is generated: feasibility of a set of constraints may be checked, estimability of a linear parametric function may be checked, and bias and variance may be decomposed by source.     

DS-optimal designs in one way ANOVA

Characterization and construction of optimal designs using the familiar optimality criteria, for example A-, D- and E-optimality are well studied in the literature. However the study of the Distance Optimality (DS-) criterion introduced by Sinha (1970) has very recently drawn attention of researchers. In the present article, we consider the singularly estimable full rank problem of estimating the full set of elementary treatment contrasts using the DS optimality criterion in the set up of a one way ANOVA model. Using a limit argument it turns out that a CRD in which difference between any two allocation numbers is at the most unity is uniquely DS-optimal. Acknowledgement. We are thankful to Prof. B. K. Sinha for suggesting the problem to us and many helpful discussions with him. We are also thankful to the referees for drawing our attention to the reference of Bischoff (1995) and many helpful comments.     

广西星级酒店数字平台建设研究

本文采用全面样本普及实体调研法,对广西456家星级酒店进行了调研分析。调查结果显示:数字平台建设方面,五星级的较好、四星级的一般、三星级的较差、二星级的非常差、一星级的基本空白;各类酒店三维虚拟数字仿真体验建设率均为0;百度搜索网页量与整体搜索指数在我国主要旅游城市酒店中均排末尾。因此,要提高广西星级酒店数字平台建设,应引进先进的数字酒店平台建设理念,提高国家"旅游饭店星级的划分及评定标准"中对数字网站建设的要求,充分利用桂林旅游实验区这一国家政策,进一步完善广西旅游中心呼叫平台中的酒店服务模块,加强旅游管理服务网站的后台服务建设。     

Are generalized call-spreads efficient?

In order to explain coexistence of a deductible for low values of the loss and an upper limit for high values of the loss in insurance contracts, we consider the exchange of risk between two rank dependent expected utility maximizers. It is shown that if the insurer (insured) takes more into account the lowest outcomes – hence maximal losses – than the insured (insurer), then the optimal contract has an upper limit (includes a deductible for high values of the loss). If furthermore, the insured (insurer) neglects the highest outcomes while the insurer (insured) does not, the optimal contract includes a deductible (full insurance) for low values of the loss.     

Fair compensation with different social concerns for forgiveness

Forgiveness is an ethical ideal that advocates that a fresh start should be conferred upon those individuals who have changed their preferences and regret their previous decisions. Despite the ethical debate that such an idea generates, only a few papers have dealt with this issue in depth, and they have just focused on the case of full compensation for regret. Therefore, based on efficiency, robustness, and ethical requirements, we characterise a social ordering function that formally connects the ideal of forgiveness to the problem of compensating individuals when they differ in both their preferences and their initial endowment. This social ordering allows us to rank allocations that may or may not be associated with different concerns for forgiveness. Specifically, it proposes reducing inequality between reference-comparable budget sets.     

A rational rank four demand system

Past parametric tests of demand system rank employed polynomial Engel curve systems. However, by Gorman's ( 1981 ) theorem, the maximum possible rank of a utility‐derived polynomial demand system is three. The present paper proposes a class of demand systems that are utility derived, are close to polynomial, and have rank four. These systems nest rational polynomial demands, and so can be used to test ranks up to four. These systems are suitable for applications where high rank is likely, such as demand systems involving a large number of goods. A test of rank using this new class of systems is applied to UK consumer demand data. Copyright © 2002 John Wiley & Sons, Ltd.     

CAUTIONARY NOTES ON THE RANK‐SIZE DISTRIBUTION

In the analysis of center populations at both the national and regional levels considerable use has been made of the rank‐size distribution. Within the extensive literature on this distribution, however, there are a number areas that are unclear, neglected, or misleading. Consideration is initially given to the form of the rank‐size distribution and to the manner in which it is related to other distributions, notably the Pareto and the lognormal. Attention is also focused on the application of the rank‐size distribution to data on center size and on the difficulties that arise in this connection, including the problem of establishing rank‐size regularity. The discussion concludes by taking issue with the contention that the rank‐size distribution is of relevance in the design and formulation of urban policy.     

Forecasting large datasets with Bayesian reduced rank multivariate models

The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance for US time series with the most promising existing alternatives, namely, factor models, large‐scale Bayesian VARs, and multivariate boosting. Specifically, we focus on classical reduced rank regression, a two‐step procedure that applies, in turn, shrinkage and reduced rank restrictions, and the reduced rank Bayesian VAR of Geweke ( 1996 ). We find that using shrinkage and rank reduction in combination rather than separately improves substantially the accuracy of forecasts, both when the whole set of variables is to be forecast and for key variables such as industrial production growth, inflation, and the federal funds rate. The robustness of this finding is confirmed by a Monte Carlo experiment based on bootstrapped data. We also provide a consistency result for the reduced rank regression valid when the dimension of the system tends to infinity, which opens the way to using large‐scale reduced rank models for empirical analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Some Decompositions of OLSEs and BLUEs Under a Partitioned Linear Model

We consider in this paper a partitioned linear model { y , X ₁ β ₁ + X ₂ β ₂ , σ ² σ } and two corresponding small models { y , X ₁ β ₁ , σ ² σ } and { y , X ₂ β ₂ , σ ² σ } . We derive necessary and sufficient conditions for (i) the ordinary least squares estimator under the full model to be the sum of the ordinary least squares estimators under the two small models; (ii) the best linear unbiased estimator under the full model to be the sum of the best linear unbiased estimators under the two small models; (iii) the best linear unbiased estimator under the full model to be the sum of the ordinary least squares estimators under the two small models. The proofs of the main results in this paper also demonstrate how to use the matrix rank method for characterizing various equalities of estimators under general linear models.     

THE ASYMPTOTIC BEHAVIOR OF SIMPLE LINEAR RANK STATISTICS

The concept of a simple linear rank statistic is essential in nonparametric theory. These statistics may be used for testing the null-hypothesis that all observations are independent and identically distributed against classes of alternatives indicated by the choice of regression constants and scores. Special cases are the two-sample Linear rank statistics and Spearman's rank correlation coefficient rho under the null-hypothesis of independence.
In this paper we shall give a survey of the asympotic distribution theory of simple linear rank statistics.     

Generalized reduced rank tests using the singular value decomposition

We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson [Annals of Mathematical Statistics (1951), 22, 327–351] sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald [Journal of the American Statistical Association (1996), 91, 1301–1309] and Gill and Lewbel [Journal of the American Statistical Association (1992), 87, 766–776] a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and Smith [Econometric Theory (2000), 16, 151–175] usage of numerical optimization for the objective function statistic of Cragg and Donald [Journal of Econometrics (1997), 76, 223–250] and ignoring the non-negativity restriction on the singular values in Ratsimalahelo [2002, Rank test based on matrix perturbation theory. Unpublished working paper, U.F.R. Science Economique, University de Franche-Comté]. In the non-stationary cointegration case, the limiting distribution of the new rank statistic is identical to that of the Johansen trace statistic.     

Local rank tests in a multivariate nonparametric relationship

Consider a multivariate nonparametric model where the unknown vector of functions depends on two sets of explanatory variables. For a fixed level of one set of explanatory variables, we provide consistent statistical tests, called local rank tests, to determine whether the multivariate relationship can be explained by a smaller number of functions. We also provide estimators for the smallest number of functions, called local rank, explaining the relationship. The local rank tests and the estimators of local rank are defined in terms of the eigenvalues of a kernel-based estimator of some matrix. The asymptotics of the eigenvalues is established by using the so-called Fujikoshi expansion along with some techniques of the theory of U-statistics. We present a simulation study which examines the small sample properties of local rank tests. We also apply the local rank tests and the local rank estimators to a demand system given by a newly constructed data set. This work can be viewed as a “local” extension of the tests for a number of factors in a nonparametric relationship introduced by Stephen Donald.     

Supplier selection with rank reversal in public tenders

For supplier selection in the public sector, the Weighted Sum Model is often used in combination with relative scoring methods that allow rank reversal. With rank reversal we refer to a changed order in the ranking of bids leading to a new winner, after removing or adding a non-optimal bid that does not win the original tender. In practice, an important reason indicated by practitioners for using methods that allow rank reversal is that it would rarely occur in practice. Based on an analysis of 303 Dutch public tenders, this research shows this is not true. In about 1 out of 5 the tenders, rank reversal occurs after adding non-optimal fictional bids to tenders that do not have quality thresholds. After removing bids, the rate is about 1 out of 40 if a curved relative scoring method is used. In addition, the research shows that rank reversal rates increase when (i) there is no quality threshold, (ii) the number of bids increases, (iii) bid price variance increases, and (iv) price weights are not very low or high. We argue that relative scoring methods that allow rank reversal should not be used in public procurement, or otherwise only in exceptional cases, as it conflicts with public procurement principles and leads to reduced overall bid value.     

交叉效率评价方法中一种改进的新单元导入保序性方法

针对交叉效率方法在评估排序时所存在的局限性,即在导入新的决策单元时,可能会使原先的决策单元(DMU)排序发生变化,本文通过建立二次权重集结交叉效率保序性模型对各DMU的权重进行二次分配,进而对交叉效率矩阵进行集结以得到最终的均衡交叉效率值。利用该均衡交叉效率值进行排序时可以消除导入新DMU时所产生的逆序现象。算例说明了该方法有效,计算结果较纳什讨价还价交叉效率保序性模型有所改进,综合计算量更小,各DMU权重更加合理,与一般交叉效率模型的效率值差异更小。     

Locally Most Powerful and Other Rank Tests for Independence – with a Contaminated Weighted Alternative

Several authors in the literature have attempted the quantification of the concept of stochastic dependence for bivariate distribution. Two weighted rank tests for testing independence against a weighted contamination alternative is proposed and their distributional properties are studied. We also derived a locally most powerful rank test for the alternative setting. The rank tests proposed are shown to be asymptotic locally most powerful for specific distributions.