Chebyshev’s inequality was recently extended to the multivariate case. In this paper we prove that the bounds in the multivariate Chebyshev’s inequality for random vectors can be attained in the limit. Hence, these bounds are the best possible bounds for this kind of regions.

Various continuous ant colony optimization (CACO) strategies are proposed by researchers to resolve continuous single response optimization problems. However, no such work is reported which also verifies suitability of CACO in case of both single and multiple response situations. In addition, as...

In this paper we examine the quality of the initial estimates of headline GDP and 10 major components of both real and nominal U.S. GDP. We ask a number of questions about various characteristics of the differences between the initial estimates, available one month after the end of the quarter,...

The K-means algorithm is commonly used with the Euclidean metric. While the use of Mahalanobis distances seems to be a straightforward extension of the algorithm, the initial estimation of covariance matrices can be complicated. We propose a novel approach for initializing covariance matrices.

In this paper we derive central limit theorems for two different types of Mahalanobis distances in situations where the dimension of the parent variable increases proportionally with the sample size. It is shown that although the two estimators are closely related and behave similarly in nite...

This paper treats the problem of estimating the inverse covariance matrix in an increasing dimension context. Specifically, three ridge-type estimators are considered, of which two new are proposed by the authors and one has been considered previously. Risk functions for deciding an appropriate...

In this paper we present an evaluation of forecasts of a vector of variables of the German economy made by different institutions. Our method permits one to evaluate the forecasts for each year and then if one is interested to combine the years. We use our method to determine an overall winner...

In this paper we present a multivariate analysis of the Federal Reserve’s forecasts. First, we evaluate the Fed’s forecasts of the ten major expenditure categories of real GDP. Second, we present a new methodology for evaluating multivariate forecasts. Finally, we use the same...

In the trade-off between bidding in the day-ahead electricity market and the real time balancing market, producers need good forecasts for balancing market prices to make informed decisions. A range of earlier published models for forecasting of balancing market prices, including a few...

This paper investigates the problem of constructing prediction regions for forecast trajectories 1 to H periods into the future—a path forecast. When the null model is only approximative, or completely unavailable, one cannot either derive the usual analytic expressions or resample from the...