We study linear subset regression in the context of the high-dimensional overall model
$y = \vartheta +\theta ' z + \epsilon $
with univariate response y and a d-vector of random regressors z, independent of
. Here, “high-dimensional” means that the number d of available explanatory variables is much larger than the number n of observations. We consider simple linear submodels where y is regressed on a set of p regressors given by
$x = M'z$
, for some
$d \times p$
matrix M of full rank
$p < n$
. The corresponding simple model, that is,
$y=\alpha +\beta ' x + e$
, is usually justified by imposing appropriate restrictions on the unknown parameter
in the overall model; otherwise, this simple model can be grossly misspecified in the sense that relevant variables may have been omitted. In this paper, we establish asymptotic validity of the standard F-test on the surrogate parameter
, in an appropriate sense, even when the simple model is misspecified, that is, without any restrictions on
whatsoever and without assuming Gaussian data.
PurposeThis paper provides a self-contained introduction to the mathematical aspects of the topological derivative.Design/methodology/approachFull justifications are given on simple model problems following a modern approach based on the averaged adjoint state technique. Extensions are discussed in relation with the literature on the field.FindingsClosed expressions of topological derivatives are obtained and commented.Originality/valueSeveral cases are covered in a unified and didactic presentation. Some elements of proof are novel.
We study the capacity of the banking system to provide liquidity to the corporate sector in times of stress and how changes in this capacity affect corporate liquidity management. We show that the contractual arrangements among banks in loan syndicates co-insure liquidity risks of credit line drawdowns and generate a network of interbank exposures. We develop a simple model and simulate the liquidity and insurance capacity of the banking network. We find that the liquidity capacity of large banks has significantly increased following the introduction of liquidity regulation, and that the liquidity co-insurance function in loan syndicates is economically important. We also find that borrowers with higher reliance on credit lines in their liquidity management have become more likely to obtain credit lines from syndicates with higher liquidity. The assortative matching on liquidity characteristics has strengthened the role of banks as liquidity providers to the corporate sector.
BackgroundPress-fitted implants are implanted by impaction to ensure adequate seating, but without overloading the components, the surgeon, or the patient. To understand this interrelationship a uniaxial discretised model of the hammer/introducer/implant/bone/soft-tissues was developed. A parametric analysis of applied energy, component materials and geometry, and interaction between implant-bone and bone-soft-tissue was performed, with implant seating and component stresses as outcome variables. ResultsTo reduce stresses without compromising seating, the following outcomes were observed: Less energy per hit with more hits / Increase hammer mass / Decrease introducer mass / Increase implant-bone resistance (eg stem roughness). Material stiffness and patient mechanics were found to be less important.ConclusionsThis simple model provides a basic understanding of how stress waves travel through the impacted system, and an understanding of their relevance to component design.
Eighty surveys of ten Scottish beaches recorded litter sizes and weights. A simple model of fragmentation explains the distribution of plastic beach litter weights, producing a logarithmic cascade in weight-frequencies having a power law exponent of 1.6. Implications of fragmentation are numerous. Heavy litter is rare, light fragments are common. Monitoring by number is sensitive to minimum observable fragment size, age of the litter, and energy of the foreshore. Mean litter item weights should be used to calculate beach plastic loadings. Presence/absence of mega litter can distort monitoring by weight. Multiple surveys are needed to estimate mega litter statistics. Monitoring by weight can change the perception of the importance of litter sources (e.g., in our surveys, contribution from fishing was 6% by number, 41% by weight). In order to introduce consistency between beach surveys using visual methods by number, a standard minimum plastic fragment size should be introduced.
We compare the statistical distributions of the geometrical properties of road networks for two representative datasets under different levels of planning: the cities comprising Metropolitan Manila show the conditions under bottom-up self-organized growth, while Brasilia and the Australian Capital Territory centered at Canberra represent the case of strict top-down planning. The distribution of segmented areas of the cities shows a dual power-law behavior, with the larger areas following the ∼1.9 scaling exponent observed in other cities, while the smaller areas show a lower exponent of ∼0.5, believed to be due to practical considerations. While all cities are found to favor the formation of straight road segments, the planned city roads have a preponderance of sinuous roads, with sinuosities approaching π. A simple model based on a nearest-neighbor directed branching coupled with sectional grid formations is proposed to capture the nontrivial statistical features observed.
AbstractSeveral real-world situations can be represented in terms of agents that have preferences over activities in which they may participate. Often, the agents can take part in at most one activity (for instance, since these take place simultaneously), and there are additional constraints on the number of agents that can participate in an activity. In such a setting, we consider the task of assigning agents to activities in a reasonable way. We introduce the simplified group activity selection problem providing a general yet simple model for a broad variety of settings, and start investigating its special case where upper and lower bounds of the groups have to be taken into account. We apply different solution concepts such as envy-freeness and core stability to our setting and provide a computational complexity study for the problem of finding such solutions.