Generalised Rank Regression Estimator with Standard Error Adjusted Lasso

One of the standard variable selection procedures in multiple linear regression is to use a penalisation technique in least‐squares (LS) analysis. In this setting, many different types of penalties have been introduced to achieve variable selection. It is well known that LS analysis is sensitive to outliers, and consequently outliers can present serious problems for the classical variable selection procedures. Since rank‐based procedures have desirable robustness properties compared to LS procedures, we propose a rank‐based adaptive lasso‐type penalised regression estimator and a corresponding variable selection procedure for linear regression models. The proposed estimator and variable selection procedure are robust against outliers in both response and predictor space. Furthermore, since rank regression can yield unstable estimators in the presence of multicollinearity, in order to provide inference that is robust against multicollinearity, we adjust the penalty term in the adaptive lasso function by incorporating the standard errors of the rank estimator. The theoretical properties of the proposed procedures are established and their performances are investigated by means of simulations. Finally, the estimator and variable selection procedure are applied to the Plasma Beta‐Carotene Level data set.     

Estimation of Population Variance from Multi-ranker Ranked Set Sampling Designs

In this article, we develop an estimator for a population variance based on a multi-ranker ranked set sampling design. In a multi-ranker design, the units are ranked by more than one ranker allowing ties whenever the confidence level of the rankers is low. The ranking information of all rankers is then combined in a meaningful way to create a single measure. This measure is used to construct the sampling design and a new estimator for the population variance. The article investigates the bias and relative efficiency of the proposed variance estimator. It is shown that the new estimator performs as good as or better than its competitors in the literature.     

Inference in the presence of ranking error in ranked set sampling

The author proposes inference techniques for ranked set sample data in the presence of judgment ranking errors. He bases his analysis on the models of Bohn & Wolfe (1994) and Frey (2007a, b), of which parameters are estimated by minimizing a distance measure. He then uses the fitted models to calibrate confidence intervals and tests. He shows the validity of his approach through simulation and illustrates its application through the construction of distribution‐free confidence intervals for the median area of apple tree leaves covered by a spray.     

Parametric inference based on judgment post stratified samples

In this paper, we consider a judgment post stratified (JPS) sample of set size $H$ from a location and scale family of distributions. In a JPS sample, ranks of measured units are random variables. By conditioning on these ranks, we derive the maximum likelihood (MLEs) and best linear unbiased estimators (BLUEs) of the location and scale parameters. Since ranks are random variables, by considering the conditional distributions of ranks given the measured observations we construct Rao-Blackwellized version of MLEs and BLUEs. We show that Rao-Blackwellized estimators always have smaller mean squared errors than MLEs and BLUEs in a JPS sample. In addition, the paper provides empirical evidence for the efficiency of the proposed estimators through a series of Monte Carlo simulations.     

Parental Speech and Gesture Input to Girls Versus Boys in Singletons and Twins

Journal of Nonverbal Behavior - Children show sex differences in early speech development, with girls producing a greater number and variety of words at an earlier age than boys (Berglund et al. in...     

Inference Based on General Linear Models for Order Restricted Randomization

This article develops statistical inference for the general linear models in order restricted randomized (ORR) designs. The ORR designs use the heterogeneity among experimental units to induce a negative correlation structure among responses obtained from different treatment regimes. This negative correlation structure acts as a variance reduction technique for treatment contrast. The parameters of the general linear models are estimated and a generalized F-test is constructed for its components. It is shown that the null distribution of the test statistic can be approximated reasonably well with an F-distribution for moderate sample sizes. It is also shown that the empirical power of the proposed test is substantially higher than the powers of its competitors in the literature. The proposed test and estimator are applied to a data set from a clinical trial to illustrate how one can improve such an experiment.     

Combining multi‐observer information in partially rank‐ordered judgment post‐stratified and ranked set samples

This paper develops two sampling designs to create artificially stratified samples. These designs use a small set of experimental units to determine their relative ranks without measurement. In each set, the units are ranked by all available observers (rankers), with ties whenever the units cannot be ranked with high confidence. The rankings from all the observers are then combined in a meaningful way to create a single weight measure. This weight measure is used to create judgment strata in both designs. The first design constructs the strata through judgment post‐stratification after the data has been collected. The second design creates the strata before any measurements are made on the experimental units. The paper constructs estimators and confidence intervals, and develops testing procedures for the mean and median of the underlying distribution based on these sampling designs. We show that the proposed sampling designs provide a substantial improvement over their competitor designs in the literature. The Canadian Journal of Statistics 41: 304–324; 2013 © 2013 Statistical Society of Canada     

Multi-sample inference for simple-tree alternatives with ranked-set samples

This paper develops a non‐parametric multi‐sample inference for simple‐tree alternatives for ranked‐set samples. The multi‐sample inference provides simultaneous one‐sample sign confidence intervals for the population medians. The decision rule compares these intervals to achieve the desired type I error. For the specified upper bounds on the experiment‐wise error rates, corresponding individual confidence coefficients are presented. It is shown that the testing procedure is distribution‐free. To achieve the desired confidence coefficients for multi‐sample inference, a nonparametric confidence interval is constructed by interpolating the adjacent order statistics. Interpolation coefficients and coverage probabilities are provided, along with the nominal levels.     

Scheduling Methods for Efficient Stamping Operations at an Automotive Company

We consider scheduling issues at Beyçelik, a Turkish automotive stamping company that uses presses to give shape to metal sheets in order to produce auto parts. The problem concerns the minimization of the total completion time of job orders (i.e., makespan) during a planning horizon. This problem may be classified as a combined generalized flowshop and flexible flowshop problem with special characteristics. We show that the Stamping Scheduling Problem is NP‐Hard. We develop an integer programming‐based method to build realistic and usable schedules. Our results show that the proposed method is able to find higher quality schedules (i.e., shorter makespan values) than both the company's current process and a model from the literature. However, the proposed method has a relatively long run time, which is not practical for the company in situations when a (new) schedule is needed quickly (e.g., when there is a machine breakdown or a rush order). To improve the solution time, we develop a second method that is inspired by decomposition. We show that the second method provides higher‐quality solutions—and in most cases optimal solutions—in a shorter time. We compare the performance of all three methods with the company's schedules. The second method finds a solution in minutes compared to Beyçelik's current process, which takes 28 hours. Further, the makespan values of the second method are about 6.1% shorter than the company's schedules. We estimate that the company can save over €187,000 annually by using the second method. We believe that the models and methods developed in this study can be used in similar companies and industries.     

Constructing quantile confidence intervals using extended simple random sample in finite populations

This paper constructs quantile confidence intervals based on extended simple random sample (SRS) from a finite population, where ranks of population units are all known. Extended simple random sample borrows additional information from unmeasured observations in the population by conditioning on the population ranks of the measured units in SRS. The confidence intervals are improved using Rao-Blackwell theorem over the conditional distribution of sample ranks given the measured sample units. Empirical evidence shows that the proposed confidence intervals have shorter lengths than confidence intervals constructed from an SRS sample.