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Gruenhage compacta and strictly convex dual norms
Full text linkWe 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
Full text linkWe 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
Get PDFThis 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 functionābased 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
Get PDFThe 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
Get PDFThe 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
Get PDFGEL 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,
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Business networks SMEs and inter-firm collaboration: a review of the research literature with implications for policy
Get PDFThis literature review, which was commissioned by the UK's Small Business Service is concerned with business networks, and their importance for the small business community. Business networks are sometimes defined as comprising only inter-firm relationships (e.g. those that exist between component supplier and a manufacturer). However, it soon becomes apparent that a broader perspective is required, if research findings are to contribute meaningful insights for policy and practice. We have therefore incorporated research evidence on personal networks, notably those associated with entrepreneurship, and on links between firms and supporting institutions, such as trade associations, government agencies and universities
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