Significance Regression: Robust Regression for Collinear Data

This paper examines robust linear multivariable regression from collinear data. A brief review of M-estimators discusses the strengths of this approach for tolerating outliers and/or perturbations in the error distributions. The review reveals that M-estimation may be unreliable if the data exhibit collinearity. Next, significance regression (SR) is discussed. SR is a successful method for treating collinearity but is not robust. A new significance regression algorithm for the weighted-least-squares error criterion (SR-WLS) is developed. Using the weights computed via M-estimation with the SR-WLS algorithm yields an effective method that robustly mollifies collinearity problems. Numerical examples illustrate the main points

Significance Regression: A Statistical Approach to Biased Linear Regression and Partial Least Squares

This paper first examines the properties of biased regressors that proceed by restricting the search for the optimal regressor to a subspace. These properties suggest features such biased regression methods should incorporate. Motivated by these observations, this work proposes a new formulation for biased regression derived from the principle of statistical significance. This new formulation, significance regression (SR), leads to partial least squares (PLS) under certain model assumptions and to more general methods under various other model kumptions. For models with multiple outputs, SR will be shown to have certain advantages over PLS. Using the new formulation a significance test is advanced for determining the number of directions to be used; for PLS, cross-validation has been the primary method for determining this quantity. The prediction and estimation properties of SR are discussed. A brief numerical example illustrates the relationship between SR and PLS

μ-sensitivities as an aid for robust identification

Identification for a model for robust control design is more complicated than for the standard linear system transfer function model-the structure of the uncertainty as well as bounds on its size must be determined. It is especially unclear as to which parts of the system should be better modeled to improve robust performance. This paper addresses this question through some new tools, the μ-sensitivities

Significance Regression: Improved Estimation from Collinear Data for the Measurement Error Model

This paper examines improved regression methods for the linear multivariable measurement error model (MEM) when the data suffers from "collinearity." The difficulty collinearity presents for reliable estinlation is discussed and a systematic procedure, significance regression (SR-MEM), is developed to address collinearity. In addition to mitigating collinearity difficulties SR-MEM produces asymptotically unbiased estimates. The use of ordinary least squares (OLS) for the MEM is examined. For collinear data OLS can improve the mean squared error of estimation over the maximum likelihood (ML) unbiased estimator in a manner analogous to ridge regression (RR). The significance regression method developed for the classical model (SR-classical) can also be used for data with measurement errors. SR-classical is similar SR-MEM and can yield better estimation than the ML estimator for collinear data. Numerical examples illustrate several points

Fertimetro, a Principle and Device to Measure Soil Nutrient Availability for Plants by Microbial Degradation Rates on Differently-Spiked Buried Threads

A novel patented method (PCT/IB2012/001157: Squartini, Concheri, Tiozzo, University of Padova) and the corresponding application devices, suitable to measure soil fertility, are presented. The availability or deficiency of specific nutrients for crops is assessed by monitoring the kinetics of progressive weakening of cotton or silk threads due to in situ microbial activity. The method is based on a nutrient-primed incremented substrate degradation principle. Threads are buried as is or pre-impregnated with N or P solutions, and the acceleration of the degradation rate for the N-supplemented or P-supplemented thread, in comparison to the untreated thread, is proportional to the lack of the corresponding nutrient in that soil. Tests were validated on corn crops in plots receiving increasing fertilizer rates in a historical rotation that has been established since 1962. The measurement carried out in May significantly correlated with the subsequent crop yields recorded in October. The analysis allows an early, inexpensive, fast, and reproducible self-assessment at field level to improve fertilization rates. The device is envisaged as a user-friendly tool for agronomy, horticulture, and any environmental applications where organic matter cycling, soil quality, and specific nutrients excess or deficiency are critical considerations

Experimental and theoretical analysis of the upper critical field in FSF trilayers

The upper critical magnetic field H_{c2} in thin-film FSF trilayer spin-valve cores is studied experimentally and theoretically in geometries perpendicular and parallel to the heterostructure surface. The series of samples with variable thicknesses of the bottom and of the top Cu_{41}Ni_{59} F-layers are prepared in a single run, utilizing a wedge deposition technique. The critical field H_{c2} is measured in the temperature range $0.4-8$ K and for magnetic fields up to 9 Tesla. A transition from oscillatory to reentrant behavior of the superconducting transition temperature versus F-layers thickness, induced by an external magnetic field, has been observed for the first time. In order to properly interpret the experimental data, we develop a quasiclassical theory, enabling one to evaluate the temperature dependence of the critical field and the superconducting transition temperature for an arbitrary set of the system parameters. A fairly good agreement between our experimental data and theoretical predictions is demonstrated for all samples, using a single set of fit parameters. This confirms adequacy of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) physics in determining the unusual superconducting properties of the studied Cu_{41}Ni_{59}/Nb/Cu_{41}Ni_{59} spin-valve core trilayers.Comment: 16 pages, 7 figures; published versio