Choice of best linear in the guass-markoff model with a singular dispersion matrix

In this paper we obtain the complete class of representations and useful subclasses of MV-UB-LE and MV-MB-LE (minimum variance unbiased and minimum bias linear estimators) of linear parametric functions in the Gauss-Markoff model (Y,Xβ, σ ²V) when V is possibly singular.     

Head over heels in debt?

The average household in the UK is in debt to the tune of nearly £9000—and that is not including the mortgage. Consumer borrowing, on credit cards, car and retail finance deals, overdrafts and unsecured personal loans was £4525 per average UK adult at the end of February 2007. Are we drowning in debt? Chris Tapp , Associate Director of Credit Action, reports.     

A more general methodology for fitting global cross-ratio models for discrete longitudinal responses

In this paper, we focus on repeated measurement problems, comprising an interesting research area in statistics. We study longitudinal data which arise when outcomes are observed repeatedly on each experimental subject at several points. We focus on a marginal approach for this type of data with lack of independence among the observations proposed by Dale [Global cross-ratio models for bivariate, discrete, ordered responses. Biometrics. 1986;42(4):909–917] for bivariate, discrete, ordered responses. We propose an alternative estimation based on divergence measures to the full likelihood method proposed in that paper. Finally, a wide simulation study and a data example that illustrates the new methodology is provided.     

ON CERTAIN CONNECTIONS BETWEEN ALGEBRAIC GEOMETRY AND STATISTICS

The Department of Mathematical Statistics of the University of Sydney invited Professor Yu. V. Linnik, of Leningrad University, to deliver a public address to be attended by, among others, members of the 36th Congress of the International Statistical Institute. A summary of this address, delivered at 8.30 p.m. on Thursday, August 30, 1967, at the University of Sydney, is given below. Professor Linnik referred to related work of other authors, including Professors C. R. Rao and P. Whittle, who were present. Professor Rao later gave a short account of his recent work. Professor A. T. James moved a vote of thanks, which was carried by acclamation by a large audience. Reprints of the paper are being sent to those members of the International Statistical Institute present at the meeting.—EDITOR.     

Size matters—how measurement defines our world

"Measurement is the contact of reason with nature"—Henry Margenau
We live in a world of measurements, says David Hand. We talk about the weight of ingredients in cooking, the scores of students in tests, the inflation rate, the distance to the moon, the strength with which an opinion is held, and so on and so on. In brief, we see the world through the spectacles of quantification. But, occasionally, distortions or fractures occur in the lenses of quantification which cast doubt on our understanding of the world–doubts which sometimes raise questions about the reality we believe we are perceiving.     

A fast algorithm for the coordinate-wise minimum distance estimation

Application of the minimum distance (MD) estimation method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally expensive. To deal with the computational cost, this paper proposes a fast algorithm which makes the best use of coordinate-wise minimization technique in order to obtain the MD estimator. R package (KoulMde) based on the proposed algorithm and written in Rcpp is available online.     

Least absolute values estimation: an introduction

A brief review and bibliography of least absolute values (LAV) estimation is given. This paper serves to introduce the other articles in this special issue on the computational aspects of LAV estimation.     

Optimal trajectory to the general equilibrium state of the unstable stochastic lattice gas of prey–predator model with pair-approximation

This paper focuses on the study of the optimal control problem of the unstable stochastic lattice gas of prey–predator model with pair-approximation. The Pontryagin minimum procedure is used to derive the optimal behaviour of the proposed system that makes it trajectory closer to its general equilibrium states with respect to a selected performance measure during a specified period of time T. Wide numerical simulations and illustrations are presented in graphs and tables.     

Robust bootstrap densities for dynamic conditional correlations: implications for portfolio selection and Value-at-Risk

ABSTRACT

Many financial decisions such as portfolio allocation, risk management, option pricing and hedge strategies are based on the forecast of the conditional variances, covariances and correlations of financial returns. Although the decisions depend on the forecasts covariance matrix little is known about effects of outliers on the uncertainty associated with these forecasts. In this paper we analyse these effects on the context of dynamic conditional correlation models when the uncertainty is measured using bootstrap methods. We also propose a bootstrap procedure to obtain forecast densities for return, volatilities, conditional correlation and Value-at-Risk that is robust to outliers. The results are illustrated with simulated and real data.     

Bay! Bar charts

Allan Reese has often asserted that authors and editors appear less able to proofread graphs than text. It is hard to prove such a claim except by parading examples that, had they been expressed in text, would fall into the category that Private Eye calls "Colemanballs"—things you would never say with brain fully engaged. Here, he provides a few such examples.     

A goodness-of-fit test using randomly selected cell boundaries

This paper describes a technique for testing for the goodness-of-fit of a set of observations on a random variable to a hypothesized distribution. The cell boundaries needed for partitioning the range of the random variable are randomly chosen using the computer, thus eliminating an arbitrary choice by the analyst. The power of this test procedure is compared to the test procedure using equal expected cell frequencies     

The role of the minimum clinically important difference and its impact on designing a trial

The minimum clinically important difference (MCID) between treatments is recognized as a key concept in the design and interpretation of results from a clinical trial. Yet even assuming such a difference can be derived, it is not necessarily clear how it should be used. In this paper, we consider three possible roles for the MCID. They are: (1) using the MCID to determine the required sample size so that the trial has a pre-specified statistical power to conclude a significant treatment effect when the treatment effect is equal to the MCID; (2) requiring with high probability, the observed treatment effect in a trial, in addition to being statistically significant, to be at least as large as the MCID; (3) demonstrating via hypothesis testing that the effect of the new treatment is at least as large as the MCID. We will examine the implications of the three different possible roles of the MCID on sample size, expectations of a new treatment, and the chance for a successful trial. We also give our opinion on how the MCID should generally be used in the design and interpretation of results from a clinical trial.     

Robust williams trent test

To investigate the biological activities of a new compound or drug, experimenters usually compare a series of increasing doses to a control. Among other objectives, one may try to investigate any possible dose-response trend and to determine the minimum effective dose among all the experimental doses. Williams (1971, 1972) proposed a procedure to test the dose-response trend and also to identify the minimum effective dose based on the normally distributed data. In this paper, we propose a similar test procedure based on the robust estimate'of the average response to perform similar analysis. The proposed method is more resistant to the outliers and more powerful than the Williams procedure when the data distribution deviates from normality. We illustrate the use of this procedure with data arising from a recent study.     

A target distribution model for nonparametric density estimation

In this paper a model is proposed which represents a wide class of continuous distributions. It is shown how the parameters of this model can be estimated leading to a distribution estimator and a corresponding density estimator. An important property of this estimator is that it can be structured to reflect a priori knowledge of the unknown distribution.

Finally, some examples are shown and some comparisons made with kernel and orthogonal series estimators.     

Description and evaluation of a nested cube experimental design

An incomplete factorial design based on an extension of the Fawiliar 2^kfactorial called a nested cube is proposed for use in response surface investigationso The simplicity and general efficiency of the nested cube suggest its suitability to many areas of research, especially that repeated at many locations orconductea over a long period. Comparisons to potentially competing designs are provided for bias in response estination due to fitting an ioappropriate model and for profiles of variance. merits of the nested cube are (1) a level of relative bias and variance judged to be favorable though not optimal, (2) an ability to utilize a minimum blag estimator not available to competing designs, and (3) a simplicity associated with use of equal spacing

and nearly equal replication on the margin for each factor level.     

Estimating coefficients of single-index regression models by minimizing variation

This paper proposes a novel estimation of coefficients in single-index regression models. Unlike the traditional average derivative estimation [Powell JL, Stock JH, Stoker TM. Semiparametric estimation of index coefficients. Econometrica. 1989;57(6):1403–1430; Hardle W, Thomas M. Investigating smooth multiple regression by the method of average derivatives. J Amer Statist Assoc. 1989;84(408):986–995] and semiparametric least squares estimation [Ichimura H. Semiparametric least squares (sls) and weighted sls estimation of single-index models. J Econometrics. 1993;58(1):71–120; Hardle W, Hall P, Ichimura H. Optimal smoothing in single-index models. Ann Statist. 1993;21(1):157–178], the procedure developed in this paper is to estimate the coefficients directly by minimizing the mean variation function and does not involve estimating the link function nonparametrically. As a result, it avoids the selection of the bandwidth or the number of knots, and its implementation is more robust and easier. The resultant estimator is shown to be consistent. Numerical results and real data analysis also show that the proposed procedure is more applicable against model free assumptions.     

Optimal blocking and foldover plans for nonregular two-level designs

This paper discusses the issue of choosing optimal designs when both blocking and foldover techniques are simultaneously employed to nonregular two-level fractional factorial designs. By using the indicator function, the treatment and block generalized wordlength patterns of the combined blocked design under a general foldover plan are defined. Some general properties of combined block designs are also obtained. Our results extend the findings of Ai et al. (2010) from regular designs to nonregular designs. Based on these theoretical results, a catalog of optimal blocking and foldover plans in terms of the generalized aberration criterion for nonregular initial design with 12, 16 and 20 runs is tabulated, respectively.     

In Memoriam: Martin Taitel,Francis E. McLntyre

A discrete uniform distribution is defined over the integers 1, 2, …, k. Following Tenenbein, who investigated the point estimation of k for a sample drawn without replacement, this paper considers a number of point estimators of k for sampling with replacement and presents conservative confidence sets for k for both methods of sampling.     

Lower bound of average centered L2-discrepancy for U-type designs

Uniform designs are widely used in various scientific investigations and industrial applications. By considering all possible level permutation of the factors, a connection between average centered L₂-discrepancy and generalized wordlength pattern for asymmetrical fractional factorial designs is derived. Moreover, we present new lower bounds to the average centered L₂-discrepancy for symmetrical and asymmetrical U-type designs. For illustration of the theoretical results, the lower bounds for symmetrical and asymmetrical U-type designs are tabulated, and numerical results indicate that our lower bounds behave well and can be recommended for use in practice.     

Best minimum bias linear estimators in gauss-markoff model

In this note we present a criterion for linear estimation which is similar to MV-MB-LE of Rao (1978) in Gauss-Markoff model (Y, XB, α²G). We call this criterion MMS-MB-LE (Minimum Mean Square Error-Minimum Bias-Linear Estimation)> Representations of solutions to such estimators similar to those of Rao (1978) are provided.