New estimators of distribution functions

ABSTRACT

This article considers the estimation of a distribution function F_X(x) based on a random sample X₁, X₂, …, X_n when the sample is suspected to come from a close-by distribution F₀(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F₀(x). As a by-product similar estimators are proposed for population quantiles.     

Ridge Autoregression Estimation: LS Method

In an AR (p)-model, least-squares estimation of the parameters is considered when it is suspected that the parameters may belong to a linear subspace and the estimated covariance matrix is ill-conditioned. Accordingly, we define five estimators and study their properties in an asymptotic setup to discover dominance properties based on asymptotic distributional bias (ADB), MSE (ADMSE) matrices, and under quadratic risks (ADQR).     

Optimum Critical Value for Pre-Test Estimator

In this paper, methods are proposed in finding the robust design in both Taguchi and Standard setups when a signal factor is present. The robust design is a set of level combinations of control factors so that the effect of controllable noise factors on response is minimum. Both univariate and multivariate methods are used in finding the influential noise factors for the determination of robust designs.     

Regression model with elliptically contoured errors

For the regression model y=X β+ε where the errors follow the elliptically contoured distribution, we consider the least squares, restricted least squares, preliminary test, Stein-type shrinkage and positive-rule shrinkage estimators for the regression parameters, β.

We compare the quadratic risks of the estimators to determine the relative dominance properties of the five estimators.     

Recurrence relations for moments of progressively censored order statistics from logistic distribution with applications to inference

In this paper, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a logistic distribution. The use of these relations in a systematic manner allows us to compute all the means, variances and covariances of progressively Type-II right censored order statistics from the logistic distribution for all sample sizes n, effective sample sizes m, and all progressive censoring schemes (R₁,…,R_m). The results established here generalize the corresponding results for the usual order statistics due to [Shah, 1966] and [Shah, 1970]. These moments are then utilized to derive best linear unbiased estimators of the location and scale parameters of the logistic distribution. A comparison of these estimators with the maximum likelihood estimations is then made. The best linear unbiased predictors of censored failure times are briefly discussed. Finally, an illustrative example is presented.     

“Chemophobia” Today: Consumers’ Knowledge and Perceptions of Chemicals

This mixed‐methods study investigated consumers’ knowledge of chemicals in terms of basic principles of toxicology and then related this knowledge, in addition to other factors, to their fear of chemical substances (i.e., chemophobia). Both qualitative interviews and a large‐scale online survey were conducted in the German‐speaking part of Switzerland. A Mokken scale was developed to measure laypeople's toxicological knowledge. The results indicate that most laypeople are unaware of the similarities between natural and synthetic chemicals in terms of certain toxicological principles. Furthermore, their associations with the term “chemical substances” and the self‐reported affect prompted by these associations are mostly negative. The results also suggest that knowledge of basic principles of toxicology, self‐reported affect evoked by the term “chemical substances,” risk‐benefit perceptions concerning synthetic chemicals, and trust in regulation processes are all negatively associated with chemophobia, while general health concerns are positively related to chemophobia. Thus, to enhance informed consumer decisionmaking, it might be necessary to tackle the stigmatization of the term “chemical substances” as well as address and clarify prevalent misconceptions.     

Assessing the value of a censored surrogate outcome

Lifetime Data Analysis - Assessing the potential of surrogate markers and surrogate outcomes for replacing a long term outcome is an active area of research. The interest in this topic is partly...     

COVID‐19, ethics of care and feminist crisis management

The COVID‐19 pandemic threatens both lives and livelihoods. To reduce the spread of the virus, governments have introduced crisis management interventions that include border closures, quarantines, strict social distancing, marshalling of essential workers and enforced homeworking. COVID‐19 measures are necessary to save the lives of some of the most vulnerable people within society, and yet in parallel they create a range of negative everyday effects for already marginalized people. Likely unintended consequences of the management of the COVID‐19 crisis include elevated risk for workers in low‐paid, precarious and care‐based employment, over‐representation of minority ethnic groups in case numbers and fatalities, and gendered barriers to work. Drawing upon feminist ethics of care, I theorize a radical alternative to the normative assumptions of rationalist crisis management. Rationalist approaches to crisis management are typified by utilitarian logics, masculine and militaristic language, and the belief that crises follow linear processes of signal detection, preparation/prevention, containment, recovery and learning. By privileging the quantifiable — resources and measurable outcomes — such approaches tend to omit considerations of pre‐existing structural disadvantage. This article contributes a new theorization of crisis management that is grounded in feminist ethics to provide a care‐based concern for all crisis affected people.