A further note on a theorem on the difference of the generalized inverses of two nonnegative definite matrices

Andrews and Phillips (1986) gave a simplified proof for the result that established the nonnegative definiteness of the difference of the Moore-Penrose inverses of two nonoegative definite matrices, a result originally due to Milliken and Akdeniz (1977), The purpose of this paper is to offer a simple proof for a generalization of this result,     

Regression analysis with two mixed forms of heteroscedasticity

Regression models are here considered in which disturbances are related to both the expectation of the dependent variable and a linear conbination of certain auxiliary variables. The maximum likelihood and weighted least squares estimators are compared in estimating the form of heteroscedasticity and regression coefficients. Also a test for heteroscedasticity is discussed. Finally an example is worked out for the purpose of illustration.     

Optimal Designs for Binary Logistic Regression with a Qualitative Classifier with Independent Levels

Dose response studies arise in many medical applications. Often, such studies are considered within the framework of binary-response experiments such as success-failure. In such cases, popular choices for modeling the probability of response are logistic or probit models. Design optimality has been well studied for the logistic model with a continuous covariate. A natural extension of the logistic model is to consider the presence of a qualitative classifier. In this work, we explore D-, A-, and E-optimal designs in a two-parameter, binary logistic regression model after introducing a binary, qualitative classifier with independent levels.     

Measurement Error and Incentive Pay

Abstract. We will analyse the optimal incentive scheme when the risk‐neutral principal contracts with many risk‐averse agents. Each agent produces an individual contribution which jointly form a total output. Agents’ efforts are unobservable and the principal cannot observe individual outputs without an error. Neither the observed individual output of an agent nor the observed total output of the whole team are then sufficient statistics for the actual individual output in the sense of Blackwell. We show that the mixed contract of the pure piece‐rate contract and of the pure team contract then dominates the pure contracts from the principal's point of view.     

Narratives as Sources of Stability and Change in Organizations: Approaches and Directions for Future Research

Although narrative analysis has made significant advances in organization and management studies, scholars have not yet unleashed its full potential. This review provides an understanding of key issues in organizational narrative analysis with a focus on the role of narratives in organizational stability and change. We start by elaborating on the characteristics of organizational narratives to provide a conceptual framework for organizational narrative analysis. We elaborate on three key approaches to narrative analysis on stability and change: realist, interpretative, and poststructuralist. We then review several topic areas where narrative analysis has so far offered the most promise: organizational change, identity, strategy, entrepreneurship, and personal change. Finally, we identify important issues that warrant attention in future research, both theoretically and methodologically.     

Gender and National Identity Constructions in the Cross‐Border Merger Context

In this article we explore ways in which vertical gender inequality is accomplished in discourse in the context of a recent chain of cross‐border mergers and acquisitions that resulted in the formation of a multinational Nordic company. We analyse social interactions of ‘doing’ gender in interviews with male senior executives from Denmark, Finland and Sweden. We argue that their explanations for the absence of women in the top echelons of the company serve to distance vertical gender inequality. The main contribution of the article is an analysis of how national identities are discursively (re)constructed in such distancing. New insights are offered to studying gender in multinationals with a cross‐cultural team of researchers. Our study sheds light on how gender intersects with nationality in shaping the multinational organization and the identities of male executives in globalizing business.     

High tick abundance and diversity of tick-borne pathogens in a Finnish city

Urban Ecosystems - The sheep tick Ixodes ricinus is the primary vector for various zoonotic diseases, including Lyme borreliosis and tick-borne encephalitis (TBE), in Europe. Because both abundance...     

Let us do the twist again

Krämer (Sankhy $\bar{\mathrm{a }}$ 42:130–131, 1980) posed the following problem: “Which are the $\mathbf{y}$ , given $\mathbf{X}$ and $\mathbf{V}$ , such that OLS and Gauss–Markov are equal?”. In other words, the problem aimed at identifying those vectors $\mathbf{y}$ for which the ordinary least squares (OLS) and Gauss–Markov estimates of the parameter vector $\varvec{\beta }$ coincide under the general Gauss–Markov model $\mathbf{y} = \mathbf{X} \varvec{\beta } + \mathbf{u}$ . The problem was later called a “twist” to Kruskal’s Theorem, which provides conditions necessary and sufficient for the OLS and Gauss–Markov estimates of $\varvec{\beta }$ to be equal. The present paper focuses on a similar problem to the one posed by Krämer in the aforementioned paper. However, instead of the estimation of $\varvec{\beta }$ , we consider the estimation of the systematic part $\mathbf{X} \varvec{\beta }$ , which is a natural consequence of relaxing the assumption that $\mathbf{X}$ and $\mathbf{V}$ are of full (column) rank made by Krämer. Further results, dealing with the Euclidean distance between the best linear unbiased estimator (BLUE) and the ordinary least squares estimator (OLSE) of $\mathbf{X} \varvec{\beta }$ , as well as with an equality between BLUE and OLSE are also provided. The calculations are mostly based on a joint partitioned representation of a pair of orthogonal projectors.