Model building with multiple dependent variables and constraints

The most widely used method for finding relationships between several quantities is multiple regression. This however is restricted to a single dependent variable. We present a more general method which allows models to be constructed with multiple variables on both sides of an equation and which can be computed easily using a spreadsheet program. The underlying principle (originating from canonical correlation analysis) is that of maximising the correlation between the two sides of the model equation. This paper presents a fitting procedure which makes it possible to force the estimated--model to satisfy constraint conditions which it is required to possess, these may arise from--theory, prior knowledge or be intuitively obvious. We also show that the least squares approach--to the problem is inadequate as it produces models which are not scale invariant.Peer reviewe

Investment Volatility : A Critique of Standard Beta Estimation and a Simple Way Forward

Thanks are due to Markus Becker for useful comments on an earlier version of this essay. Beta is a widely used quantity in investment analysis. We review the common interpretations that are applied to beta in finance and show that the standard method of estimation least squares regression is inconsistent with these interpretations. We present the case for an alternative beta estimator which is more appropriate, as well as being easier to understand and to calculate. Unlike regression, the line fit we propose treats both variables in the same way. Remarkably, it provides a slope that is precisely the ratio of the volatility of the investments rate of return to the volatility of the market index rate of return (or the equivalent excess rates of returns). Hence, this line fitting method gives an alternative beta, which corresponds exactly to the relative volatility of an investment - which is one of the usual interpretations attached to beta. Keywords- investment analysis, financial risk, volatility, systematic risk

Fitting equations to data with the perfect correlation relationship

Copyright and all rights therein are retained by the authors. All persons copying this information are expected to adhere to the terms and conditions invoked by each author's copyright. These works may not be re-posted without the explicit permission of the copyright holdersWe present a simple method for estimating a single relationship between multiple variables, which are all treated symmetrically i.e. there is no distinction between dependent and independent variables. This is of interest when estimating a law from observations in the natural sciences, although workers in the social sciences may also find this of interest when fitting relationships to data. All variables are assumed to have error but no information about the error is assumed. Unlike other symmetric methods, the weights or coefficients can be obtained easily – indeed, these can be expressed in terms of least squares coefficients. The approach has the important properties of providing a functional relationship which is scale invariant and uniqu

Selecting the best statistical distribution using multiple criteria

When selecting a statistical distribution to describe a set of data there are a number of criteria that can be used. Rather than select one of these criteria, we look at how multiple criteria can be combined to make the final selection. Two approaches have previously been presented in Computers and Industrial Engineering. We review these, and present a simpler method based on multiplicative aggregation. This has the advantage of being able to combine measures which are not measured on the same scale without having to use a normalisation procedure. Moreover, this method is scale-invariant, thus re-scaling the criteria values does not affect the final ranking. The method requires strictly positive criteria values measured on a ratio scale.Peer reviewe

A better measure of relative prediction accuracy for model selection and model estimation

Surveys show that the mean absolute percentage error (MAPE) is the most widely used measure of forecast accuracy in businesses and organizations. It is however, biased: When used to select among competing prediction methods it systematically selects those whose predictions are too low. This is not widely discussed and so is not generally known among practitioners. We explain why this happens. We investigate an alternative relative accuracy measure which avoids this bias: the log of the accuracy ratio: log (prediction / actual). Relative accuracy is particularly relevant if the scatter in the data grows as the value of the variable grows (heteroscedasticity). We demonstrate using simulations that for heteroscedastic data (modelled by a multiplicative error factor) the proposed metric is far superior to MAPE for model selection. Another use for accuracy measures is in fitting parameters to prediction models. Minimum MAPE models do not predict a simple statistic and so theoretical analysis is limited. We prove that when the proposed metric is used instead, the resulting least squares regression model predicts the geometric mean. This important property allows its theoretical properties to be understood.Peer reviewe

On constructing a composite indicator with multiplicative aggregation and the avoidance of zero weights in DEA

Peer reviewe

Analysis of reported error in Monte Carlo rendered images

Evaluating image quality in Monte Carlo rendered images is an important aspect of the rendering process as we often need to determine the relative quality between images computed using different algorithms and with varying amounts of computation. The use of a gold-standard, reference image, or ground truth (GT) is a common method to provide a baseline with which to compare experimental results. We show that if not chosen carefully the reference image can skew results leading to significant misreporting of error. We present an analysis of error in Monte Carlo rendered images and discuss practices to avoid or be aware of when designing an experiment

Measuring efficiency and productivity in professional football teams: Evidence from the English Premier League

Professional football clubs are unusual businesses, their performance judged on and off the field of play. This study is concerned with measuring the efficiency of clubs in the English Premier League. Information from clubs’ financial statements is used as a measure of corporate performance. To measure changes in efficiency and productivity the Malmquist non-parametric technique has been used. This is derived from the Data Envelopment Analysis (DEA) linear programming approach, with Canonical Correlation Analysis (CCA) being used to ensure the cohesion of the input-output variables. The study concludes that while clubs operate close to efficient levels for the assessed models, there is limited technological advance in their performance in terms of the displacement of the technological frontier

Nail lacquer films’ surface energies and in vitro water-resistance and adhesion do not predict their in vivo residence

The in vivo residence of nail lacquers (which are ideal topical drug carriers for the treatment of nail diseases) determines their frequency of application, and is thereby expected to influence patient adherence and success of treatment. Thus in vitro measurements to indicate lacquers’ in vivo residence are routinely conducted during formulation development. However the literature on in vitro-in vivo correlations is severely limited. Thus, the aim of the work discussed in this paper was to investigate correlations between in vivo residence and in vitro film resistance to water, in vitro film adhesion and surface energy of lacquer films. In vivo measurements were conducted on fingernails in six volunteers. Seven commercially available nail lacquers were tested in commonly-used measurements. Correlations between in vivo residence and in vitro water resistance and adhesion were found to be extremely poor. The surface energies of the lacquer films (which were between 33 and 39 mJ/m2) were also not predictive of in vivo residence. High density polyethylene (HDPE) sheet – whose surface energy was determined to be similar to that of the human nailplate – was found to be a suitable model for the nailplate (when investigating surface energy) and was used in a number of experiments