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Squares Estimator (square + estimator)
Kinds of Squares Estimator Selected AbstractsOn the sensitivity of the restricted least squares estimators to covariance misspecificationTHE ECONOMETRICS JOURNAL, Issue 3 2007Alan T.K. Wan Summary, Traditional econometrics has long stressed the serious consequences of non-spherical disturbances for the estimation and testing procedures under the spherical disturbance setting, that is, the procedures become invalid and can give rise to misleading results. In practice, it is not unusual, however, to find that the parameter estimates do not change much after fitting the more general structure. This suggests that the usual procedures may well be robust to covariance misspecification. Banerjee and Magnus (1999) proposed sensitivity statistics to decide if the Ordinary Least Squares estimators of the coefficients and the disturbance variance are sensitive to deviations from the spherical error assumption. This paper extends their work by investigating the sensitivity of the restricted least squares estimator to covariance misspecification where the restrictions may or may not be correct. Large sample results giving analytical evidence to some of the numerical findings reported in Banerjee and Magnus (1999) are also obtained. [source] Real-Time OD Estimation Using Automatic Vehicle Identification and Traffic Count DataCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 1 2002Michael P. Dixon A key input to many advanced traffic management operations strategies are origin,destination (OD) matricies. In order to examine the possibility of estimating OD matricies in real-time, two constrained OD estimators, based on generalized least squares and Kalman filtering, were developed and tested. A one-at-a-time processing method was introduced to provide an efficient organized framework for incorporating observations from multiple data sources in real-time. The estimators were tested under different conditions based on the type of prior OD information available, the type of assignment available, and the type of link volume model used. The performance of the Kalman filter estimators also was compared to that of the generalized least squares estimator to provide insight regarding their performance characteristics relative to one another for given scenarios. Automatic vehicle identification (AVI) tag counts were used so that observed and estimated OD parameters could be compared. While the approach was motivated using AVI data, the methodology can be generalized to any situation where traffic counts are available and origin volumes can be estimated reliably. The primary means by which AVI data was utilized was through the incorporation of prior observed OD information as measurements, the inclusion of a deterministic link volume component that makes use of OD data extracted from the latest time interval from which all trips have been completed, and through the use of link choice proportions estimated based on link travel time data. It was found that utilizing prior observed OD data along with link counts improves estimator accuracy relative to OD estimation based exclusively on link counts. [source] Constrained Kalman Filtering: Additional ResultsINTERNATIONAL STATISTICAL REVIEW, Issue 2 2010Adrian Pizzinga Summary This paper deals with linear state space modelling subject to general linear constraints on the state vector. The discussion concentrates on four topics: the constrained Kalman filtering versus the recursive restricted least squares estimator; a new proof of the constrained Kalman filtering under a conditional expectation framework; linear constraints under a reduced state space modelling; and state vector prediction under linear constraints. The techniques proposed are illustrated in two real problems. The first problem is related to investment analysis under a dynamic factor model, whereas the second is about making constrained predictions within a GDP benchmarking estimation. Résumé Cet article traite des modèles espace-état sujets aux restrictions linéaires générales sur le vecteur d'état. La discussion se concentre autour de quatre aspects: le filtrage de Kalman restreint versus l'estimateur de moindres carrés restreint recursive; une nouvelle preuve du filtrage de Kalman restreint sous le cadre de l'espérance conditionelle; restrictions linéaires aux modèles espace-état réduits; et la prédiction d'état sous restrictions linéaires. Les techniques proposées sont illustrées par deux problèmes réels. Le premier problème est concerné par l'analyse d'investissement sous un modèle à facteur dynamique, tandis que le second concerne les prédictions restreintes dans l'estimation de benchmarking. [source] Asymptotic prediction of mean squared error for long-memory processes with estimated parametersJOURNAL OF FORECASTING, Issue 8 2008Naoya Katayama Abstract In this paper we deal with the prediction theory of long-memory time series. The purpose is to derive a general theory of the convergence of moments of the nonlinear least squares estimator so as to evaluate the asymptotic prediction mean squared error (PMSE). The asymptotic PMSE of two predictors is evaluated. The first is defined by the estimator of the differencing parameter, while the second is defined by a fixed differencing parameter: in other words, a parametric predictor of the seasonal autoregressive integrated moving average model. The effects of misspecifying the differencing parameter is a long-memory model are clarified by the asymptotic results relating to the PMSE. The finite sample behaviour of the predictor and the model selection in terms of PMSE of the two predictors are examined using simulation, and the source of any differences in behaviour made clear in terms of asymptotic theory. Copyright © 2008 John Wiley & Sons, Ltd. [source] Sparse partial least squares regression for simultaneous dimension reduction and variable selectionJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2010Hyonho Chun Summary., Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data. [source] On the non-negative garrotte estimatorJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2007Ming Yuan Summary., We study the non-negative garrotte estimator from three different aspects: consistency, computation and flexibility. We argue that the non-negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form. In particular, we consider using the lasso, the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non-negative garrotte. We prove that the non-negative garrotte has the nice property that, with probability tending to 1, the solution path contains an estimate that correctly identifies the set of important variables and is consistent for the coefficients of the important variables, whereas such a property may not be valid for the initial estimators. In general, we show that the non-negative garrotte can turn a consistent estimate into an estimate that is not only consistent in terms of estimation but also in terms of variable selection. We also show that the non-negative garrotte has a piecewise linear solution path. Using this fact, we propose an efficient algorithm for computing the whole solution path for the non-negative garrotte. Simulations and a real example demonstrate that the non-negative garrotte is very effective in improving on the initial estimator in terms of variable selection and estimation accuracy. [source] First-order rounded integer-valued autoregressive (RINAR(1)) processJOURNAL OF TIME SERIES ANALYSIS, Issue 4 2009M. Kachour Abstract., We introduce a new class of autoregressive models for integer-valued time series using the rounding operator. Compared with classical INAR models based on the thinning operator, the new models have several advantages: simple innovation structure, autoregressive coefficients with arbitrary signs, possible negative values for time series and possible negative values for the autocorrelation function. Focused on the first-order RINAR(1) model, we give conditions for its ergodicity and stationarity. For parameter estimation, a least squares estimator is introduced and we prove its consistency under suitable identifiability condition. Simulation experiments as well as analysis of real data sets are carried out to attest the model performance. [source] Minimum , -divergence estimation for arch modelsJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2006S. Ajay Chandra Abstract., This paper considers a minimum , -divergence estimation for a class of ARCH(p) models. For these models with unknown volatility parameters, the exact form of the innovation density is supposed to be unknown in detail but is thought to be close to members of some parametric family. To approximate such a density, we first construct an estimator for the unknown volatility parameters using the conditional least squares estimator given by Tjøstheim [Stochastic processes and their applications (1986) Vol. 21, pp. 251,273]. Then, a nonparametric kernel density estimator is constructed for the innovation density based on the estimated residuals. Using techniques of the minimum Hellinger distance estimation for stochastic models and residual empirical process from an ARCH(p) model given by Beran [Annals of Statistics (1977) Vol. 5, pp. 445,463] and Lee and Taniguchi [Statistica Sinica (2005) Vol. 15, pp. 215,234] respectively, it is shown that the proposed estimator is consistent and asymptotically normal. Moreover, a robustness measure for the score of the estimator is introduced. The asymptotic efficiency and robustness of the estimator are illustrated by simulations. The proposed estimator is also applied to daily stock returns of Dell Corporation. [source] Do Parental Transfers Reduce Youths' Incentives to Work?LABOUR, Issue 4 2009Tao Gong The results from a fixed-effects two-stage least squares estimator suggest that: (i) parental pocket money reduces youths' incentives to work; (ii) parental allowances have a non-linear effect on hours worked; (iii) the subsample of siblings shows similar patterns that parental transfers have a negative impact on hours worked, although the magnitudes are slightly weaker than the full sample; and (iv) the response to parental transfers varies by age. [source] A Recursive Thick Frontier Approach to Estimating Production Efficiency,OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2 2006Rien J. L. M. Wagenvoort Abstract We introduce a new panel data estimation technique for production and cost functions, the recursive thick frontier approach (RTFA). RTFA has two advantages over existing econometric frontier methods. First, technical inefficiency is allowed to be dependent on the explanatory variables of the frontier model. Secondly, RTFA does not hinge on distributional assumptions on the inefficiency component of the error term. We show by means of simulation experiments that RTFA outperforms the popular stochastic frontier approach and the ,within' ordinary least squares estimator for realistic parameterizations of a productivity model. Although RTFAs formal statistical properties are unknown, we argue, based on these simulation experiments, that RTFA is a useful complement to existing methods. [source] On inference for a semiparametric partially linear regression model with serially correlated errorsTHE CANADIAN JOURNAL OF STATISTICS, Issue 4 2007Jinhong You Abstract The authors consider a semiparametric partially linear regression model with serially correlated errors. They propose a new way of estimating the error structure which has the advantage that it does not involve any nonparametric estimation. This allows them to develop an inference procedure consisting of a bandwidth selection method, an efficient semiparametric generalized least squares estimator of the parametric component, a goodness-of-fit test based on the bootstrap, and a technique for selecting significant covariates in the parametric component. They assess their approach through simulation studies and illustrate it with a concrete application. L'inférence dans le cadre d'un modèle de régression semiparamétrique partiellement linéaire à termes d'erreur corrélés en série Les auteurs s'intéressent à un modèle de régression semiparamétrique partiellement linéaire à termes d'erreur corrélés en série. Ils proposent une façon originale d'estimer la structure d'erreur qui a l'avantage de ne faire intervenir aucune estimation non paramétrique. Ceci leur permet de développer une procédure d'inférence comportant un choix de fen,tre, l'emploi de la méthode des moindres carrés généralisés pour l'estimation semiparamétrique efficace de la composante paramétrique, un test d'adéquation fondé sur le rééchantillonnage et une technique de sélection des covariables significatives de la composante paramétrique. Ils évaluent leur approche par voie de simulation et en donnent une illustration concrète. [source] A unified approach to estimation of nonlinear mixed effects and Berkson measurement error modelsTHE CANADIAN JOURNAL OF STATISTICS, Issue 2 2007Liqun Wang Abstract Mixed effects models and Berkson measurement error models are widely used. They share features which the author uses to develop a unified estimation framework. He deals with models in which the random effects (or measurement errors) have a general parametric distribution, whereas the random regression coefficients (or unobserved predictor variables) and error terms have nonparametric distributions. He proposes a second-order least squares estimator and a simulation-based estimator based on the first two moments of the conditional response variable given the observed covariates. He shows that both estimators are consistent and asymptotically normally distributed under fairly general conditions. The author also reports Monte Carlo simulation studies showing that the proposed estimators perform satisfactorily for relatively small sample sizes. Compared to the likelihood approach, the proposed methods are computationally feasible and do not rely on the normality assumption for random effects or other variables in the model. Une stratégie d'estimation commune pour les modèles non linéaires à effets mixtes et les modèles d'erreur de mesure de Berkson Les modèles à effets mixtes et les modèles d'erreur de mesure de Berkson sont très usités. Ils par-tagent certaines caractéristiques que l'auteur met à profit pour élaborer une stratégie d'estimation commune. II considère des modèles dans lesquels la loi des effets aléatoires (ou des erreurs de mesure) est paramé-trique tandis que celles des coefficients de régression aléatoires (ou de variables exogènes non observées) et des termes d'erreur ne le sont pas. II propose une estimation des moindres carrés au second ordre et une approche par simulation fondées sur les deux premiers moments conditionnels de la variable endogène, sachant les variables exogènes observées. Les deux estimateurs s'avèrent convergents et asymptotiquement gaussiens sous des conditions assez générales. L'auteur fait aussi état d'études de Monte-Carlo attestant du bon comportement des deux estimations dans des échantillons relativement petits. Les méthodes proposées ne posent aucune difficulté particulière au plan numérique et au contraire de l'approche par vraisemblance, ne supposent ni la normalité des effets aléatoires, ni celle des autres variables du modèle. [source] On the sensitivity of the restricted least squares estimators to covariance misspecificationTHE ECONOMETRICS JOURNAL, Issue 3 2007Alan T.K. Wan Summary, Traditional econometrics has long stressed the serious consequences of non-spherical disturbances for the estimation and testing procedures under the spherical disturbance setting, that is, the procedures become invalid and can give rise to misleading results. In practice, it is not unusual, however, to find that the parameter estimates do not change much after fitting the more general structure. This suggests that the usual procedures may well be robust to covariance misspecification. Banerjee and Magnus (1999) proposed sensitivity statistics to decide if the Ordinary Least Squares estimators of the coefficients and the disturbance variance are sensitive to deviations from the spherical error assumption. This paper extends their work by investigating the sensitivity of the restricted least squares estimator to covariance misspecification where the restrictions may or may not be correct. Large sample results giving analytical evidence to some of the numerical findings reported in Banerjee and Magnus (1999) are also obtained. [source] Nonlinear econometric models with cointegrated and deterministically trending regressorsTHE ECONOMETRICS JOURNAL, Issue 1 2001Yoosoon Chang This paper develops an asymptotic theory for a general class of nonlinear non-stationary regressions, extending earlier work by Phillips and Hansen (1990) on linear cointegrating regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the convergence rate and the limiting distribution are critically dependent upon the type of the regression function. For integrable regression functions, the parameter estimates converge at a reduced n1/4 rate and have mixed normal limit distributions. On the other hand, if the regression functions are homogeneous at infinity, the convergence rates are determined by the degree of the asymptotic homogeneity and the limit distributions are non-Gaussian. It is shown that nonlinear least squares generally yields inefficient estimators and invalid tests, just as in linear nonstationary regressions. The paper proposes a methodology to overcome such difficulties. The approach is simple to implement, produces efficient estimates and leads to tests that are asymptotically chi-square. It is implemented in empirical applications in much the same way as the fully modified estimator of Phillips and Hansen. [source] Estimation of Nonlinear Models with Measurement ErrorECONOMETRICA, Issue 1 2004Susanne M. Schennach This paper presents a solution to an important econometric problem, namely the root n consistent estimation of nonlinear models with measurement errors in the explanatory variables, when one repeated observation of each mismeasured regressor is available. While a root n consistent estimator has been derived for polynomial specifications (see Hausman, Ichimura, Newey, and Powell (1991)), such an estimator for general nonlinear specifications has so far not been available. Using the additional information provided by the repeated observation, the suggested estimator separates the measurement error from the "true" value of the regressors thanks to a useful property of the Fourier transform: The Fourier transform converts the integral equations that relate the distribution of the unobserved "true" variables to the observed variables measured with error into algebraic equations. The solution to these equations yields enough information to identify arbitrary moments of the "true," unobserved variables. The value of these moments can then be used to construct any estimator that can be written in terms of moments, including traditional linear and nonlinear least squares estimators, or general extremum estimators. The proposed estimator is shown to admit a representation in terms of an influence function, thus establishing its root n consistency and asymptotic normality. Monte Carlo evidence and an application to Engel curve estimation illustrate the usefulness of this new approach. [source] Computer Algebra Derivation of the Bias of Linear Estimators of Autoregressive ModelsJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2006Y. Zhang Abstract., A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large-sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the Burg estimator's bias because this problem is too intractable without using computer algebra. The asymptotic bias coefficient to O(1/n) of Yule,Walker as well as least squares estimates is also derived in AR(3) models. Our asymptotic results show that for the AR(3), just as in the AR(2), the Yule,Walker estimates have a large bias when the parameters are near the nonstationary boundary. The least squares and Burg estimates are much better in this situation. Simulation results confirm our findings. [source] A comparison of three estimators of the Weibull parametersQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 4 2001Katina R. Skinner Abstract Using mean square error as the criterion, we compare two least squares estimates of the Weibull parameters based on non-parametric estimates of the unreliability with the maximum likelihood estimates (MLEs). The two non-parametric estimators are that of Herd,Johnson and one recently proposed by Zimmer. Data was generated using computer simulation with three small sample sizes (5, 10 and 15) with three multiply-censored patterns for each sample size. Our results indicate that the MLE is a better estimator of the Weibull characteristic value, ,, than the least squares estimators considered. No firm conclusions may be made regarding the best estimate of the Weibull shape parameter, although the use of maximum likelihood is not recommended for small sample sizes. Whenever least squares estimation of both Weibull parameters is appropriate, we recommend the use of the Zimmer estimator of reliability. Copyright © 2001 John Wiley & Sons, Ltd. [source] Bootstrapping Autoregression under Non-stationary VolatilityTHE ECONOMETRICS JOURNAL, Issue 1 2008Ke-Li Xu Summary This paper studies robust inference in autoregression around a polynomial trend with stable autoregressive roots under non-stationary volatility. The formulation of the volatility process is quite general including many existing deterministic and stochastic non-stationary volatility specifications. The aim of the paper is two-fold. First, it develops a limit theory for least squares estimators and shows how non-stationary volatility affects the consistency, convergence rates and asymptotic distributions of the slope and trend coefficients estimators in different ways. This complements the results recently obtained by Chung and Park (2007, Journal of Econometrics 137, 230,59. Second, it studies the recursive wild bootstrap procedure of Gonçalves and Kilian (2004, Journal of Econometrics 123, 89,120) in the presence of non-stationary volatility, and shows its validity when the estimates are asymptotically mixed Gaussian. Simulations are performed to compare favourably the recursive wild bootstrap with other inference procedures under non-stationary volatility. [source] On the sensitivity of the restricted least squares estimators to covariance misspecificationTHE ECONOMETRICS JOURNAL, Issue 3 2007Alan T.K. Wan Summary, Traditional econometrics has long stressed the serious consequences of non-spherical disturbances for the estimation and testing procedures under the spherical disturbance setting, that is, the procedures become invalid and can give rise to misleading results. In practice, it is not unusual, however, to find that the parameter estimates do not change much after fitting the more general structure. This suggests that the usual procedures may well be robust to covariance misspecification. Banerjee and Magnus (1999) proposed sensitivity statistics to decide if the Ordinary Least Squares estimators of the coefficients and the disturbance variance are sensitive to deviations from the spherical error assumption. This paper extends their work by investigating the sensitivity of the restricted least squares estimator to covariance misspecification where the restrictions may or may not be correct. Large sample results giving analytical evidence to some of the numerical findings reported in Banerjee and Magnus (1999) are also obtained. [source] | ||||||||||||||||||||||||||||