Geoadditive expectile regression

Quantile regression has emerged as one of the standard tools for regression analysis that enables a proper assessment of the complete conditional distribution of responses even in the presence of heteroscedastic errors. Quantile regression estimates are obtained by minimising an asymmetrically weighted sum of absolute deviations from the regression line, a decision theoretic formulation of the estimation problem that avoids a full specification of the error term distribution. Recent advances in mean regression have concentrated on making the regression structure more flexible by including nonlinear effects of continuous covariates, random effects or spatial effects. These extensions often rely on penalised least squares or penalised likelihood estimation with quadratic penalties and may therefore be difficult to combine with the linear programming approaches often considered in quantile regression. As a consequence, geoadditive expectile regression based on minimising an asymmetrically weighted sum of squared residuals is introduced. Different estimation procedures are presented including least asymmetrically weighted squares, boosting and restricted expectile regression. The properties of these procedures are investigated in a simulation study and an analysis on rental fees in Munich is provided where the geoadditive specification allows for an analysis of nonlinear effects of the size of flats or the year of construction and the spatial distribution of rents simultaneously.     

Statistical Analysis for Decision Making

In this article we consider a generalization of the univariate g-and-h distribution to the multivariate situation with the aim of providing a flexible family of multivariate distributions that incorporate skewness and kurtosis. The approach is to modify the underlying random variables and their quantiles, directly giving rise to a family of distributions in which the quantiles rather than the densities are the foci of attention. Using the ideas of multivariate quantiles, we show how to fit multivariate data to our multivariate g-and-h distribution. This provides a more flexible family than the skew-normal and skew-elliptical distributions when quantiles are of principal interest. Unlike those families, the distribution of quadratic forms from the multivariate g-and-h distribution depends on the underlying skewness. We illustrate our methods on Australian athletes data, as well as on some wind speed data from the northwest Pacific.     

On the Determination of Single Sampling Attribute Plans Based upon a Linear Cost Model and a Prior Distribution

The linear cost model previously formalized by Hald [4], [5], [9] is reviewed. Techniques are described which permit easy determination of sampling plans based on that model. The degenerate, the beta, and the two point distributions are considered as prior distributions of p, the process fraction defective. For calculations only standard tables and a desk calculator are required.     

A Programmed Introduction to PERT

This paper treats multiple sequential sampling plans for attributes as finite Markov chains, and thereby demonstrates methods for evaluating various properties of such plans. Procedures for obtaining points on the operating characteristic curves and for computing the average total number of items sampled are provided.     

Bulk Sampling: Problems and Lines of Attack

An attempt is made to formulate a specified type of “bulk sampling” as an abstract field for general study. Recommendations are made for definitions of terms. Populations involved are described and means are defined. The problems of randomness, bias and blending are discussed. The formulation of theoretical variance models and their use in attaining optimum sampling plans are illustrated with particular reference to fertilizer and coal. The need for large amounts of empirical research and the desirability of current controls are indicated.     

The estimation of extreme quantiles of wind velocity using L-moments in the peaks-over-threshold approach

The paper evaluates the effectiveness of the method of L-moments for estimating parameters of the Pareto distribution model of peaks over a sufficiently high threshold, and compares its performance against a widely used method of de Haan (de Haan L. Extreme value statistics. In: Galambos J, Lechner J, Simin E, editor. Extreme value theory and applications, vol. 1. 1994. p. 93–122). Monte Carlo simulations and actual wind speed data collected at various stations in the United States have been utilized in this study. In the de Haan method, the first two moments of peaks of log-transformed data are used for the parameter estimation, whereas the L-moment method utilizes linear combinations of expectations of order statistics of peaks in the original data. Despite the procedural differences, the paper shows that the de Haan and two L-moments based estimates of the tail shape parameter are in fairly close agreement in simulated data as well as in the US wind speed data. Furthermore, higher order estimates of the shape parameter are obtained using the L-skewness of peaks data. Such estimates appear to provide a more stable upper bound, which can be useful in identifying meaningful values of design quantiles.     

TOWARDS A MODELING OF NATURAL SYSTEMS

We percept the infinitely various and diverse world as a huge system of systems. In the classification of them the one entity can be singled out and be called the growing systems. This paper presents an attempt of modeling such systems. It resulted with some non-trivial inferences and suggests methods of studying and controlling such systems.     

Forecasting wind power quantiles using conditional kernel estimation

The efficient management of wind farms and electricity systems benefit greatly from accurate wind power quantile forecasts. For example, when a wind power producer offers power to the market for a future period, the optimal bid is a quantile of the wind power density. An approach based on conditional kernel density (CKD) estimation has previously been used to produce wind power density forecasts. The approach is appealing because: it makes no distributional assumption for wind power; it captures the uncertainty in forecasts of wind velocity; it imposes no assumption for the relationship between wind power and wind velocity; and it allows more weight to be put on more recent observations. In this paper, we adapt this approach. As we do not require an estimate of the entire wind power density, our new proposal is to optimise the CKD-based approach specifically towards estimation of the desired quantile, using the quantile regression objective function. Using data from three European wind farms, we obtained encouraging results for this new approach. We also achieved good results with a previously proposed method of constructing a wind power quantile as the sum of a point forecast and a forecast error quantile estimated using quantile regression.     

Maximum entropy distribution under moments and quantiles constraints

When the results of a measurement are transferred from one stage in the chain of traceability to the next, the information gathered about the measurement is summarised. The summary involves, for example, details about applied measurement methods, environmental conditions, and measurement results including measurement uncertainty. The information about uncertainty usually takes the form of summary statistics such as an estimate, a standard deviation and a coverage interval specified by two quantiles. The information is used to construct a probability distribution for a given property or characteristic of an artefact, which is needed when the artefact is used as a reference in a subsequent stage. But in order to ensure impartiality in the process to establish the probability distribution, a general rule should be applied, for example, the principle of maximum entropy. In this paper, the application of this principle to establish a probability distribution when the mentioned summary statistics are available will be discussed, and its extension to moment constraints to satisfy the requirements of metrology will be introduced.     

Some General Remarks on Consulting in Statistics

This paper deals with obtaining a prediction interval on a future observation X, in an ordered sample of size n from a two-parameter exponential distribution for the situation where some or all the first r observations X ₁ < X ₂ < … < X _r , 1 ≤ r < s ≤ n, have been observed. The intervals are based on the statistic Z = (X _s , – X _r )/S _v , where S _v , is a function of the observations X ₀ ≡ A < X ₁ < X ₂ < … < X _r , such that X _s – X _r , and S _v , are independent variables and 2vS_v /σ has the distribution χ²(2v). The expressions for the quantiles z_p are given and some problems of numerical determination of z_p 's are discussed. The results can be also applied to related distributions.