On the robustness of the generalized fused lasso to prior specifications

Using networks as prior knowledge to guide model selection is a way to reach structured sparsity. In particular, the fused lasso that was originally designed to penalize differences of coefficients corresponding to successive features has been generalized to handle features whose effects are structured according to a given network. As any prior information, the network provided in the penalty may contain misleading edges that connect coefficients whose difference is not zero, and the extent to which the performance of the method depend on the suitability of the graph has never been clearly assessed. In this work we investigate the theoretical and empirical properties of the adaptive generalized fused lasso in the context of generalized linear models. In the fixed \(p\) setting, we show that, asymptotically, adding misleading edges in the graph does not prevent the adaptive generalized fused lasso from enjoying asymptotic oracle properties, while forgetting suitable edges can be more problematic. These theoretical results are complemented by an extensive simulation study that assesses the robustness of the adaptive generalized fused lasso against misspecification of the network as well as its applicability when theoretical coefficients are not exactly equal. Our contribution is also to evaluate the applicability of the generalized fused lasso for the joint modeling of multiple sparse regression functions. Illustrations are provided on two real data examples.     

New recursive estimators of the time-average variance constant

Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC with \(O(1)\) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with \(O(1)\) computational complexity. One of them is uniformly better than Wu’s estimator in terms of asymptotic mean squared error (MSE) at a cost of slightly higher memory complexity. The other preserves the \(O(1)\) memory complexity and is better then Wu’s estimator in most situations. Moreover, the first estimator is nearly optimal in the sense that its asymptotic MSE is \(2^{10/3}3^{-2} \fallingdotseq 1.12\) times that of the optimal off-line TAVC estimator.     

Approximate Bayesian computation with composite score functions

Both approximate Bayesian computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.     

Computing the log concave NPMLE for interval censored data

In analyzing interval censored data, a non-parametric estimator is often desired due to difficulties in assessing model fits. Because of this, the non-parametric maximum likelihood estimator (NPMLE) is often the default estimator. However, the estimates for values of interest of the survival function, such as the quantiles, have very large standard errors due to the jagged form of the estimator. By forcing the estimator to be constrained to the class of log concave functions, the estimator is ensured to have a smooth survival estimate which has much better operating characteristics than the unconstrained NPMLE, without needing to specify a parametric family or smoothing parameter. In this paper, we first prove that the likelihood can be maximized under a finite set of parameters under mild conditions, although the log likelihood function is not strictly concave. We then present an efficient algorithm for computing a local maximum of the likelihood function. Using our fast new algorithm, we present evidence from simulated current status data suggesting that the rate of convergence of the log-concave estimator is faster (between \(n^{2/5}\) and \(n^{1/2}\)) than the unconstrained NPMLE (between \(n^{1/3}\) and \(n^{1/2}\)).     

A Proportional Hazards Regression Model for the Subdistribution with Covariates‐adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate‐dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate‐dependent censoring. We consider a covariate‐adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate‐adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate‐adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks.     

Predictive Inference for Big,Spatial, Non‐Gaussian Data: MODIS Cloud Data and its Change‐of‐Support

Remote sensing of the earth with satellites yields datasets that can be massive in size, nonstationary in space, and non‐Gaussian in distribution. To overcome computational challenges, we use the reduced‐rank spatial random effects (SRE) model in a statistical analysis of cloud‐mask data from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board NASA's Terra satellite. Parameterisations of cloud processes are the biggest source of uncertainty and sensitivity in different climate models’ future projections of Earth's climate. An accurate quantification of the spatial distribution of clouds, as well as a rigorously estimated pixel‐scale clear‐sky‐probability process, is needed to establish reliable estimates of cloud‐distributional changes and trends caused by climate change. Here we give a hierarchical spatial‐statistical modelling approach for a very large spatial dataset of 2.75 million pixels, corresponding to a granule of MODIS cloud‐mask data, and we use spatial change‐of‐Support relationships to estimate cloud fraction at coarser resolutions. Our model is non‐Gaussian; it postulates a hidden process for the clear‐sky probability that makes use of the SRE model, EM‐estimation, and optimal (empirical Bayes) spatial prediction of the clear‐sky‐probability process. Measures of prediction uncertainty are also given.     

Intergenerational class mobility in contemporary Britain: political concerns and empirical findings

In Britain in recent years social mobility has become a topic of central political concern, primarily as a result of the effort made by New Labour to make equality of opportunity rather than equality of condition a focus of policy. Questions of the level, pattern and trend of mobility thus bear directly on the relevance of New Labour's policy analysis, and in turn are likely be crucial to the evaluation of its performance in government. However, politically motivated discussion of social mobility often reveals an inadequate grasp of both empirical and analytical issues. We provide new evidence relevant to the assessment of social mobility - in particular, intergenerational class mobility - in contemporary Britain through cross-cohort analyses based on the NCDS and BCS datasets which we can relate to earlier cross-sectional analyses based on the GHS. We find that, contrary to what seems now widely supposed, there is no evidence that absolute mobility rates are falling; but, for men, the balance of upward and downward movement is becoming less favourable. This is overwhelmingly the result of class structural change. Relative mobility rates, for both men and women, remain essentially constant, although there are possible indications of a declining propensity for long-range mobility. We conclude that under present day structural conditions there can be no return to the generally rising rates of upward mobility that characterized the middle decades of the twentieth century - unless this is achieved through changing relative rates in the direction of greater equality or, that is, of greater fluidity. But this would then produce rising rates of downward mobility to exactly the same extent - an outcome apparently unappreciated by, and unlikely to be congenial to, politicians preoccupied with winning the electoral 'middle ground'.     

Managing The Lactating Body: The Breast-Feeding Project and Privileged Motherhood

Drawing on interviews with twenty-five mostly white, educated, work-force experienced and class-privileged mothers, this paper explores how these women construct the lactating body as a carefully managed site and breast-feeding as a project—a task to be researched, planned, implemented, and assessed, with reliance on expert knowledge, professional advice, and consumption. The framing of breast-feeding as a project contrasts with the emphases on pleasure, embodied subjectivity, relationality, and empowerment that characterizes much of the recent breast-feeding literature across the humanities and social sciences. I argue that the project frame sheds light on the amount of work and self-discipline involved in compliance with broader middle-class mothering standards set in the consumerist, technological, medicalized, and professionalized contexts that shape parenting in late capitalist America.

Myths of Women and Their Reflection in a Therapy Group

One essential dilemma for modern clinical social work involves the relationship between the processes taking place inside the self and the social, cultural, and political developments affecting a person from the outside. The group-analysis approach focuses on four levels of relationships and communication within the group, among others a primordial level of shared myths, archetypical images, and the collective unconscious as an important component of psychotherapy. This article describes group-analysis therapy with women, analyzing a therapeutic process that used social myths to explore the formative institutionalization processes participants had undergone, thereby expanding themselves, growing, and changing.