Optimal spline spaces for L2L^2 nn-width problems with boundary conditions

In this paper we show that, with respect to the $L^2$ norm, three classes of functions in $H^r(0,1)$, defined by certain boundary conditions, admit optimal spline spaces of all degrees $\geq r-1$, and all these spline spaces have uniform knots.Comment: 17 pages, 4 figures. Fixed a typo. Article published in Constructive Approximatio

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;

Partial robust M-regression.

Partial Least Squares (PLS) is a standard statistical method in chemometrics. It can be considered as an incomplete, or 'partial', version of the Least Squares estimator of regression, applicable when high or perfect multicollinearity is present in the predictor variables. The Least Squares estimator is well-known to be an optimal estimator for regression, but only when the error terms are normally distributed. In the absence of normality, and in particular when outliers are in the data set, other more robust regression estimators have better properties. In this paper a 'partial' version of M-regression estimators will be defined. If an appropriate weighting scheme is chosen, partial M-estimators become entirely robust to any type of outlying points, and are called Partial Robust M-estimators. It is shown that partial robust M-regression outperforms existing methods for robust PLS regression in terms of statistical precision and computational speed, while keeping good robustness properties. The method is applied to a data set consisting of EPXMA spectra of archaeological glass vessels. This data set contains several outliers, and the advantages of partial robust M-regression are illustrated. Applying partial robust M-regression yields much smaller prediction errors for noisy calibration samples than PLS. On the other hand, if the data follow perfectly well a normal model, the loss in efficiency to be paid for is very small.Advantages; Applications; Calibration; Data; Distribution; Efficiency; Estimator; Least-squares; M-estimators; Methods; Model; Optimal; Ordinary least squares; Outliers; Partial least squares; Precision; Prediction; Projection-pursuit; Regression; Robust regression; Robustness; Simulation; Spectometric quantization; Squares; Studies; Variables; Yield;

Influence properties of partial least squares regression.

Regression; Partial least squares; Least-squares; Squares; Squares regression;

Corporate restructuring

We survey the empirical literature on corporate nancial restructuring, including breakup transactions (divestitures, spin-o s, equity carveouts, tracking stocks), leveraged recapitalizations, and leveraged buyouts (LBOs). For each transaction type, we survey techniques, deal nancing, transaction volume, valuation e ects and potential sources of restructuring gains. Many breakup transactions are a response to excessive conglomeration and reverse costly diversi cation discounts. The empirical evidence shows that the typical restructuring creates substantial value for shareholders. The value-drivers include elimination of costly cross-subsidizations characterizing internal capital markets, reduction in nancing costs for subsidiaries through asset securitization and increased divisional transparency, improved (and more focused) investment programs, reduction in agency costs of free cash ow, implementation of executive compensation schemes with greater pay-performance sensitivity, and increased monitoring by lenders and LBO sponsors. Buyouts after the turn of the century created value similar to LBOs of the 1980s. Recent developments include consortiums of private equity funds (club deals), exits through secondary buyouts (sale to another LBO fund), and evidence of persistence in fund returns. LBO deal nancing has evolved towards lower leverage ratios. In Europe, recent deals are nanced with less leveraged loans and mezzanine debt and more high-yield debt than before. Future research challenges include integrating analyses across transaction types and nancing mixes, and producing unbiased estimates of the expected return from buyout investments in the presence of limited data on portfolio companies that do not return to public status

Ca_3AlSb_3: an inexpensive, non-toxic thermoelectric material for waste heat recovery

Thermoelectric materials directly convert thermal energy into electrical energy, offering a promising solid-state solution for waste heat recovery. For thermoelectric devices to make a significant impact on energy and the environment the major impediments are the efficiency, availability and toxicity of current thermoelectric materials. Typically, efficient thermoelectric materials contain heavy elements such as lead and tellurium that are toxic and not earth abundant. Many materials with unusual structures containing abundant and benign elements are known, but remain unexplored for thermoelectric applications. In this paper we demonstrate, with the discovery of high thermoelectric efficiency in Ca_3AlSb_3, the use of elementary solid-state chemistry and physics to guide the search and optimization of such materials

Robust continuum regression.

Several applications of continuum regression (CR) to non-contaminated data have shown that a significant improvement in predictive power can be obtained compared to the three standard techniques which it encompasses (ordinary least squares (OLS), principal component regression (PCR) and partial least squares (PLS)). For contaminated data continuum regression may yield aberrant estimates due to its non-robustness with respect to outliers. Also for data originating from a distribution which significantly differs from the normal distribution, continuum regression may yield very inefficient estimates. In the current paper, robust continuum regression (RCR) is proposed. To construct the estimator, an algorithm based on projection pursuit (PP) is proposed. The robustness and good efficiency properties of RCR are shown by means of a simulation study. An application to an X-ray fluorescence analysis of hydrometallurgical samples illustrates the method's applicability in practice.Regression; Applications; Data; Ordinary least squares; Least-squares; Squares; Partial least squares; Yield; Outliers; Distribution; Estimator; Projection-pursuit; Robustness; Efficiency; Simulation; Studies;

Robust continuum regression.

Several applications of continuum regression to non-contaminated data have shown that a significant improvement in predictive power can be obtained compared to the three standard techniques which it encompasses (Ordinary least Squares, Principal Component Regression and Partial Least Squares). For contaminated data continuum regression may yield aberrant estimates due to its non-robustness with respect to outliers. Also for data originating from a distribution which significantly differs from the normal distribution, continuum regression may yield very inefficient estimates. In the current paper, robust continuum regression (RCR) is proposed. To construct the estimator, an algorithm based on projection pursuit is proposed. The robustness and good efficiency properties of RCR are shown by means of a simulation study. An application to an X-ray fluorescence analysis of hydrometallurgical samples illustrates the method's applicability in practice.Advantages; Applications; Calibration; Continuum regression (CR); Data; Distribution; Efficiency; Estimator; Least-squares; M-estimators; Methods; Model; Optimal; Ordinary least squares; Outliers; Partial least squares; Precision; Prediction; Projection-pursuit; Regression; Research; Robust continuum regression (RCR); Robust multivariate calibration; Robust regression; Robustness; Simulation; Squares; Studies; Variables; Yield;

Merger negotiations with stock market feedback

Merger negotiations routinely occur amidst economically significant a target stock price runups. Since the source of the runup is unobservable (is it a target stand-alone value change and/or deal anticipation?), feeding the runup back into the offer price risks "paying twice" for the target shares. We present a novel structural empirical analysis of this runup feedback hypothesis. We show that rational deal anticipation implies a nonlinear relationship between the runup and the offer price markup (offer price minus runup). Our large-sample tests confirm the existence of this nonlinearity and reject the feedback hypothesis for the portion of the runup not driven by the market return over the runup period. Also, rational bidding implies that bidder takeover gains are increasing in target runups, which our evidence supports. Bidder toehold acquisitions in the runup period are shown to fuel target runups, but lower rather than raise offer premiums. We conclude that the parties to merger negotiations interpret market-adjusted target runups as reflecting deal anticipation.Merger negotiations; stock market feedback