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The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a class of random Laplacian matrices with independent off-diagonal entries, this bound is essentially tight: the largest eigenvalue is, up to lower order terms, often the size of the largest diagonal. entry. Besides being a simple tool to obtain precise estimates on the largest eigenvalue of a class of random Laplacian matrices, our main result settles a number of open problems related to the tightness of certain convex relaxation-based algorithms. It easily implies the optimality of the semidefinite relaxation approaches to problems such as [Formula omitted] Synchronization and stochastic block model recovery. Interestingly, this result readily implies the connectivity threshold for Erdos-Rényi graphs and suggests that these three phenomena are manifestations of the same underlying principle. The main tool is a recent estimate on the spectral norm of matrices with independent entries by van Handel and the author., Author(s): Afonso S. Bandeira [sup.1] Author Affiliations: (Aff1) 0000 0004 1936 8753, grid.137628.9, Department of Mathematics and Center for Data Science, Courant Institute of Mathematical Sciences, New York University, , [...]

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings. However, many problems arising from statistics, image processing and other fields have the structure that while one of the two functions has an easy proximal mapping, the other function is smoothly convex but does not have an easy proximal mapping. Therefore, the classical alternating direction methods cannot be applied. To deal with the difficulty, we propose in this paper an alternating direction method based on extragradients. Under the assumption that the smooth function has a Lipschitz continuous gradient, we prove that the proposed method returns an [Formula omitted]-optimal solution within [Formula omitted] iterations. We apply the proposed method to solve a new statistical model called fused logistic regression. Our numerical experiments show that the proposed method performs very well when solving the test problems. We also test the performance of the proposed method through solving the lasso problem arising from statistics and compare the result with several existing efficient solvers for this problem; the results are very encouraging., Author(s): Tianyi Lin [sup.1] , Shiqian Ma [sup.1] , Shuzhong Zhang [sup.2] Author Affiliations: (1) 0000 0004 1937 0482grid.10784.3aDepartment of Systems Engineering and Engineering Management, The Chinese University of Hong [...]

Traditional regression assumes that the only data available are measurements of the value of the dependent variable for each combination of values for the independent variable. However, in many settings [...]

This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis provides sharp results on the 'out-of-sample' prediction error, as opposed to the 'in- sample' (fixed design) error. The analysis also reveals the effect of errors in the estimated covariance structure, as well as the effect of modeling errors, neither of which effects are present in the fixed design setting. The proofs of the main results are based on a simple decomposition lemma combined with concentration inequalities for random vectors and matrices. Keywords Linear regression * Ordinary least squares * Ridge regression * Randomized approximation, Mathematics Subject Classification Primary 62J07 * Secondary 62J05 1 Introduction In the random design setting for linear regression, we are provided with samples of covariates and responses, ([x.sub.1], [y.sub.1]), ([x.sub.2], [...]

In forest inventories, it is often of interest to calculate amounts of usable wood volume in trees. This usually requires knowledge of how much of the total volume is unusable (cull) due to form or decay deficiencies. This information is primarily obtained when collecting data on sample plots, although the assessments are often difficult and subjective. To provide an alternative, methods were developed to estimate individual-tree cull attributes. The procedure initially involves classification using logistic regression to assign trees to one of three categories (no cull, intermediate cull, entirely cull) based on probability cut points. Subsequently, trees classified as having intermediate cull are assigned a cull amount predicted from a generalized linear regression model. The best results for cull prediction were obtained using cut points that minimized absolute prediction error; however, better prediction of net cubic volume of trees was realized when the errors were weighted by tree size. The model-based approach may be particularly useful in obtaining temporal consistency, such that trend estimates may better reflect the actual change in forest resources. Resume: Dans les inventaires forestiers, on est souvent interesse a calculer le volume de bois utilisable dans les arbres. Cela exige habituellement de connaitre la proportion du volume total qui n'est pas utilisable (rebut) a cause de la forme ou de la carie. Cette information est obtenue principalement lors de la collecte de donnees dans des placettes echantillons mais l'evaluation est souvent difficile et subjective. Dans le but d'offrir une alternative, des methodes ont ete developpees pour estimer les attributs du rebut d'arbres individuels. La procedure implique d'abord une classification a l'aide d'une regression logistique pour repartir les arbres dans trois categories (pas de rebut, partiellement rebut, totalement rebut) sur la base de points de decoupage des probabilites. Par la suite, les arbres places dans la classe intermediaire se voient attribuer une quantite de rebut predite par un modele de regression generalise. Les meilleurs resultats pour la prediction de la quantite de rebut ont ete obtenus en utilisant des points de decoupage qui minimisent l'erreur de prediction absolue. Cependant, la prediction du volume net des arbres etait meilleure lorsque les erreurs etaient ponderees par la dimension des arbres. L'approche fondee sur une modele peut etre particulierement utile pour assurer une coherence temporelle de telle sorte que les estimations de la tendance puissent mieux refleter les changements reels dans les ressources forestieres. [Traduit par la Redaction], Introduction One of the most important aspects of forest inventory is estimating tree volume. More specifically, of interest is determining the amount of usable material for specified wood products. Two [...]

We consider two-phase sampling schemes where one component of the auxiliary information is known in every point ('wall-to-wall') and a second component is available only in the large sample of the first phase, whereas the second phase yields a subsample with the terrestrial inventory. This setup is of growing interest in forest inventory thanks to the recent advances in remote sensing, in particular, the availability of LiDAR data. We propose a new two-phase regression estimator for global and local estimation and derive its asymptotic design-based variance. The new estimator performs better than the classical regression estimator. Furthermore, it can be generalized to cluster sampling and two-stage tree sampling within plots. Simulations and a case study with LiDAR data illustrate the theory. Resume: Cet article propose un nouvel estimateur pour les inventaires forestiers utilisant des plans de sondage a deux phases pour lesquels l'information auxiliaire consiste en une premiere composante exhaustive connue en chaque point et une seconde composante connue seulement aux points du grand echantillon de la premiere phase. La deuxieme phase consiste en un sous-echantillon des points de la premiere phase dans lesquels l'inventaire terrestre est effectue. Ce contexte est appele a jour un role croissant grace aux developpements recents dans l'aquisition de donnees par teledetection. Nous proposons un nouvel estimateur par regression, aussi bien pour l'estimation globale que locale, et nous donnons sa variance asymptotique sous le plan de sondage. Le nouvel estimateur peut etre adapte aux inventaire par satellites et avec tirage double des arbres au niveau de la placette terrestre. Un exemple utilisant des donnees LiDAR et des simulations illustrent la theorie. Le nouvel estimateur a de meilleures performance que l'estimateur de regression classique., 1. Introduction The motivation for this work is due to the increasing need for using national or regional inventories for local estimation to meet tighter budgetary constraints, which is only [...]

The Q-e scheme is remarkably useful in interpreting and predicting the reactivity of a monomer in free radical copolymerizations. In the present work, two support vector regression (SVR) models were developed to predict parameters Q and e in the Q-e scheme. Quantum chemical descriptors used to build SVR models were calculated, for the first time, from transition state species with structures [C.sup.1][H.sub.3]--[C.sup.2][HR.sup.3]* or *[C.sup.1][H.sub.2]--[C.sup.2][H.sub.2][R.sup.3], formed from vinyl monomer [C.sub.1][H.sub.2] = [C.sup.2]H[R.sup.3] + H*. The optimal v-SVR model of lnQ (C = 130, v = 0.2, and γ = 1.0) based on 70 monomers has the root mean square (rms) error of 0.336 and correlation coefficient (R) of 0.982. The optimal ζ-SVR model of e (C = 1.2, γ = 3, and ζ = [10.sup.-2]) produces rms = 0.259 and R = 0.963. Compared with previous models, the SVM models in this article have better predictive performance. Results of the study suggest that calculating quantum chemical descriptors from the transition state structures to predict parameters Q and e in the Q-e scheme is feasible. This investigation encourages the further application of transition state descriptors to other quantitative structure-activity relationships (QSARs). POLYM. ENG. SCI., 53:2151-2158, 2013. @ 2013 Society of Plastics Engineers, INTRODUCTION As the most widely used general reactivity scheme, the Q--e scheme is remarkably useful in interpreting and predicting the reactivity of a monomer containing a double bond in radical [...]

Epidemiological studies assessing general and abdominal obesity measures or their combination for mortality prediction have shown inconsistent results. We aimed to systematically review the associations of body mass index (BMI), waist-to-hip ratio (WHR), waist circumference (WC) and waist-to-height ratio (WHtR) with all-cause mortality in prospective cohort studies. In this systematic review, which includes a meta-regression analysis, we analysed the associations with all-cause mortality of BMI, WHR, WC and WHtR in prospective cohort studies available in Medline, Embase, the Cochrane Database of Systematic Reviews and Esbiobase from inception through 7 May 2010. A total of 18 studies met the inclusion criteria, comprising 689465 participants and 48 421 deaths during 5-24 years of follow-up. The studies were heterogeneous, mainly due to differences in categorization of anthropometric parameters (AP) and different approaches to statistical analysis. Both general and abdominal obesity measures were significantly associated with mortality. In analyses using categorical variables, BMI and WC showed predominantly U- or J-shaped associations with mortality, whereas WHR and WHtR demonstrated positive relationships with mortality. All measures showed similar risk patterns for upper quantiles in comparison to reference quantiles. The parameters of general and abdominal obesity each remained significantly associated with mortality when adjusted for the other. This evidence suggests that abdominal obesity measures such as WC or WHR, show information independent to measures of general obesity and should be used in clinical practice, in addition to BMI, to assess obesity-related mortality in adults. European Journal of Clinical Nutrition (2013) 67, 573-585; doi: 10.1038/ejcn.2013.61; published online 20 March 2013 Keywords: body mass index; waist circumference; waist-to-hip ratio; mortality, INTRODUCTION Obesity is a major public health concern worldwide. (1) According to a recent estimate, there are 1.46 billion overweight adults (body mass index (BMI) ≥ 25 kg/[m.sup.2]) and 503 [...]

The objective of this study is to introduce an effective and practical model, based on non-parametric regression, to instantaneously estimate multivariate imputations replacing multiple missing variables during multiple time periods. The developed model was essentially designed for system-oriented, real-world applications. In an empirical study with real- world data, the proposed model, on the whole, outperformed the seasonal auto-regressive integrated moving average (ARIMA). The analysis of the results indicates that the introduced model was more applicable to multivariate imputation during multiple time intervals than that of ARIMA. In addition, it was revealed that ARIMA could somewhat deform the relationship between the volume (q) and speed (s), whereas the developed model reproduced the q-s relationship more similarly than ARIMA. Moreover, the proposed model is very simple and does not require system operators to input or recalibrate any external parameters because it was developed for applications of real data management systems. Key words: multivariate, multiple time periods, imputation, system-oriented approach, NPR. L'objectif de cette etude est d'introduire un modele efficace et pratique base sur la regression non parametrique pour estimer instantanement les imputations a plusieurs variables remplacant plusieurs variables manquantes durant plusieurs periodes de temps. Le modele developpe etait essentiellement concu pour les applications reelles orientees systeme. Dans une etude empirique avec des donnees reelles, le modele propose a, en general, surclasse le modele ARIMA (autoregressif a moyenne mobile integree) saisonnier. L' analyse des resultats indique que le modele introduit etait plus facilement applicable al' imputation a plusieurs variables durant plusieurs intervalles de temps que ceux de ARIMA. De plus, il a ete decouvert que ARIMA pouvait quelque peu deformer la relation entre le volume (q) et la vitesse (s), alors que le modele developpe reproduisait la relation q-s mieux que ARIMA. De plus, le modele propose est tres simple et n'exige pas que les operateurs systeme entrent ou recalibrent quelque parametre externe que ce soit parce qu'il a ete developpe pour des applications de systemes de gestion de donnees reelles. Mots-cles : variables multiples, periodes de temps multiples, imputation, approche orientee systeme, regression non parametrique (NPR). [Traduit par la Redaction], 1. Introduction The implementation of intelligent transportation systems (ITSs) has made tremendous quantities of historical traffic data available. In many cases, these data are kept in data management systems (DMSs), [...]

CONTEXT: It is generally believed that women's lack of decision-making power may restrict their use of modern contraceptives. However, few studies have examined the different dimensions of women's empowerment and [...]

CONTEXT: In many developing countries, fertility has declined steadily in recent decades, while the average strength of family planning programs has increased and social conditions have improved. However, it is [...]

Sewer deterioration, prevalent in municipalities throughout Canada, prompted the Quebec provincial government to implement a 1% renewal rate of the conduit facilities as to meet the goals of the national water plan adopted in 2002. Some of the most affected municipalities are usually the ones already under tight budget constraints, and cannot therefore afford the use of CCTV inspections in assessing the state of their sewage systems. This paper proposes a probabilistic model devised to survey the current conduit deterioration state caused by maintenance and operational conditions. Based on the multinomial logistic regression, this model--successfully applied to a case study in Quebec--shows the temporal deterioration of conduits for different material types. On average, it correctly predicted 54% of outcomes for transition probabilities involving both condition classes 1 (excellent) and 2 (good), and it showed a 59% correct prediction for class 3 condition (fair). This model is a recommended tool--applicable in combination with current exploratory techniques--for an effective prevention of conduits failure. Key words: sewers, deterioration, logistic regression. La plupart des municipalites au Canada font face a des problemes lies a la deterioration des conduites d'assainissement urbain. Le gouvernement du Quebec demande ainsi aux municipalites de pouvoir atteindre un taux de remplacement annuel de 1 % afin de rencontrer les objectifs du plan national de l'eau lance en 2002. Etant donne les contraintes budgetaires, les municipalites ne sont pas toujours en mesure d'effectuer des inspections televisees (CCTV) afin de prevoir le moment d'intervention dans leurs reseaux. De ce fait, il parait tout indique d'elaborer un modele probabiliste devant permettre de determiner le niveau d'operation et d'entretien des conduites. Base sur la regression logistique multinomiale, le modele developpe dans cette etude evalue la deterioration des conduites des differents materiaux en fonction du temps. Ce modele a permis de predire correctement dans 54 % de cas la probabilite de transition impliquant une conduite a l' etat 1 (excellent) et 2 (bon) alors que 59 % des cas ont ete predits avec succes pour les probabilites de transition impliquant une conduite a l'etat 3 (acceptable) pour deux municipalites du Quebec. Cet outil est suggere pour aider les gestionnaires a anticiper le dysfonctionnement des reseaux. Mots-cles: conduites, degradation de la performance des conduites, regression multinomiale. [Traduit par la Redaction], 1. Introduction Numerous Canadian municipalities are experiencing rapid deterioration and sanitary issues due to their aging sewer networks. In Quebec, the situation is so dire that the provincial government put [...]

It is fundamental for monitoring and assessment of national forest biomass to develop generalized single-tree biomass models suitable for large-scale forest biomass estimation. However, the compatibility of forest biomass estimates among different scales is a real problem. Based on the aboveground biomass data of Masson pine (Pinus massoniana Lamb.) in southern China, generalized single-tree biomass equations applying to national and regional forest biomass estimation were constructed using the dummy variable model method, which provided an effective approach to solving the compatibility of forest biomass estimates among different scales. The results show that aboveground biomass estimates of individual trees with the same diameter are different to some extent among the forest origins and geographic regions and that a dummy model with specific (local) parameters is better than a population-average model. The dummy variable model can be applied to develop other generalized compatible models such as tree volume equations. Resume: Il est primordial pour le suivi et l'evaluation de la biomasse des forets nationales de developper des modeles generalises de biomasse d'arbre individuel appropries pour l'estimation de la biomasse forestiere a grande echelle. Cependant, la compatibilite des estimations de biomasse forestiere entre differentes echelles est un reel probleme. Sur la base de donnees de biomasse aerienne du pin de Masson (Pinus massoniana Lamb.) dans le sud de la Chine, des equations generales de biomasse d'arbre individuel, applicables a l'estimation de la biomasse forestiere regionale et nationale, ont ete elaborees a l'aide de la methode des variables instrumentales. Cette approche s'est averee efficace pour resoudre le probleme de compatibilite entre les estimations de biomasse forestiere a differentes echelles. Les resultats montrent que les estimations de biomasse aerienne d'arbres individuels qui ont le meme diametre sont dans une certaine mesure differentes selon l'origine de la foret et la region geographique, et que le modele qui contient des variables fictives avec des parametres specifiques (locaux) est meilleur qu'un modele de moyenne de population. Le modele qui comprend des variables fictives peut etre utilise pour developper d'autres modeles generaux compatibles tels que les equations du volume des arbres. [Traduit par la Redaction], Introduction Because forest ecosystems play irreplaceable roles in regulating global carbon balance and mitigating global climate change, forest biomass monitoring is becoming more important (Tomppo et al. 2010). It is [...]

Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a standardized logistic regression coefficient (1) that can be used in the same way across a broad range of problems as the standardized linear regression coefficient and also to suggest the adequacy of other approaches for limited purposes. This article reviews the state of knowledge regarding the use of standardized coefficients in general and standardized logistic regression coefficients in particular, and makes specific recommendations on how to best use (and avoid abusing) standardized logistic regression coefficients., In the social and behavioral sciences, there is extensive use of models (interpreted usually as predictive and frequently as causal) involving a single dependent (outcome, response, criterion) variable and two [...]

This paper presents a novel control-oriented model of the raw emissions of diesel engines. An extended quasistationary approach is developed where some engine process variables, such as combustion or cylinder charge characteristics, are used as inputs. These inputs are chosen by a selection algorithm that is based on genetic-programming techniques. Based on the selected inputs, a hybrid symbolic regression algorithm generates the adequate nonlinear structure of the emission model. With this approach, the model identification efforts can be reduced significantly. Although this symbolic regression model requires fewer than eight parameters to be identified, it provides results comparable to those obtained with artificial neural networks. The symbolic regression model is capable of predicting the behavior of the engine in operating points not used for the model parametrization, and it can be adapted easily to other engine classes. Results from experiments under steady-state and transient operating conditions are used to show the accuracy of the presented model. Possible applications of this model are the optimization of the engine system operation strategy and the derivation of virtual sensor designs. [DOI: 10.1115/1.3204510]

Abstract Infants' auditory processing abilities have been shown to predict subsequent language development. In addition, poor auditory processing skills have been shown for some individuals with specific language impairment. Methods [...]

A common objective in designing for human variability is to consider the variability in body size and shape of the target user population. Since anthropometric data specific to the user population of interest are seldom available, the variability is approximated. This is done in a number of ways, including the use of data from populations that are well-documented (e.g., the military, proportionality constants, and digital human models. These approaches have specific limitations, including a failure to consider the effects of lifestyle and demography, resulting in products, tasks, and environments that are inappropriately sized for the actual user population, causing problems with safety, fit, and performance. This paper explores a regression-based approach in a context where the demographic distributions of descriptors (e.g., race/ethnicity, age, and fitness) are dissimilar for the database and target population. Also examined is a stratified regression model involving the development of independent anthropometry-estimation models for each racial group. When using regression with residual variance, stratification on the predictor demographics to obtain estimates of gender, stature, and BMI distributions is shown to be sufficiently robust for usual database-target population combinations. Consideration of demographic variables in development of the regression model provides marginal improvement, but could be appropriate in specific situations. [DOI: 10.1115/1.4000831]

A modified Regression Error Specification Test (RESET) with a central chi-square limit distribution is presented. The modified test is used to study purchasing power parity in five countries.

Many investigators use the reduced major axis (RMA) instead of ordinary least squares (OLS) to define a line of best fit for a bivariate relationship when the variable represented on the X-axis is measured with error. OLS frequently is described as requiring the assumption that X is measured without error while RMA incorporates an assumption that there is error in X. Although an RMA fit actually involves a very specific pattern of error variance, investigators have prioritized the presence versus the absence of error rather than the pattern of error in selecting between the two methods. Another difference between RMA and OLS is that RMA is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which is Y, while OLS is asymmetric, so that the slope and resulting interpretation of the data are changed when the variables assigned to X and Y are reversed. The concept of error is reviewed and expanded from previous discussions, and it is argued that the symmetry-asymmetry issue should be the criterion by which investigators choose between RMA and OLS. This is a biological question about the relationship between variables. It is determined by the investigator, not dictated by the pattern of error in the data. If X is measured with error but OLS should be used because the biological question is asymmetric, there are several methods available for adjusting the OLS slope to reflect the bias due to error. RMA is being used in many analyses for which OLS would be more appropriate. KEY WORDS regression; error variance; least-squares; statistics DOI 10.1002/ajpa.21090

Quantifying the mechanical properties of nanomaterials is challenged by its small size, difficulty of manipulation, lack of reliable measurement techniques, and grossly varying measurement conditions and environment. A recently proposed approach is to estimate the elastic modulus from a force-deflection physical model based on the continuous bridged-deformation of a nanobelt/nanowire using an atomic force microscope tip under different contact forces. However, the nanobelt may have some initial bending, surface roughness and imperfect physical boundary conditions during measurement, leading to large systematic errors and uncertainty in data quantification. In this article, a statistical modeling technique, sequential profile adjustment by regression (SPAR), is proposed to account for and eliminate the various experimental errors and artifacts. SPAR can automatically detect and remove the systematic errors and therefore gives more precise estimation of the elastic modulus. This research presents an innovative approach that can potentially have a broad impact in quantitative nanomechanics and nanoelectronics. model selection | nanomechanics | nanostructure | profile adjustment | regression modeling

In this paper, we consider a periodic review inventory problem where demand in each period is modeled by linear regression. We use a Bayesian formulation to update the regression parameters as new information becomes available. We find that a state-dependent base-stock policy is optimal and we give structural results. One interesting finding is that our structural results are not analogous to classical results in Bayesian inventory research. This departure from classical results is due to the role that the independent variables play in the Bayesian regression formulation. Because of the computational complexity of the optimal policy, we propose a combination of two heuristics that simplifies the Bayesian inventory problem. Through analytical and numerical evaluation, we find that the heuristics provide near-optimal results. Key words: Bayesian regression; inventory production; stochastic models; approximations heuristics History: Received July 27, 2006; accepted November 24, 2008, by Paul H. Zipkin, operations and supply chain management. Published online in Articles in Advance March 6, 2009., 1. Introduction Regression models forecast a variable by estimating its relationship to other variables. It is one of the most widely used statistical tools and is often applied to forecast [...]

We present a case study demonstrating that without data and code archives reproducibility is more the exception than the rule, especially if modern, complex algorithms are employed. Specifically, we show that stochastic extensions of OLS, as required in some combinatorial optimization problems arising in high-breakdown robust regression, can be difficult to replicate in the absence of detailed information on tuning parameters and further computational issues. Keywords: Combinatorial optimization, least squares, replication, robust regression, stochastic algorithm DOI 10.3233/JEM-2009-0314

The Blinder-Oaxaca (B-O) decomposition has been widely used in continuous outcome comparisons between two groups of people; however, controversies and limitations with this method remain. In this paper, operating under the same-model structure, we suggest employing a multiple regression using a dummy variable to represent discrimination, and we compare this strategy with results obtained from a B-O decomposition and a Neumark decomposition, both in theory and using a simulation study. In addition, we extend these methods to cover binary outcomes. Keywords: Blinder-Oaxaca decompostion, Neumark decomposition, multiple regression, discrimination DOI 10.3233/JEM-2009-0320

In this paper, estimation of a regression function from independent and identically distributed random variables is considered. Estimates are defined by minimization of the empirical [L.sub.2] risk over a class of functions, which are defined as maxima of minima of linear functions. Results concerning the rate of convergence of the estimates are derived. In particular, it is shown that for smooth regression functions satisfying the assumption of single index models, the estimate is able to achieve (up to some logarithmic factor) the corresponding optimal one-dimensional rate of convergence. Hence, under these assumptions, the estimate is able to circumvent the so-called curse of dimensionality. The small sample behavior of the estimates is illustrated by applying them to simulated data. Index Terms--Adaptation, dimension reduction, [L.sub.2] error, nonparametric regression, rate of convergence, single index model.

For years, organizational scholars have sought effective ways to evaluate the importance of predictors included in a regression analysis. Recent techniques, such as general dominance weights and relative weights, have shown great promise for guiding evaluations of predictor importance. Nevertheless, questions remain regarding how one should investigate relative importance in the presence of a multidimensional criterion variable. The purpose of this article is to extend understanding of relative importance statistics to multivariate designs. The authors review the concept of relative importance and discuss a new procedure for calculating estimates of importance in the presence of multiple correlated criteria. Finally, a published correlation matrix is reanalyzed and a Monte Carlo simulation conducted to compare the new procedure with another technique for estimating importance. Unlike canonical solutions, which are often uninterpretable, the proposed multivariate relative weights provide an intuitive index regarding the relationship between predictors and criteria. Implications for organizational researchers are discussed. Keywords: multiple regression, relative importance, relative weights, relative weight analysis, dominance analysis

We examine a consistent test for the correct specification of a regression function with dependent data. The test is based on the supremum of the difference between the parametric and nonparametric estimates of the regression model. Rather surprisingly, the behaviour of the test depends on whether the regressors are deterministic or stochastic. In the former situation, the normalization constants necessary to obtain the limiting Gumbel distribution are data dependent and difficult to estimate, so it may be difficult to obtain valid critical values, whereas, in the latter, the asymptotic distribution may not be even known. Because of that, under very mild regularity conditions, we describe a bootstrap analogue for the test, showing its asymptotic validity and finite sample behaviour in a small Monte-Carlo experiment. Keywords: Functional specification; Variable selection; Nonparametric kernel regression: Frequency domain bootstrap

Flow-through low-pressure chromatographic separations capitalized on the sequential injection chromatographic (SIC) concept are for the first time coupled to second-order multivariate regression models based on multivariate curve resolution-alternating least-squares (MCR-ALS) for outperforming current chromatographic methods in terms of resolution efficiency. The proposed SIC-MCR-ALS method involving sequential injection separation on short monolithic columns along with isocratic elution fosters ultrafast reversed-phase separations of complex multicomponent mixtures regardless of peak overlapping and retention parameters. The ruggedness of SIC systems is enhanced by removing the solenoid valves from the flow network, thus diminishing the column back pressure effects. As a consequence, the flow setup admitted mobile-phase flow rates much higher than those traditionally enabled in SIC. To ascertain the improved peak capacity of the SIC-MCR-ALS procedure, five phenolic species commonly used in disinfectant products and featuring similar UV spectra and close retention times in short reversed-phase silica-based monolithic phases are selected as model compounds and determined in just 1 min using mobile-phase flow rates of [greater than or equal to] 2 mL [min.sup.-1]. Notwithstanding the fact that the five phenolic derivatives co-elute in a single chromatographic band, thus rendering resolution values ranging from 0.05 to 1.11, the concentration profiles and the pure spectra of each individual phenol species could be concurrently obtained. Quantitative validation of the chromatographic-chemometric method demonstrated both the reliability of the results and the enhanced resolution of mixtures with regard to former SIC systems with no need for thorough optimization of the separation conditions.

In this study, we test one aspect of Rodin's hypothesis concerning age-related decline in mastery: The effect of frequent contact with the health care sector on mastery. We conducted cross-sectional and longitudinal multiple regression analyses to examine the effect of general physician (GP) visits on mastery. In the cross-sectional analyses, a higher number of GP visits is associated with lower mastery, but this relationship is substantially weakened when physical health is entered into the analysis. These results are confirmed in the longitudinal analysis. The effect of GP visits on mastery thus appears to be significantly confounded by physical health problems. These findings direct attention away from the role of contact with the health care sector in influencing perceived mastery and toward the importance of physical health status as both a cause and potential consequence of changes in perceived control with age.

The average width of a simultaneous confidence band has been used by several authors (e.g., Naiman and Piegorsch) as a criterion for the comparison of different confidence bands. In this article the area of the confidence set that corresponds to a confidence band is used as a new criterion. For simple linear regression, comparisons have been carried out under this new criterion between hyperbolic bands, two-segment bands, and three-segment bands, which include constant width bands as special cases. It is found that if one requires a confidence band over the whole range of the covariate, then the best confidence band is given by the Working and Hotelling hyperbolic band. Furthermore, if one needs a confidence band over a finite interval of the covariate, then a restricted hyperbolic band can again be recommended, although a three-segment band may be very slightly superior in certain cases. KEY WORDS: Confidence bands; Confidence sets; Probability inequalities; Minimum area; Simple linear regression.

A deterioration model that studies regression models to estimate future asset management expenditure is proposed.

The purpose was to analyze a large-scale database, a national sample of 1,108 heads of households collected by AT&T, to show that behavioral frequencies of the activities of consumer diary panelists may regress toward the population mean during the diary-keeping period given social desirability bias produced by the conditioning effect of keeping diaries. This effect is distinguished from regression toward the mean, a statistical phenomenon reflecting happenstance of extreme initial values. Social desirability bias is demonstrated in two ways--by observing decreasing coefficients of variation over time and by detecting a greater proportion of panelists' behavioral frequencies moving toward the population mean than moving away from it. Both cannot be explained by regression toward the mean. Social desirability bias was manifest only during the early stages of the diary-keeping period and only for activities high in involvement. The presence of social desirability bias in diary panels implies that, when people are subjected to observation, diary observations may be contaminated, leading to the mistaken impression that the population is more homogeneous than it actually is. Thus it is important for researchers to monitor the diary panel carefully to detect social desirability bias when engaged in longitudinal studies.

Impact of linear regression selection for multiple criteria decision making using stochastic methods, is analyzed.

Effectiveness of partially adaptive estimation methods in regression analysis and mathematical modelling is discussed.

A method for validating metamodels during linear regression in simulation is presented.

This article considers the analysis of clustered data via partial linear regression models. Adopting the idea of modeling the within-cluster correlation from the method of generalized estimating equations, a least squares type estimate of the slope parameter is obtained through piecewise local polynomial approximation of the nonparametric component. This slope estimate has several advantages: (a) It attains [n.sup.1/2]-consistency without undersmoothing; (b) it is efficient when correct within-cluster correlation is used, assuming multivariate normality of the error; (c) the preceding properties hold regardless of whether or not the nonparametric component is of cluster level; and (d) this estimation method naturally extends to deal with generalized partial linear models. Simulation studies and a real example are presented in support of the theory. KEY WORDS: Asymptotic bias; Clustered data; Generalized partial linear regression model; Mean squared error; Nonparametric curve estimation; Piecewise local polynomial method.

This article studies the estimation of conditional quantiles of counts. Given the discreteness of the data, some smoothness must be artificially imposed on the problem. We show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques. The performance and implementation of the estimators are illustrated by simulations and an application. KEY WORDS: Jittering; Quantile regression; Smoothing.

This article addresses the problem of finding a relationship between the univariate predictor and the response when regression errors, created in part by known auxiliary covariates, are too large for a reliable regression estimation. A typical example is a controlled random design experiment with a large number of covariates, where the statistician is interested in the effect of a particular covariate and this effect is blurred by a large regression noise created by other covariates. This article develops a theory of asymptotically optimal nonparametric univariate regression estimation in the presence of auxiliary covariates. Here optimality means mimicking the performance of an oracle that knows the effects of auxiliary covariates on the response. The asymptotic theory shows that such an optimal estimation is possible, and also explains how to evaluate the noise created by auxiliary covariates and how to develop an estimator for the interesting case of small sample sizes. The concept of modeling regression noise is well known in analysis of covariance (ANCOVA), and here it is applied in the optimal way to a nonparametric regression setting. A procedure for small sample sizes, denoised scattergram, is tested on simulated examples and a real dataset with 84 observations and 9 auxiliary covariates; the results justify the practical feasibility of the developed method. The method also allows a practitioner to visualize how a dataset would appear if the effects of auxiliary covariates were eliminated and to determine why an exhibited regression function has any given particular shape. Many practical recommendations (in particular, how to use known shape restrictions) are presented and discussed. The asymptotic theory, a numerical study, and analysis of a real dataset indicate that the proposed method of reducing the variance of regression errors created by auxiliary covariances is feasible, is easy to implement, and improves the likelihood of a meaningful regression analysis. KEY WORDS: Analysis of covariance; Asymptotic methods; Curse of multidimensionality; Denoised scattergram; Oracle approach; Small sample size.

175 individuals recruited from urban universities (n = 82) and the surrounding community (120 women, 55 men; 82 18- to 25-yr.-olds, 26 26- to 34-yr.-olds, 44 35- to 50-yr.-olds, 23 50 yr. old or over) completed a sensation seeking scale and measures of the frequency with which they used specific media and selected specific television programming, film, and music genres. Regression analyses showed Sensation Seeking to be associated positively with Movie Theatre Attendance and with the Selection of Urban Music Genres. Sensation Seeking was also associated negatively with Selection of Light Film Genres.