Notes on the Markowitz portfolio selection method

A proof of the validity of Markowitz's critical line method is given for a more general situation than discussed by Markowitz. Next for the Markowitz case with a positive definite covariance matrix explicit expressions are derived for all efficient portfolios. Using these expressions it can be shown that the critical line in the (μ,α²) plane is a representation of a function which is not necessarily differentiable everywhere.     

Challenging Small‐Scale Farming: A Non‐Parametric Analysis of the (Inverse) Relationship Between Farm Productivity and Farm Size in Burundi

We use a non‐parametric approach to investigate the (inverse) relationship between farm productivity and farm size. A kernel regression is used on data of mixed cropping systems to study the determinants of production including different factors that have been identified in literature as missing variables in the testing of the inverse relationship such as soil quality, location and household heterogeneity. Household data on farm activities and crop production were gathered from 640 households in 2007 in two Northern provinces of Burundi. Our results do not reject the findings of an inverse relationship between farm size and productivity. However, we find that size returns vary substantially with farm size, that is, between 0.2 for the smallest farms and 0.8 for the largest farms. Other factors that significantly affect production include soil quality. Finally, we find a significant positive association between food security and farm size.     

Semiparametric regression models and sensitivity analysis of longitudinal data with nonrandom dropouts

We propose a family of regression models to adjust for nonrandom dropouts in the analysis of longitudinal outcomes with fully observed covariates. The approach conceptually focuses on generalized linear models with random effects. A novel formulation of a shared random effects model is presented and shown to provide a dropout selection parameter with a meaningful interpretation. The proposed semiparametric and parametric models are made part of a sensitivity analysis to delineate the range of inferences consistent with observed data. Concerns about model identifiability are addressed by fixing some model parameters to construct functional estimators that are used as the basis of a global sensitivity test for parameter contrasts. Our simulation studies demonstrate a large reduction of bias for the semiparametric model relatively to the parametric model at times where the dropout rate is high or the dropout model is misspecified. The methodology's practical utility is illustrated in a data analysis.     

Efficient frontier estimation: a maximum entropy approach

An alternative efficiency estimation approach is developed utilizing generalized maximum entropy (GME). GME combines the strengths of both SFA and DEA, allowing for the estimation of a frontier that is stochastic, without making an ad hoc assumption about the distribution of the efficiency component. GME results approach SFA results as the one-sided inefficiency bounds used by GME shrink. Results similar to DEA are achieved as the bounds increase. The GME results are distributed like DEA, but yield virtually the same rankings as SFA. The results suggest that GME may provide a link between various estimators of efficiency.

广西龙胜壮族民居的研究及保护建议——以龙脊古壮寨为例

广西龙胜县龙脊村是壮族人民最具有代表性的聚居地之一,其壮族传统民居在几百年的历史发展中形成了自身独特建筑风格。但是,现代社会的发展使该地民居正面临着民族特色不断流失的威胁。文章通过实地测绘和采访,对其中具有代表性的民居案例进行解析和比较,总结出该地民居的建筑形式与功能、建造技术与习俗等特征;通过对比新旧时期建筑的变化而针对现有民居所存在的矛盾提出保护和发展建议。同时,提出了计算机参数化的研究方法,以期对龙脊村壮族民居的发展提供参考。     

Economic Efficiency and Frontier Techniques

Abstract. Most of the literature related to the measurement of economic efficiency has based its analysis either on parametric or on non‐parametric frontier methods. The choice of estimation method has been an issue of debate, with some researchers preferring the parametric and others the non‐parametric approach. The aim of this paper is to provide a critical and detailed review of both core frontier methods. In our opinion, no approach is strictly preferable to any other. Moreover, a careful consideration of their main advantages and disadvantages, of the data set utilized, and of the intrinsic characteristics of the framework under analysis will help us in the correct implementation of these techniques. Recent developments in frontier techniques and economic efficiency measurement such as Bayesian techniques, bootstrapping, duality theory and the analysis of sampling asymptotic properties are also considered in this paper.     

Statistical Approaches for Non‐parametric Frontier Models: A Guided Tour

A rich theory of production and analysis of productive efficiency has developed since the pioneering work by Tjalling C. Koopmans and Gerard Debreu. Michael J. Farrell published the first empirical study, and it appeared in a statistical journal (Journal of the Royal Statistical Society), even though the article provided no statistical theory. The literature in econometrics, management sciences, operations research and mathematical statistics has since been enriched by hundreds of papers trying to develop or implement new tools for analysing productivity and efficiency of firms. Both parametric and non‐parametric approaches have been proposed. The mathematical challenge is to derive estimators of production, cost, revenue or profit frontiers, which represent, in the case of production frontiers, the optimal loci of combinations of inputs (like labour, energy and capital) and outputs (the products or services produced by the firms). Optimality is defined in terms of various economic considerations. Then the efficiency of a particular unit is measured by its distance to the estimated frontier. The statistical problem can be viewed as the problem of estimating the support of a multivariate random variable, subject to some shape constraints, in multiple dimensions. These techniques are applied in thousands of papers in the economic and business literature. This ‘guided tour’ reviews the development of various non‐parametric approaches since the early work of Farrell. Remaining challenges and open issues in this challenging arena are also described. © 2014 The Authors. International Statistical Review © 2014 International Statistical Institute     

半参数模型在重力异常点插值格网化中的应用

半参数模型是参数模型和非参数模型的混合模型,其应用前景十分广泛。本文介绍了半参数模型中的补偿最小二乘法,并用实测数据验证了该方法的有效性,通过算例分析,该方法应用于重力异常插值格网化是可行的。     

基于Rhino+Grasshopper的风景环境复杂地形道路选线设计算法模型研究

在风景园林规划设计中,当前使用ArcGIS作为道路自动选线工具的研究较多,但该方法在小区域内无法取得较为精准的选线结果。基于Rhino+Grasshopper平台,对Dijkstra最短路径算法、遗传算法及道路选线影响因素进行研究,构建了参数化风景环境道路自动选线模型。使用参数化设计生成的路径符合风景区低影响开发和低成本建设的原则,且路径曲线最大限度满足风景区道路极限平曲线现行规范值。构建的参数化模型可以解决所有同类型问题且便于调整和优化,为风景环境道路选线提供了新的解决方法。