Estimation of two ordered normal means when a covariance matrix is known

Estimation of two normal means with an order restriction is considered when a covariance matrix is known. It is shown that restricted maximum likelihood estimator (MLE) stochastically dominates both estimators proposed by Hwang and Peddada [Confidence interval estimation subject to order restrictions. Ann Statist. 1994;22(1):67–93] and Peddada et al. [Estimation of order-restricted means from correlated data. Biometrika. 2005;92:703–715]. The estimators are also compared under the Pitman nearness criterion and it is shown that the MLE is closer to ordered means than the other two estimators. Estimation of linear functions of ordered means is also considered and a necessary and sufficient condition on the coefficients is given for the MLE to dominate the other estimators in terms of mean squared error.     

Gender and citizenship in academic career progression: an intersectional,meso-scale analysis in German higher education institutions

ABSTRACT

In tune with the fundamental shift in Germany’s skill-b(i)ased immigration policy since 2005, higher education institutions (HEIs) are increasingly becoming ‘magnets’ for a skilled migrant workforce. While ‘internationalisation’ is often understood as something to be celebrated and (further) accomplished, some observers speak of clear signs of discriminatory experiences among racialised and migrant academics. This is a new aspect, as social inequalities have by and large been considered in migration studies to be the sole terrain of labour mobility into less-skilled sectors of the economy. Meanwhile, abundant literature on gender and higher education shows that women academics have poorer access to career progression than men, demonstrating gender-based academic career inequalities. However, the insights generated in these two strands of scholarship have seldom been in conversation with one another. This paper takes stock of the lack of an intersectional perspective, focusing on citizenship and gender within HEIs as hiring meso-level organisations that are becoming increasingly transnationalised. It explores the intersectionality of citizenship and gender in accessing academic career advancement by examining three key career stages, that is, doctoral researchers, postdoctoral researchers, and professors, in two case-study HEIs.     

Improved estimators for the common mean and ordered means of two normal distributions with ordered variances

We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959). Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators which take into account both order restrictions. However, in estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is discussed.     

Estimation of the optimal portfolio weights by shrinking the mean vector towards a linear subspace

To obtain estimators of mean-variance optimal portfolio weights, Stein-type estimators of the mean vector that shrink a sample mean towards the grand mean have been applied. However, the dominance of these estimators has not been shown under the loss function used in the estimation problem of the mean-variance optimal portfolio weights, which is different than the quadratic function for the case in which the covariance matrix is unknown. We analytically give the conditions for Stein-type estimators that shrink towards the grand mean, or more generally, towards a linear subspace, to improve upon the classical estimators, which are obtained by simply plugging in sample estimates. We also show the dominance when there are linear constraints on portfolio weights.