The Influence Function of Penalized Regression Estimators

To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse least trimmed squares (LTS) estimator have been proposed. The robustness of these regression methods can be measured with the influence function. It quantifies the effect of infinitesimal perturbations in the data. Furthermore it can be used to compute the asymptotic variance and the mean squared error. In this paper we compute the influence function, the asymptotic variance and the mean squared error for penalized M-estimators and the sparse LTS estimator. The asymptotic biasedness of the estimators make the calculations nonstandard. We show that only M-estimators with a loss function with a bounded derivative are robust against regression outliers. In particular, the lasso has an unbounded influence function.Comment: appears in Statistics: A Journal of Theoretical and Applied Statistics, 201

Influence functions, followers and command games

We study and compare two frameworks: a model of influence, and command games. In the influence model, in which players are to make a certain acceptance/rejection decision, due to influence of other players, the decision of a player may be different from his inclination. We study a relation between two central concepts of this model: influence function, and follower function. We deliver sufficient and necessary conditions for a function to be a follower function, and we describe the structure of the set of all influence functions that lead to a given follower function. In the command structure introduced by Hu and Shapley, for each player a simple game called the command game is built. One of the central concepts of this model is the concept of command function. We deliver sufficient and necessary conditions for a function to be a command function,and describe the minimal sets generating a normal command game. We also study the relation between command games and influence functions. A sufficient and necessary condition for the equivalence between an influence function and a normal command game is delivered.influence function, follower function, lower and upper inverses, kernel, command game, command function, minimal sets generating a command game

Influence of human pressures on large river structure and function

A large river study was conducted as part of the Cross Departmental Research Pool (CDRP) ecological integrity project to (i) provide an overview of the macroinvertebrate faunas of large rivers, including those in deep-water habitats, and (ii) to elucidate links between these faunas, river function and anthropogenic stressors. Eleven sites on 6th-order or 7th-order rivers were sampled; four in the South Island and seven in the North Island. We measured (i) macroinvertebrate communities colonising wood, riffles (where present), littoral habitats (1.5 m deep) (ii) ecosystem metabolism using a single-station open-channel approach based on natural changes in dissolved oxygen concentration over a 24-hour period, and (iii) wood and cellulose breakdown. Relationships were investigated between these response variables and reach-scale assessments of habitat quality, underlying upstream and segment environmental variables provided in the Freshwater Environments of New Zealand (FWENZ) database, and anthropogenic pressure variables provided by the Waters of National Importance (WONI) database

Material removal investigation in bonnet polishing of CoCr alloy

The manufacture of orthopaedic joint bearings surfaces requires exceptionally high levels of control of not only the surface finish but also the surface form. In the case of hip joints, the form of femoral head should be controlled to within ± 50ìm from a given diameter. It has been shown that a better form control of bearing component could enhance clearances creating the correct volume of lubrication to fill the bearing surface gap and reduce wear particle generation. This element is especially critical for the new generation non-spherical head designs. Bonnet polishing which is used successfully in the area of optics is potentially an excellent finishing process to control the form and finish of artificial joints. In the process of form control polishing an “influence function” which defines the material removal rate is of vital importance in developing a corrective polishing procedure. However, the effects of polishing parameters (such as precess angle, head speed, tool pressure and tool offset) on influence function are not very clear for CoCr alloys. These elements must be assessed if a deterministic polishing process is to be developed. Therefore, it is of paramount importance to understand the contribution of each polishing factors to influence function and consequent part polishing. This study has investigated the effects of polishing parameters on influence function, including geometric size and volumetric material removal rate (MRR). The experimental results indicate that the polishing parameter of precess angle and tool offset affect the geometric size of influence function significantly; the polishing parameter of head speed and tool pressure affect the geometric size of influence function to a lesser degree; the polishing parameter of precess angle, head speed and tool offset affect MRR greatly

Influence properties of partial squares regression.

In this paper, we compute the influence function for partial least squares regression. Thereunto, we design two alternative algorithms, according to the PLS algorithm used. One algorithm for the computation of the influence function is based on the Helland PLS algorithm, whilst the other is compatible with SIMPLS.The calculation of the influence function leads to new influence diagnostic plots for PLS. An alternative to the well known Cook distance plot is proposed, as well as a variant which is sample specific.Moreover, a novel estimate of prediction variance is deduced. The validity of the latter is corroborated by dint of a Monte Carlo simulation.Influence function; Design; Algorithms; Simulation;

Why Trade Associations Matter: Exploring Function, Meaning, and Influence

We explore the organizational characteristics of trade associations (TAs) and suggest theoretical approaches for undertaking research into or involving TAs in management and organization studies. Through emphasizing the role of TAs within and between industries and at the interface of business and society, we consider how TAs generate meaning and influence