Gruenhage compacta and strictly convex dual norms

We prove that if K is a Gruenhage compact space then C(K)* admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and X* is the |.|-closed linear span of K, where K is a Gruenhage compact in the w*-topology and |.| is equivalent to a coarser, w*-lower semicontinuous norm on X*, then X* admits an equivalent, strictly convex dual norm. We give a partial converse to the first result by showing that if T is a tree, then C(T)* admits an equivalent, strictly convex dual norm if and only if T is a Gruenhage space. Finally, we present some stability properties satisfied by Gruenhage spaces; in particular, Gruenhage spaces are stable under perfect images

Trees, linear orders and G\^ateaux smooth norms

We introduce a linearly ordered set Z and use it to prove a necessity condition for the existence of a G\^ateaux smooth norm on C(T), where T is a tree. This criterion is directly analogous to the corresponding equivalent condition for Fr\'echet smooth norms. In addition, we prove that if C(T) admits a G\^ateaux smooth lattice norm then it also admits a lattice norm with strictly convex dual norm.Comment: A different version of this paper is to appear in J. London Math. So

Automatic positive semidefinate HAC covariance matrix and GMM estimation

This paper proposes a new class of heteroskedastic and autocorrelation consistent (HAC) covariance matrix estimators. The standard HAC estimation method reweights estimators of the autocovariances. Here we initially smooth the data observations themselves using kernel function–based weights. The resultant HAC covariance matrix estimator is the normalized outer product of the smoothed random vectors and is therefore automatically positive semidefinite. A corresponding efficient GMM criterion may also be defined as a quadratic form in the smoothed moment indicators whose normalized minimand provides a test statistic for the overidentifying moment conditions

Efficient information theoretic inference for conditional moment restrictions

The generalized method of moments estimator may be substantially biased in finite samples, especially so when there are large numbers of unconditional moment conditions. This paper develops a class of first order equivalent semi-parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel-weighted version of the Cressie-Read power divergence family of discrepancies. This approach is similar in spirit to the empirical likelihood methods of Kitamura, Tripathi and Ahn (2004) and Tripathi and Kitamura (2003). These efficient local methods avoid the necessity of explicit estimation of the conditional Jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations.Conditional Moment Restrictions, Local Cressie-Read Minimum Discrepancy, GMM, Semi-Parametric Efficiency

Local GEL methods for conditional moment restrictions

The principal purpose of this paper is to adapt to the conditional moment context the GEL unconditional moment methods described in Smith(1997, 2001) and Newey and Smith(2004). In particular we develop GEL estimators which achieve the semiparametric efficiency lower bound. The requisite GEL criteria are constructed by local smoothing and parallel the local semiparametric efficient EL method formulated by Kitamura, Tripathi and Ahn (2004) for conditional moment restrictions. A particular advantageof these efficient local methods is the avoidance of the necessity of providing explicit estimators for the Jacobian and conditional variance matrices. The class of local GEL estimators admits a number of alternative first order equivalent estimators such as local EL, local ET and local CUE as in the unconditional moment restrictions case. The paper also provides a local GEL criterion function test statistic for parametric restrictions.Conditional Moment Restrictions, Local Generalized Empirical Likelihood, GMM, Semi-Parametric Efficiency

GEL Criteria for Moment Condition Models

GEL methods which generalize and extend previous contributions are defined and analysed for moment condition models specified in terms of weakly dependent data. These procedures offer alternative one-step estimators and tests that are asymptotically equivalent to their efficient two-step GMM counterparts. The basis for GEL estimation is via a smoothed version of the moment indicators using kernel function weights which incorporate a bandwidth parameter. Examples for the choice of bandwidth parameter and kernel function are provided. Efficient moment estimators based on implied probabilities derived from the GEL method are proposed, a special case of which is estimation of the stationary distribution of the data. The paper also presents a unified set of test statistics for over-identifying moment restrictions and combinations of parametric and moment restriction hypotheses.GMM, Generalized Empirical Likelihood, Efficient Moment Estimation,

The Feelings Group: A Quantitative and Qualitative Evaluation of the Outcomes of a Smaller Anger Management Group for Clients who have a Learning Disability

Referrals concerning problems with anger for people with learning disability (LD) are relatively common as they are thought to be prone to difficulty in managing their anger (Willner, et al., 2002), a problem associated with aggressive behaviour (Novaco, 1994). Aggression is also prevalent in this population, with obvious inherent risks to themselves and others (Harris, 1993; Kiely & Pankhurst, 1998). Research on direct therapy in people with a learning disability (LD) indicates that there was a period of disdain for these types of approaches (Sinason, 1992). This was followed by a period marked by doubt around the value of using cognitive principles in particular (Willner, 2006), which was eventually overcome by a more positive and less discriminatory approach (Willner, 2005). This hesitancy has delayed the generation of robust empirical evaluation, which has yet to catch up (Willner, Jones, Tams & Green, 2002). The guidelines from the NHS are then activated whereby “in the absence of well designed randomised trials, clinicians may legitimately draw upon analysis of expert opinion and past experience” (Department of Health, 1996; p26). In some ways this offers freedom to adopt novel approaches or ones adapted from principle applied in other areas of clinical work, however, it also represents a difficulty in operating using evidence-based practice (Willner, 2005), which to some may represent a ‘professional minefield’ (Mead, 2000). In the emergent evidence-base for interventions for anger in this group, one important distinction has been made between ‘anger management’ and ‘anger treatment’ (Novaco et al., 2000), where the former is seen as a psycho educational approach whilst the latter explicitly combines assessment with treatment. Anger treatment also “centrally involves substantial cognitive restructuring and the acquisition of arousal reduction and behavioural coping skills” (Rose, et al., 2000, p172) This article presents the results from a small anger-management group for clients with a learning disability that was to be called “The Feelings Group”, which was based on the “Self awareness group” resource pack from Willner & Tomlinson (Psychology Department, Learning Disabilities Directorate, Bro Morgannwg NHS trust). This intervention boasted effectiveness in an RCT evaluation published in an article by Willner and colleagues (2002). The data was taken as part of service evaluation for the group. Informed consent was given by the clients involved to write about the group in an article