Bayes estimation of the mean of a variance mixture of multivariate normal distributions is considered under sum of squared errors loss. We find broad class of priors (also in the variance mixture of normal class) which result in proper and generalized Bayes minimax estimators. This paper extends the results of Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264] in a manner similar to that of Maruyama [Admissible minimax estimators of a mean vector of scale mixtures of multivariate normal distribution, J. Multivariate Anal. 21 (2003) 69-78] but somewhat more in the spirit of Fourdrinier et al. [On the construction of bayes minimax estimators, Ann. Statist. 26 (1998) 660-671] for the normal case, in the sense that we construct classes of priors giving rise to minimaxity. A feature of this paper is that in certain cases we are able to construct proper Bayes minimax estimators satisfying the properties and bounds in Strawderman [Minimax estimation of location parameters for certain spherically symmetric distribution, J. Multivariate Anal. 4 (1974) 255-264].We also give some insight into why Strawderman's results do or do not seem to apply in certain cases. In cases where it does not apply, we give minimax estimators based on Berger's [Minimax estimation of location vectors for a wide class of densities, Ann. Statist. 3 (1975) 1318-1328] results. A main condition for minimaxity is that the mixing distributions of the sampling distribution and the prior distribution satisfy a monotone likelihood ratio property with respect to a scale parameter.

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This study examines the relationship between food waste and gender, income, and where students live. The research aligns with the United Nations Sustainable Development Goals 2, 11, and 12; moreover, the massive global food shortage in 2022 due to the conflict between Russia and Ukraine makes saving food a priority. A questionnaire was used to collect data from 201 students at the United Arab Emirates University (UAEU). A large proportion of the respondents were female (71.6%). The most common reasons cited by the respondents for food waste were over purchasing (31% of respondents), attitude (26.5%), and poor management (24%), while the most common reasons for having extra-cooked food were expecting guests (46%) and wanting to eat the food that had been prepared (35%). The majority of the respondents (57%) agreed that young people waste more food than older people. The methodology used in this study could be adopted by other researchers around the globe, and the output may help in developing policies and designing educational material for food waste intervention programs. Beneficiaries may therefore include food producers/consumers, environmental departments, and charitable organizations. The research contributes to the knowledge about food waste, perception, and intervention programs.

The modeling of bivariate dependence is usually accomplished with symmetric copula models. However, many examples on real datasets show that this hypothesis of symmetry may frequently fail to hold, so there is a need for inferential methods using asymmetric dependence structures. In this paper, useful tools for modeling non-exchangeable dependence structures are developed under a broad class of asymmetric copulas introduced by Khoudraji (1995). A special attention is given to the testing of the composite hypothesis that the underlying copula of a population belongs to this general class of models. The problem of selecting a specific Khoudraji-type copula via goodness-of-fit testing is considered as well, hence providing a complete set of tools for inference when facing bivariate data exhibiting an asymmetric dependence structure. Monte Carlo simulations show that the newly introduced methodologies work well in small and moderate sample sizes. Their usefulness for copula modeling is illustrated on real data sets exhibiting patterns of asymmetric dependence.