Multivariate control charts based on a projection approach

Summary: In this paper the projection approach of Runger (1996) is applied to construct control charts for a multivariate process. It is assumed that a shift in the mean might only occur in a known subspace of the parameter space. The projection method permits a reduction of the dimensionality of the control problem.Several control schemes based on projections are introduced. We consider CUSUM type charts as well as EWMA schemes. The underlying variables are assumed to be independent and normally distributed. Using the average run length all control charts are compared with each other. Moreover, it is analyzed how sensitive the charts react on a false choice of the subspace.     

Milieu – ein wenig beachteter Faktor im Coaching

This article focuses on the importance of milieu for professional development, for opportunities to get certain positions in society or becoming a member of specific communities. Finding access to new milieus, dealing with the encounter of milieus is a competency, which can not really be trained. In order to dealing constructively with the issue taboos in society and in the field of consulting must be identified and over come.     

Statistical inference of the efficient frontier for dependent asset returns

In the paper we consider the three characteristics of the efficient frontier. These characteristics are estimated by substituting the unknown parameters by the sample counterparts. Assuming that the asset returns follow a stationary Gaussian process it is shown that the estimated characteristics are asymptotically normally distributed. This result is used to determine the joint asymptotic distribution of the estimated portfolio return and the estimated portfolio variance in the case of the expected utility portfolio and the tangency portfolio, respectively.     

Dezentrale Koordination von Stoffströmen in Recyclingnetzwerken

New legal regulations assign an extended product responsibility to the manufacturers, e.g. in the field of Waste Electrical and Electronic Equipment. Therefore, recycling of discarded products becomes increasingly important. For Waste Electrical and Electronic equipment, recycling is usually carried out by service providers, which are organised in recycling networks. In such networks of independent companies, centralized planning is not possible and therefore, a decentralized coordination mechanism is necessary. Within the article, a 2-level coordination approach is developed. This approach seems to be a good starting point for an efficient assignment of recycling tasks within the network, if a central planner is not present. The functionality of the approach is demonstrated based on an example.     

Estimation of a linear model in transformed variables under microaggregation by individual ranking

We consider the least squares estimation of a linear regression model in transformed variables from a data set that has been microaggregated by means of the individual ranking method. It is shown that the least squares estimators are consistent even in the case where variable transformations are carried out after microaggregation. Applying individual ranking techniques to a data set thus guarantees the analytical validity of the microaggregated data for a wide class of statistical models.     

On the existence of unbiased estimators for the portfolio weights obtained by maximizing the Sharpe ratio

We consider the problem of estimating the portfolio weights obtained by maximizing the Sharpe ratio. Assuming that the underlying asset returns are independent and multivariate normally distributed, Okhrin and Schmid (J. Econom. 134:235–256, 2006) showed that the frequently used sample estimators of these weights do not have a first moment. This paper proves that an unbiased estimator of the Sharpe ratio portfolio weights does not exist at all. Moreover, we show that there is no asymptotically unbiased estimator of these weights within the family of estimators which are bounded by cylinder functions.     

The Healthcare Systems of the USA and Canada: Forever on Divergent Paths?

Over all OECD healthcare systems, we identify increasing similarities and common trends, especially with regard to the role of the state. Yet two countries, the USA and Canada, have 'parted at the crossroads' since the 1960s and therefore are quite frequently cited as examples for the opposite trend, i.e. for divergence. According to our position, it is far from evident that this trend has still been dominant in the past 15 years. In our contribution, we show that the USA and Canada have become more similar regarding the role of the state in financing, service provision and the regulation of healthcare systems. Furthermore, the article investigates potential explanations. We find that a most influential explanatory factor is the healthcare system itself, its deficiencies and functional requirements as reflected in the specific system type. As the system types of the USA and Canada vary, so too do their adaptive responses to problem pressure. By systematically acquiring non-system-specific elements, i.e. characteristics which were originally less developed or completely absent, the systems grow more similar and therefore converge.     

Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series

The purpose of this paper is to jointly monitor the mean vector and the covariance matrix of multivariate nonlinear times series. The underlying target process is assumed to be a constant conditional correlation process Bollerslev (Rev Econ Stat 72:498–505, 1990) or a dynamic conditional correlation model Engle (J Bus Econ Stat 20:339–350, 2002). We introduce several EWMA and CUSUM control charts. These control schemes are based on univariate EWMA statistics, multivariate EWMA recursions, and different types of cumulative sums. The recursions are applied to local measures for means and covariances, e.g. the present observations and the conditional covariances. Further, they are applied to means and covariances of residuals. The control statistics are obtained by computing the Mahalanobis distance between the EWMA or CUSUM statistics and their expectations if no change occurs. Via Monte Carlo simulation the performance of the proposed charts is compared. Our empirical study illustrates an application of these control procedures to bivariate logarithmic returns of the European indices FTSE100 and DAX. In order to assess the performance of the introduced schemes we apply the average run length and the maximum conditional expected delay.     

The effect of conditional heteroskedasticity on common statistical procedures for means and variances

Summary: Commonly used standard statistical procedures for means and variances (such as the t–test for means or the F–test for variances and related confidence procedures) require observations from independent and identically normally distributed variables. These procedures are often routinely applied to financial data, such as asset or currency returns, which do not share these properties. Instead, they are nonnormal and show conditional heteroskedasticity, hence they are dependent. We investigate the effect of conditional heteroskedasticity (as modelled by GARCH(1,1)) on the level of these tests and the coverage probability of the related confidence procedures. It can be seen that conditional heteroskedasticity has no effect on procedures for means (at least in large samples). There is, however, a strong effect of conditional heteroskedasticity on procedures for variances. These procedures should therefore not be used if conditional heteroskedasticity is prevalent in the data.*We are grateful to the referees for their useful and constructive comments.