Optimal B-robust estimators for the parameters of the Burr XII distribution

The Burr XII distribution offers a flexible alternative to the distributions that play important role for modelling data in reliability, risk and process capability. However, estimating the shape parameters of the Burr XII distribution is a challenging problem. The classical estimation methods such as maximum likelihood and least squares are often used to estimate the parameters of the Burr XII distribution, but these methods are very sensitive to the outliers in the data. Thus, a robust estimation method alternative to the classical methods is needed to find robust estimators that are less sensitive to the outliers in the data. The purpose of this paper is to use the optimal B-robust estimation method [Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA. Robust statistics: the approach based on influence functions. New York: Wiley; 1986] to obtain robust estimators for the shape parameters of the Burr XII distribution. The simulation results show that the optimal B-robust estimators generally outperform the classical estimators in terms of the bias and root mean square errors when there are outliers in data.     

A Bayesian discovery procedure

Summary.  We discuss a Bayesian discovery procedure for multiple-comparison problems. We show that, under a coherent decision theoretic framework, a loss function combining true positive and false positive counts leads to a decision rule that is based on a threshold of the posterior probability of the alternative. Under a semiparametric model for the data, we show that the Bayes rule can be approximated by the optimal discovery procedure, which was recently introduced by Storey. Improving the approximation leads us to a Bayesian discovery procedure, which exploits the multiple shrinkage in clusters that are implied by the assumed non-parametric model. We compare the Bayesian discovery procedure and the optimal discovery procedure estimates in a simple simulation study and in an assessment of differential gene expression based on microarray data from tumour samples. We extend the setting of the optimal discovery procedure by discussing modifications of the loss function that lead to different single-thresholding statistics. Finally, we provide an application of the previous arguments to dependent (spatial) data.     

Bayesian estimation for the Pareto income distribution

The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function. This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized for the doubly truncated gamma prior distribution. Now deceased.     

Constructing optimal designs for fitting pharmacokinetic models

We consider some computational issues that arise when searching for optimal designs for pharmacokinetic (PK) studies. Special factors that distinguish these are (i) repeated observations are taken from each subject and the observations are usually described by a nonlinear mixed model (NLMM), (ii) design criteria depend on the model fitting procedure, (iii) in addition to providing efficient parameter estimates, the design must also permit model checking, (iv) in practice there are several design constraints, (v) the design criteria are computationally expensive to evaluate and often numerical integration is needed and finally (vi) local optimisation procedures may fail to converge or get trapped at local optima.We review current optimal design algorithms and explore the possibility of using global optimisation procedures. We use these latter procedures to find some optimal designs.For multi-purpose designs we suggest two surrogate design criteria for model checking and illustrate their use.     

Linearity of regression for non-adjacent record values

Let X₁,X₂,… be a sequence of iid random variables having a continuous distribution; by R₁,R₂,… denote the corresponding record values. All the distributions allowing linearity of regressions either E(R_m+k|R_m) or E(R_m|R_m+k) are identified.     

Maximum entropy sampling and optimal Bayesian experimental design

When Shannon entropy is used as a criterion in the optimal design of experiments, advantage can be taken of the classical identity representing the joint entropy of parameters and observations as the sum of the marginal entropy of the observations and the preposterior conditional entropy of the parameters. Following previous work in which this idea was used in spatial sampling, the method is applied to standard parameterized Bayesian optimal experimental design. Under suitable conditions, which include non-linear as well as linear regression models, it is shown in a few steps that maximizing the marginal entropy of the sample is equivalent to minimizing the preposterior entropy, the usual Bayesian criterion, thus avoiding the use of conditional distributions. It is shown using this marginal formulation that under normality assumptions every standard model which has a two-point prior distribution on the parameters gives an optimal design supported on a single point. Other results include a new asymptotic formula which applies as the error variance is large and bounds on support size.     

Bayesian locally optimal design of knockout tournaments

The elimination or knockout format is one of the most common designs for pairing competitors in tournaments and leagues. In each round of a knockout tournament, the losers are eliminated while the winners advance to the next round. Typically, the goal of such a design is to identify the overall best player. Using a common probability model for expressing relative player strengths, we develop an adaptive approach to pairing players each round in which the probability that the best player advances to the next round is maximized. We evaluate our method using simulated game outcomes under several data-generating mechanisms, and compare it to random pairings, to the standard knockout format, and to two variants of the standard format.     

城市土地优化配置与集约利用评价模型剖析

采用综合分析法和文献综述法,对城市土地优化配置和集约利用的内涵进行了解释,归纳总结了用于城市土地优化配置与集约利用评价模型,以期在城市土地优化配置与集约利用中得到应用,并逐步改进。     

Opportunities of the minimum Anderson–Darling estimator as a variant of the maximum likelihood method

We reveal that the minimum Anderson–Darling (MAD) estimator is a variant of the maximum likelihood method. Furthermore, it is shown that the MAD estimator offers excellent opportunities for parameter estimation if there is no explicit formulation for the distribution model. The computation time for the MAD estimator with approximated cumulative distribution function is much shorter than that of the classical maximum likelihood method with approximated probability density function. Additionally, we research the performance of the MAD estimator for the generalized Pareto distribution and demonstrate a further advantage of the MAD estimator with an issue of seismic hazard analysis.     

Inferences on functions of Pareto parameters with application to income inequality measures

The Theil, Pietra, Éltetö and Frigyes measures of income inequality associated with the Pareto distribution function are expressed in terms of parameters defining the Pareto distribution. Inference procedures based on the generalized variable method, the large sample method, and the Bayesian method for testing of, and constructing confidence interval for, these measures are discussed. The results of Monte Carlo study are used to compare the performance of the suggested inference procedures from a population characterized by a Pareto distribution.