The problem of how to determine portfolio weights so that the variance of portfolio returns is minimized has been given considerable attention in the literature, and several methods have been proposed. Some properties of these estimators, however, remain unknown, and many of their relative strengths and weaknesses are therefore difficult to assess for users. This paper contributes to the field by comparing and contrasting the risk functions used to derive efficient portfolio weight estimators. It is argued that risk functions commonly used to derive and evaluate estimators may be inadequate and that alternative quality criteria should be considered instead. The theoretical discussions are supported by a Monte Carlo simulation and two empirical applications where particular focus is set on cases where the number of assets (p) is close to the number of observations (n).

This paper argues that traditional measures of innovation as a univariate phenomenon may not be dynamic enough to adequately describe the complex nature of innovation. Consequently, the purpose is to develop a multidimensional index of innovation that is able to reflect innovation enablers and outputs. The index may then be used (i) to assess and quantify temporal changes of innovation, (ii) to describe regional differences and similarities of innovation, and (iii) serve as exogenous variables to analyze the importance of innovation for other economic phenomena. Our index is defined in a four-dimensional space of orthogonal axes. An empirical case study is used for demonstration of the index, where 44 variables are collected for all municipalities in Sweden. The index spanning the four-dimensional innovation comprises size, accessibility, firm performance, and agglomeration. The proposed index offers a new way of defining and analyzing innovation and should have a wide range of important applications in a world where innovation is receiving a great deal of recognition.

This paper derives first-order sampling moments of individual Mahalanobis distances (MD) in cases when the dimension p of the variable is proportional to the sample size n. Asymptotic expected values when n, p → ∞ are derived under the assumption p/n → c, 0 ⩽ c < 1. It is shown that some types of standard estimators remain unbiased in this case, while others are asymptotically biased, a property that appears to be unnoticed in the literature. Second order moments are also supplied to give some additional insight to the matter.

The problem of how to maximize the return on a given portfolio of assets within the theory of Markowitz has been given considerable attention in the literature and improvements of standard methods continues to progress. Recent developments, often based on Stein estimators or other regularized estimators, usually focus on settings when the numbers of assets (say p) is close to the number of observations (n) since this is the scenario met in most real applications. Before any specific method is applied investors would want to know the basic properties and the relative performance of them. The performance of any estimation method, however, depends on which quality criterea of judgement is being used. Proposed methods may be optimal with respect to precision of the parameters involved in the portfolio procedure, on the proximity between estimated vs true global minimum variance portfolio (GMVP) weights, on the out-of-sample performance etc. Moreover, regularized estimators are often associated with very complicated or even unknown sampling distributions, which in turn complicate statistical inference drastically. The extent to which a method allows for statistical inference therefore also becomes an important matter when judging the properties of a data driven GMVP estimator. In this paper we give an in-depth discussion of risk critereas and their impact on GMVP optimization. A Monte Carlo simulation investigating the properties of some common estimators, including a new one proposed by the authors, with respect to several quality critereas is included to compare and contrast recent proposals. An empirical study is also included using Stockholm stock exchange data. 

Course syllabuses, outlines or similar academic documents specifying the content of a course will often be a helpful tool both for teachers and students to grasp the content and purpose of a course. In many cases, however, the compilation of such documents is a painstaking process for the educator designing it, and is a task that many teachers will shun. In this paper we propose a fairly simple pedagogical model for designing specific learning outcomes that the students are expected to attain after completion of a course.

In this paper we generalize four tests of multivariate linear hypothesis to panel data unit root testing. The test statistics are invariant to certain linear transformations of data and therefore simulated critical values may conveniently be used. It is demonstrated that all four tests remains well behaved in cases of where there are heterogeneous alternatives and cross-correlations between marginal variables. A Monte Carlo simulation is included to compare and contrast the tests with two well-established ones.

Ridge estimators are usually examined through Monte Carlo simulations since their properties are difficult to obtain analytically. In this paper we argue that a simulation design commonly used in the literature will give biased results of Monte Carlo simulations in favour of ridge regression over ordinary least square (OLS) estimators. Specifically, it is argued that the properties of ridge estimators that are functions of pdistinct regressor eigenvalues should not be evaluated through Monte Carlo designs using only two distinct eigenvalues.

Our research examines the role of airports in regional development. Specifically, we examine two things: (1) the factors associated with whether or not a metro will have an airport, and (2) the effect of airport activities on regional economic development. Based on multiple regression analysis for U.S. metros, our research generates four key findings. First, airports are more likely to be located in larger metros with higher shares of cultural workers and warmer winters. Second, airports add significantly to regional development measured as economic output per capita. Third, the effect of airports on regional development occurs through two channels—their capacity to move both people and cargo, with the former being somewhat more important. Fourth, the impact of airports on regional development varies with their size and scale.