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;

Influence properties of partial least squares regression.

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

Document markup - Why? How?

"In this paper the author argues that markup and writing belong to related systems for storing information and/ or speech and that there is no clear border between the two. In addition he argues that marking up text done as more or less separate from ordinary writing has been used in Western scholarly work at least since the times of the library in the Museum in Alexandria and up until today. Markup means that some part of a document is identified and some statement is made about the linguistic and/ or textual status and interpretative frame of that part or it is extracted for some scholarly purpose. The ways and means by which this is done may vary. It will depend both on the aim: why exactly do we wish to identify this part of the text? And on the technology available: papyrus scrolls and reed pens make for different markup than what is done with computer stored texts. In this paper selected uses for digital text and markup are discussed with examples mainly taken from the electronic edition of Henrik Ibsen's Writings." (author's abstract

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;

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;

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

Valence band study of thermoelectric Zintl-phase SrZn_2Sb_2 and YbZn_2Sb_2: X-ray photoelectron spectroscopy and density functional theory

The electronic structure of SrZn_2Sb_2 and YbZn_2Sb_2 is investigated using density functional theory and high-resolution x-ray photoemission spectroscopy. Both traditional Perdew-Burke-Ernzerhof and state-of-the-art hybrid Heyd-Scuseria-Ernzerhof functionals have been employed to highlight the importance of proper treatment of exchange-dependent Zn  3d states, Yb 4f states, and band gaps. The role of spin-orbit corrections in light of first-principles transport calculations are discussed and previous claims of Yb^(3+) valence are investigated with the assistance of photoelectron as well as scanning and transmission electron microscopy