Robust estimation and testing in one-way ANOVA for Type II censored samples: skew normal error terms

Censoring can be occurred in many statistical analyses in the framework of experimental design. In this study, we estimate the model parameters in one-way ANOVA under Type II censoring. We assume that the distribution of the error terms is Azzalini's skew normal. We use Tiku's modified maximum likelihood (MML) methodology which is a modified version of the well-known maximum likelihood (ML) in the estimation procedure. Unlike ML methodology, MML methodology is non-iterative and gives explicit estimators of the model parameters. We also propose new test statistics based on the proposed estimators. The performances of the proposed estimators and the test statistics based on them are compared with the corresponding normal theory results via Monte Carlo simulation study. A real life data is analysed to show the implementation of the methodology presented in this paper at the end of the study.     

Two-way ANOVA when the distribution of the error terms is skew t

In this article, we assume that the distribution of the error terms is skew t in two-way analysis of variance (ANOVA). Skew t distribution is very flexible for modeling the symmetric and the skew datasets, since it reduces to the well-known normal, skew normal, and Student's t distributions. We obtain the estimators of the model parameters by using the maximum likelihood (ML) and the modified maximum likelihood (MML) methodologies. We also propose new test statistics based on these estimators for testing the equality of the treatment and the block means and also the interaction effect. The efficiencies of the ML and the MML estimators and the power values of the test statistics based on them are compared with the corresponding normal theory results via Monte Carlo simulation study. Simulation results show that the proposed methodologies are more preferable. We also show that the test statistics based on the ML estimators are more powerful than the test statistics based on the MML estimators as expected. However, power values of the test statistics based on the MML estimators are very close to the corresponding test statistics based on the ML estimators. At the end of the study, a real life example is given to show the implementation of the proposed methodologies.     

Trimmed likelihood estimators for lifetime experiments and their influence functions

We study the behaviour of trimmed likelihood estimators (TLEs) for lifetime models with exponential or lognormal distributions possessing a linear or nonlinear link function. In particular, we investigate the difference between two possible definitions for the TLE, one called original trimmed likelihood estimator (OTLE) and one called modified trimmed likelihood estimator (MTLE) which is the finite sample version of a form for location and linear regression used by Bednarski and Clarke [Trimmed likelihood estimation of location and scale of the normal distribution. Aust J Statist. 1993;35:141–153, Asymptotics for an adaptive trimmed likelihood location estimator. Statistics. 2002;36:1–8] and Bednarski et al. [Adaptive trimmed likelihood estimation in regression. Discuss Math Probab Stat. 2010;30:203–219]. The OTLE is always an MTLE but the MTLE may not be unique even in cases where the OLTE is unique. We compare especially the functional forms of both types of estimators, characterize the difference with the implicit function theorem and indicate situations where they coincide and where they do not coincide. Since the functional form of the MTLE has a simpler form, we use it then for deriving the influence function, again with the help of the implicit function theorem. The derivation of the influence function for the functional form of the OTLE is similar but more complicated.     

Threshold Incentives and Sales Variance

In this paper, we analyze the impact of two forms of commonly used threshold‐based incentive schemes on the observed sales variability. The first form of the incentive comprises an additional marginal payment on crossing a specified sales threshold and the second form of the incentive scheme comprises a lumpsum bonus payment on crossing the predetermined sales threshold. We model the effect of such incentives under two specific scenarios: an exclusive dealership selling a single product and a non‐exclusive dealer selling two competing products. For an exclusive dealer, we show that a bonus contract not only increases the expected sales, but, more importantly, decreases the sales (order) variance. Consequently, the bonus‐based scheme allows the manufacturer to regulate sales variance better. With a non‐exclusive dealer, the sales variance increases substantially with an additional marginal payment contract. However, our analysis suggests that the bonus contract continues to perform better in this case, too, if the threshold level is set appropriately using the underlying demand distribution.     

A Meta-analysis of Gender Differences in Attitudes Toward Seeking Professional Psychological Help

Abstract

Objective: The present study aims to examine gender differences in attitudes toward professional psychological help–seeking behavior and how gender differences could be affected by other cultural factor such as race. Participants: The authors selected studies that involved undergraduate and graduate students as samples, making the total number of participants in this meta-analysis 5,713. Methods: Statistical procedures were administrated by the MIX (Meta-analysis with Interactive eXplanations) program, which does meta-analyses. Results and Conclusions: The results indicated that gender itself was a significant predictor on attitudes toward seeking professional psychological help. In addition, individual's cultural background (eg, Western versus non-Western ethnicity) moderated the gender differences on attitudes toward seeking professional psychological help. Practical implications for mental health professionals in college settings were discussed.     

An empirical investigation of advanced manufacturing technology investment patterns: Evidence from a developing country

Advanced manufacturing technology (AMT) investment patterns in developing countries is in need of further investigation, particularly in the light of the conflicting evidence from the literature. This paper provides new evidence on AMT investment patterns from the Turkish automotive industry and develops a taxonomy by exploring the relationships between AMT investment patterns, ownership structure, firm size and performance. Analysis of industry survey data suggests the existence of three groups with different AMT investment strategies. Results suggest that AMT investment patterns are not only significantly correlated with firm performance or ownership, but also reveals significant differences in manufacturing performance across investment patterns.