Stochastic proximal-gradient algorithms for penalized mixed models

Motivated by penalized likelihood maximization in complex models, we study optimization problems where neither the function to optimize nor its gradient has an explicit expression, but its gradient can be approximated by a Monte Carlo technique. We propose a new algorithm based on a stochastic approximation of the proximal-gradient (PG) algorithm. This new algorithm, named stochastic approximation PG (SAPG) is the combination of a stochastic gradient descent step which—roughly speaking—computes a smoothed approximation of the gradient along the iterations, and a proximal step. The choice of the step size and of the Monte Carlo batch size for the stochastic gradient descent step in SAPG is discussed. Our convergence results cover the cases of biased and unbiased Monte Carlo approximations. While the convergence analysis of some classical Monte Carlo approximation of the gradient is already addressed in the literature (see Atchadé et al. in J Mach Learn Res 18(10):1–33, 2017), the convergence analysis of SAPG is new. Practical implementation is discussed, and guidelines to tune the algorithm are given. The two algorithms are compared on a linear mixed effect model as a toy example. A more challenging application is proposed on nonlinear mixed effect models in high dimension with a pharmacokinetic data set including genomic covariates. To our best knowledge, our work provides the first convergence result of a numerical method designed to solve penalized maximum likelihood in a nonlinear mixed effect model.

     

Bayesian Estimation of Stochastic Discount Factors

This article provides a Bayesian method of estimating the marginal posterior distributions for stochastic discount factors associated with observed asset returns. These estimates can be used to provide measures of fit for asset-pricing models and to identify broad features of the characteristics that should be explained. These measures of fit can be used to supplement model-evaluation exercises based on Hansen–Jagannathan bounds     

亚东商埠史话

文章追溯当年西藏亚东商埠开市的起因、背景、过程及其后果,论述了亚东曾是中国近代史上英帝国主义侵略西藏而产生的边境贸易市场的历史,认为在当今国家昌盛、对外开放取得巨大成就的同时,更要牢记历史,增强时代感和责任感,坚定不移地维护祖国统一和西藏的稳定与发展。     

A sequential testing procedure for outliers and structural change

In this paper a test for outliers based on externally studentized residuals is shown to be related to a test for predictive failure. The relationships between a test for outliers, a test for a correlated mean shift and a test for an intercept shift are developed. A sequential testing procedure for outliers and structural change is shown to be independent, so that the overall size of the joint test can be determined exactly. It is established that a joint test for outliers and constancy of variances cannot be performed.     

Parameter estimation of complex mixed models based on meta-model approach

Complex biological processes are usually experimented along time among a collection of individuals, longitudinal data are then available. The statistical challenge is to better understand the underlying biological mechanisms. A standard statistical approach is mixed-effects model where the regression function is highly-developed to describe precisely the biological processes (solutions of multi-dimensional ordinary differential equations or of partial differential equation). A classical estimation method relies on coupling a stochastic version of the EM algorithm with a Monte Carlo Markov Chain algorithm. This algorithm requires many evaluations of the regression function. This is clearly prohibitive when the solution is numerically approximated with a time-consuming solver. In this paper a meta-model relying on a Gaussian process emulator is proposed to approximate the regression function, that leads to what is called a mixed meta-model. The uncertainty of the meta-model approximation can be incorporated in the model. A control on the distance between the maximum likelihood estimates of the mixed meta-model and the maximum likelihood estimates of the exact mixed model is guaranteed. Eventually, numerical simulations are performed to illustrate the efficiency of this approach.     

Testing for heteroscedasticity in a dynamic simultaneous equation model

This paper generalizes the Lagrange multiplier test for heteroscedasticity to a dynamic simultaneous equation model. A proof ofthe validity of the test is given. Small sample proper- ties of the Lagrange multiplier test and its 'studentized' version, under normal and non-normal errors, are investigated using a Monte Carlo experiment.     

Relative leader–member exchange,negative affectivity and social identification: A moderated-mediation examination

We argue that leader–member exchange (LMX) standing relative to the LMX relationships of other coworkers (RLMX) in workgroups may influence employees' job performance. Based on social comparison and social identity theories, we develop a moderated-mediation model of the psychological processes linking RLMX and job performance, and test it on a sample of 252 employees and 42 managers working in two large banks. Results of hierarchical regression analyses provide support for the model. We found that RLMX was positively related to social identification after controlling for perceptions of LMX; and also that social identification mediated the relationship between RLMX and job performance. We found further that negative affectivity moderated the relationship between RLMX and social identification which, in turn, also mediated the interactive effect on job performance.     

The robustness of tests of outliers and functional form

The purpose of this paper is to examine the robustness in finite samples of a test for outliers based on the maximum internally studentized residual and the RESET test for functional form misspecification. The effects of incorrect specification on the adequate detection of outliers and the presence of one or more outliers on the rejection frequencies of RESET are analysed. It is found that, ingeneral, the test for outliers does not seem to be robust to functional form misspecification, while the rejection frequencies of RESET can be reduced, sometimes dramatically, in the presence of outliers.     

Repositioning Risk in Social Work Education: Reflections Arising from the Threat of SARS to Social Work Students in Hong Kong during their Field Practicum

The social work profession has always been involved in dealing with uncertainty and risk in the life politics of clients. However, it is not easy for young social work students to translate this philosophical disposition into their real life practice with clients. In spring 2003, when the SARS epidemic broke out in Hong Kong, a group of social work students from the Chinese University of Hong Kong were doing their fieldwork practicum. Suddenly confronted by a collective sense of risk in their role as social workers, the students went through a period of unrest, as performing their helping duties brought with it a simultaneous exposure to personal risk. This paper is based on four focus group interviews with these social work students, to understand how they processed their experience of risk during their exposure to the SARS crisis, and how they connected the experience to their social work practice with clients. It is found that the predicament arising from the exposure to personal risk brought about by the SARS crisis during the students' field placement engendered the reflective process that enabled a renewed and personalized meaning of professionalism. The results provide a basis for reflection among social work educators on the role of risk in the training of prospective social workers, and on how social work education can better prepare students for practice in a high‐risk environment.     

Energy cost during locomotion across snow: a comparison of four types of snowshoes with snowshoe design considerations

Snowshoes are a common method of locomotion across snow but no investigations has previously examined the energy cost of different snowshoe models or looked for desirable snowshoe design characteristics. To this end, four Marines were studied while walking at 4 km/h in four different types of snowshoes. They traversed a field with an average grade of 2.4%, walking once downhill and once uphill with each snowshoe. Expired respiratory gases (for energy cost measures) and heart rates were collected continuously during the walk. The Pride Assault and US Army Standard models had a lower energy cost than the Montana Light model and tended to have a lower cost than the British Assault model. Correlations between snowshoe mass/surface area ratios and energy cost were 0.81 and 0.72 on the uphill and downhill portions of the course, respectively. Examination of the physical attributes of the snowshoes suggested several design characteristics may be favorable from an energy cost perspective: 1) a hinge-and-binding system that allows the snowshoe to be dragged across the snow, 2) an upturned front that pushes snow away and allows a more horizontal (less vertical) displacement of the snowshoe during locomotion, 3) a narrow profile that avoids leg abduction, and 4) a lower mass to surface area ratio. Further research will be necessary to determine the importance of these factors because of the limited number of subjects and the single snow condition examined here.