Leverage and cochrane-orcutt estimation in linear regression

Stemann, Dietmar; Trenkler, Götz

doi:10.1080/03610929308831088

Cited by 12 publications

(7 citation statements)

References 6 publications

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“…Some authors agreed that the effect of not including the first observation is not always magnificent as suggested by Cochrane and Orcutt [13]. Stemann and Trenkler [14] extended the approach of Puterman [12] to the general linear model with the first order autoregressive errors and showed the effect of the presence of a constant term on a leverage point when the correlation of the error term was large in absolute value. Barry et al [15] extended the study of influential observations to the regression model with AR(2) errors and developed the diagnostic techniques using a hat matrix.…”

Section: Introductionmentioning

confidence: 99%

“…One should see the work of Stemann and Trenkler [14] on the influence technique when considering the regression model with more than one regressors in the presence and absence of constant term. On the other hand, Barry et al [15] extended the approach of Puterman to the influence of initial observations and subset of observations in linear regression model with AR(2) errors.…”

Section: Influence and Hat Matrixmentioning

confidence: 99%

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Influential Observations in Stochastic Model of Divisia Index Numbers with AR(1) Errors

Burney¹,

Maqsood²

2014

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We use the general form of hat matrix and DFBETA measures to detect the influential observations in order to estimate the Divisia price index number when the error structure is first order serial correlation. An example is presented with reference to price data of Pakistan. Hat values show the noteworthy findings that the corresponding weights of consumer items have large influence on the parameter estimates and are not affected by the parameter of autoregressive process AR(1). Whereas DFBETAs for Divisia index numbers depend on both the weights and autoregressive parameter.

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Section: Introductionmentioning

confidence: 99%

Section: Influence and Hat Matrixmentioning

confidence: 99%

Influential Observations in Stochastic Model of Divisia Index Numbers with AR(1) Errors

Burney¹,

Maqsood²

2014

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“…When the GLS is used, the first leverage goes to 1 at ρ → 1 for a constant mean model while it goes to 0 at ρ → −1 for a regression through the origin model. Stemann & Trenkler (1993) expanded Puterman (1988)'s investigation to the model which contained multiple regressors and they noted that if the model had constant term, then the first leverages close to 1 at |ρ| → 1. Let's examine the behaviours of first leverages for different ρ and k. It can be realized in Figure 4 that the first transformed observation has a large leverage value as |ρ| → 1.…”

Section: An Example: Macroeconomics Datamentioning

confidence: 99%

“…In time series data, if the observations show inter-correlation, especially in cases where the time intervals are little, the concept of autocorrelation occurs. Leverages in general linear regression model (GLRM) with autocorrelation problem has been considered by several authors (Özkale & Açar, 2015;Puterman, 1988;Roy & Guria, 2004;Stemann & Trenkler, 1993). Especially there are more studies under the autocorrelation problem from the first-order autoregressive errors, AR(1).…”

Section: Introductionmentioning

confidence: 99%

Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure

Açar

2020

Journal of Advanced Research in Natural and Applied Sciences

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The determination of leverage observations have been frequently investigated through ordinary least squares and some biased estimators proposed under the multicollinearity problem in the linear regression models. Recently, the identification of leverage and influential observations have been also popular on the general linear regression models with correlated error structure. This paper proposes a new projection matrix and a new quasiprojection matrix to determination of leverage observations for principal component regression and r-k class estimators, respectively, in general linear regression model with first-order autoregressive error structure. Some useful properties of these matrices are presented. Leverage observations obtained by generalized least squares and ridge regression estimators available in the literature have been compared with proposed principal component regression and r-k class estimators over a simulation study and a numerical example. In the literature, the first leverage is considered separately due to the first-order autoregressive error structure. Therefore, the behaviours of first leverages obtained by principal component regression and r-k class estimators has been also investigated according to the autocorrelation coefficient and biasing parameter through applications. The results showed that the leverage of the first observation obtained by principal component regression and r-k estimators is smaller than that obtained by generalized least squares and ridge regression estimators. In addition, as the autocorrelation coefficient goes to -1, the leverage of the first transformed observation decreases for PCR and r-k class estimators, while its increases while the autocorrelation coefficient goes to 1.

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“…Some authors agreed that the effect of not including the first observation is not always magnificent as suggested by Cochrane and Orcutt [20] (see also Kadiyala [9]). Stemann and Trenkler [21] extended the approach of Puterman [19] to the regression model with more than one regressor and showed that the effect of the presence of a constant term on a leverage point when the magnitude of error correlation was large. Pena [22] proposed a new statistic, called Pena's statistic, used to measure the influence of an observation based on how this value is being influenced by the rest of data.…”

Section: Introductionmentioning

confidence: 99%

Extracting the Influential Commodities in Stochastic Model of Simple Laspeyre Price Index Numbers with AR(2) Errors

Maqsood¹,

Burney²

2014

OJS

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This paper, on the first hand, deals with the problem of estimation of Laspeyre price index number when the errors are assumed to be generated from AR(2) process. The general expression of hat matrix and DFBETA measure to find the influential consumer commodities in stochastic Laspeyre price model with AR(2) errors are developed on the other. The hat values show the noteworthy findings that the corresponding weights of consumer items have large influence on the parameter estimates for simple Laspeyre price index number and are not affected by the parameter of autoregressive process of order two. While, DFBETA measures are the functions of both weights and autocorrelation parameters. Lastly, an example is presented with reference to price data of Pakistan, and shows its practical importance in financial time series.

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Leverage and cochrane-orcutt estimation in linear regression

Cited by 12 publications

References 6 publications

Influential Observations in Stochastic Model of Divisia Index Numbers with AR(1) Errors

Influential Observations in Stochastic Model of Divisia Index Numbers with AR(1) Errors

Identification of Leverage Points in Principal Component Regression and r-k Class Estimators with AR(1) Error Structure

Extracting the Influential Commodities in Stochastic Model of Simple Laspeyre Price Index Numbers with AR(2) Errors

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