A comparison of forecasts from least absolute value and least squares regression

A Monte Carlo simulation is used to compare forecasts from least absolute value and least squares estimated regression equations. When outliers are present, the least absolute value forecasts are shown to be superior to least squares forecasts. The results emphasize the importance of exercising caution when using forecasts from least squares estimated regressions. Use of least absolute value regression (or some other robust regression method) instead of, or as an adjunct to, least squares is recommended. The comparison of forecasts from the two methods provides one way of assessing whether the least squares forecasts have been adversely affected by outliers. If outliers are present, the least absolute value regression forecasts can be used.     

On the history of the principle of least squares

Communicated by C. Truesdell     

A constrained least squares method for estimating the effects of an unknown monotonically intervening factor

A constrained least squares method is developed for the estimation of the effects of an unknown intervening causal factor in regression analysis, when the unknown factor shifts the regression hyperplane monotonically upwards (downwards) over time. As an illustration, we estimate the price elasticity of cigarettes in the USA and the systematic shifts of the demand curve for cigarettes during the time period 1964-86 (these shifts presumably reflecting the heightened awareness of the general public of the potential dangers of smoking).     

Forecasting from fallible data: Correcting prediction bias with stein-rule least squares

In the presence of fallible data, standard estimation and forecasting techniques are biased and inconsistent. Surprisingly, the magnitude of this bias tends to increase, and not diminish, in time series applications as more observations become available. A solution to this ever-present problem, Stein-rule least squares (SRLS), is offered. It corrects for the bias and inconsistency of traditional estimators and provides a means for significantly improving the predictive accuracy of regression-based forecasting techniques. A Monte Carlo study of the forecasting accuracy of SRLS, compared to its alternatives reveals its practical significance and small sample behaviour.     

Gauss's geodesy and the axiom of parallels

It is a myth that Gauss measured a certain large triangle specifically to determine its angle sum; he did so in order to link his triangulation of Hanover with contiguous ones. The sum of the angles differed from 180° by less than two thirds of a second; he is known to have mentioned in conversation that this constituted an approximate verification of the axiom of parallels (which he regarded as an empirical matter because his studies of hyperbolic trigonometry had led him to recognize the possibility of logical alternatives to Kant and Euclid). However, he never doubted Euclidean geometry in his geodetic work. On the contrary, he continually used 180° angle sums as a powerful check for observational errors, which helped him to achieve standards of precision equivalent to today's. Nor did he ever plan an empirical investigation of the geometrical structure of space.     

The composition of Taft E s o constants: An application of biased alternatives to least squares

Summary A systematic analysis of the composition of E _s ^o like rate constants clearly revealed that Taft E _s ^o -values depend upon the size of the substituents. Further evidence in favor of this view is adduced even in a case where OLS led to the conclusion that E _s ^o should be completely independent of the size of the substituents, since biased estimators (PCRA, LRRA) showed that this statement is not correct. Furthermore, it seems that the magnitude of the steric effect represented by E _s ^o is a function of the thickness of the substituent along 2 directions perpendicular on its main axis and is not influenced by its length.Acknowledgment. We would like to thank Prof. J.T. Webster, Department of Statistics, Southern Methodist University, Dallas, for sending us s computer program of latent root regression analysis. We also thank the referees whose insightful comments were most helpful in improving the presentation.     

The curvature argument

Dasgupta (2015) has recently put forward a novel argument, which he calls the ‘curvature argument’, that aims to show that Galilean spacetime is not an ideal setting for our classical theory of motion. This paper examines the curvature argument and argues that it is not sound. The discussion yields a remark about the conditions under which a ‘symmetry argument’ demonstrates that a particular spacetime is a non-ideal setting for our theory of motion.     

Why the ultimate argument for scientific realism ultimately fails

In this paper, I argue that the ultimate argument for Scientific Realism, also known as the No-Miracles Argument (NMA), ultimately fails as an abductive defence of Epistemic Scientific Realism (ESR), where (ESR) is the thesis that successful theories of mature sciences are approximately true. The NMA is supposed to be an Inference to the Best Explanation (IBE) that purports to explain the success of science. However, the explanation offered as the best explanation for success, namely (ESR), fails to yield independently testable predictions that alternative explanations for success do not yield. If this is correct, then there seems to be no good reason to prefer (ESR) over alternative explanations for success.     

On argument ex suppositione falsa

In my opinion it cannot be denied but that your discourse carries with it much of probability, arguing, as we say, ex suppositione, namely, granting that the Earth moves with the two motions assigned it by Copernicus; but, if one excludes those motions, all that you have said is vain and invalid; and for the exclusion of that hypothesis, it is very manifestly hinted by your discourse itself.     

Latin squares of the sixth order

Zusammenfassung Euler hatte in seiner Originalabhandlung über die lateinischen Quadrate vermutet, daß kein Paar wechselseitig orthogonaler 6×6 Quadrate existiert, was einige Jahre später bewiesen wurde. Man fand dann aber, daß diese 6×6 lateinischen Quadrate einige interessante orthogonale Verteilungen in einem schwächeren als demEulerschen Sinne besitzen, die zum Teil klassifiziert und aufgezählt werden konnten. Die vorliegende Note charakterisiert die erhaltenen Resultate und gibt einige interessante Symmetrieeigenschaften dieser Verteilungen an.     

David Hume's no-miracles argument begets a valid No-Miracles Argument

Hume's essay ‘Of Miracles’ has been a focus of controversy ever since its publication. The challenge to Christian orthodoxy was only too evident, but the balance-of-probabilities criterion advanced by Hume for determining when testimony justifies belief in miracles has also been a subject of contention among philosophers. The temptation for those familiar with Bayesian methodology to show that Hume's criterion determines a corresponding balance-of-posterior probabilities in favour of miracles is understandable, but I will argue that their attempts fail. However, I show that his criterion generates a valid form of the so-called No-Miracles Argument appealed to by modern realist philosophers, whose own presentation of it, despite their possession of the probabilistic machinery Hume himself lacked, is invalid.     

Scepticism,relativism and the argument from the criterion

This article explores the relationship between epistemic relativism and Pyrrhonian scepticism. It is argued that a fundamental argument for contemporary epistemic relativism derives from the Pyrrhonian problem of the criterion. Pyrrhonian scepticism is compared and contrasted with Cartesian scepticism about the external world and Humean scepticism about induction. Epistemic relativism is characterized as relativism due to the variation of epistemic norms, and is contrasted with other forms of cognitive relativism, such as truth relativism, conceptual relativism and ontological relativism. An argument from the Pyrrhonian problem of the criterion to epistemic relativism is presented, and is contrasted with three other arguments for epistemic relativism. It is argued that the argument from the criterion is the most fundamental argument for epistemic relativism. Finally, it is noted how the argument of the present paper fits with the author’s previous suggestion that a particularist response to the Pyrrhonian sceptic may be combined with a naturalistic view of epistemic warrant to meet the challenge of epistemic relativism.     

The first molecular models for an electromagnetic

The first models for an electromagnetic theory of dispersion are presented and an attempt is made to demonstrate the important role played by study of this phenomenon at the end of the nineteenth century. As well as indicating the need to have a better understanding of the microscopic properties of matter, dispersion also contributed (through the results obtained by Helmholtz) to the discussion over the nature of X-rays and was fundamental for introduction of Lorentz's electron theory.     

At least two toxins are involved inEscherichia coli mastitis

Summary Culture filtrate ofEscherichia coli produces changes in the bovine udder identical to those seen in experimental infections with the same organism.E. coli endotoxin produces an acute inflammatory response but none of the cell damage induced by culture filtrate. It appears therefore that at least 2 toxins are involved in the disease.Acknowledgments. We are grateful to Mrs K. Wells, Miss H. Meads and Miss A. Ashford for technical assistance.