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.     

Bounds for the least squares extrapolation in non‐linear AR(1) processes

It is proved that formula for least squares extrapolation in stationary non‐linear AR(1) process is valid also for non‐stationary non‐linear AR(1) processes. This formula depends on the distribution of the corresponding white noise. If the non‐linear function used in the model is non‐decreasing and concave, upper and lower bounds are derived for least squares extrapolation such that the bounds depend only on the expectation of the white noise. It is shown in an example that the derived bounds in some cases give a good approximation to the least squares extrapolation. Copyright © 2001 John Wiley & Sons, Ltd.     

Forecasting carbon price using a multi-objective least squares support vector machine with mixture kernels

For improving forecasting accuracy and trading performance, this paper proposes a new multi-objective least squares support vector machine with mixture kernels to forecast asset prices. First, a mixture kernel function is introduced into taking full use of global and local kernel functions, which is adaptively determined following a data-driven procedure. Second, a multi-objective fitness function is proposed by incorporating level forecasting and trading performance, and particle swarm optimization is used to synchronously search the optimal model selections of least squares support vector machine with mixture kernels. Taking CO₂ assets as examples, the results obtained show that compared with the popular models, the proposed model can achieve higher forecasting accuracy and higher trading performance. The advantages of the mixture kernel function and the multi-objective fitness function can improve the forecasting ability of the asset price. The findings also show that the models with a high-level forecasting accuracy cannot always have a high trading performance of asset price forecasting. In contrast, high directional forecasting usually means a high trading performance.     

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.     

Using wavelets to obtain a consistent ordinary least squares estimator of the long‐memory parameter

We develop an ordinary least squares estimator of the long‐memory parameter from a fractionally integrated process that is an alternative to the Geweke and Porter‐Hudak (1983) estimator. Using the wavelet transform from a fractionally integrated process, we establish a log‐linear relationship between the wavelet coefficients' variance and the scaling parameter equal to the log‐memory parameter. This log‐linear relationship yields a consistent ordinary least squares estimator of the long‐memory parameter when the wavelet coefficients' population variance is replaced by their sample variance. We derive the small sample bias and variance of the ordinary least squares estimator and test it against the GPH estimator and the McCoy–Walden maximum likelihood wavelet estimator by conducting a number of Monte Carlo experiments. Based upon the criterion of choosing the estimator which minimizes the mean squared error, the wavelet OLS approach was superior to the GPH estimator, but inferior to the McCoy–Walden wavelet estimator for the processes simulated. However, given the simplicity of programming and running the wavelet OLS estimator and its statistical inference of the long‐memory parameter we feel the general practitioner will be attracted to the wavelet OLS estimator. Copyright © 1999 John Wiley & Sons, Ltd.     

Projection of population structure in China using least squares support vector machine in conjunction with a Leslie matrix model

China is a populous country that is facing serious aging problems due to the single‐child birth policy. Debate is ongoing whether the liberalization of the single‐child policy to a two‐child policy can mitigate China's aging problems without unacceptably increasing the population. The purpose of this paper is to apply machine learning theory to the demographic field and project China's population structure under different fertility policies. The population data employed derive from the fifth and sixth national census records obtained in 2000 and 2010 in addition to the annals published by the China National Bureau of Statistics. Firstly, the sex ratio at birth is estimated according to the total fertility rate based on least squares regression of time series data. Secondly, the age‐specific fertility rates and age‐specific male/female mortality rates are projected by a least squares support vector machine (LS‐SVM) model, which then serve as the input to a Leslie matrix model. Finally, the male/female age‐specific population data projected by the Leslie matrix in a given year serve as the input parameters of the Leslie matrix for the following year, and the process is iterated in this manner until reaching the target year. The experimental results reveal that the proposed LS‐SVM‐Leslie model improves the projection accuracy relative to the conventional Leslie matrix model in terms of the percentage error and mean algebraic percentage error. The results indicate that the total fertility ratio should be controlled to around 2.0 to balance concerns associated with a large population with concerns associated with an aging population. Therefore, the two‐child birth policy should be fully instituted in China. However, the fertility desire of women tends to be low due to the high cost of living and the pressure associated with employment, particularly in the metropolitan areas. Thus additional policies should be implemented to encourage fertility.     

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.