A Measure of Production Performance

Kokic, Philip; Chambers, Ray; Breckling, Jens; Beare, Stewe

doi:10.1080/07350015.1997.10524722

Cited by 34 publications

(24 citation statements)

References 15 publications

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“…Figure 7 (left panel) reports the spatial distribution of the M-quantile coefficients, the q i 's, which reflects variability not explained by the covariates. A similar reasoning in a completely different context can be found in Kokic et al, 29 where M-quantile regression is employed to measure production performance and units are ranked according to their M-quantile coefficient after accounting for covariates. The estimated relative risks from SPNBMQ(d) model and those obtained using NBGAM model (d) (for a discussion of P-splines models for disease mapping see Goicoa et al 17 ).…”

Section: Resultsmentioning

confidence: 99%

“…On the other hand, M-quantile models can be used to characterize overdispersion in a different way by attaching to each observed count a so-called 'M-quantile coefficient'. The Mquantile coefficient associated with the observed value y i of a continuously distributed random variable Y and an associated covariate value x i is the value q i such thatQ q i ðx i ; cÞ ¼ y i , 29,33 i.e. that value of q for which the fitted value reproduces the observed one.…”

Section: Disease Mapping Via Spnbmqmentioning

confidence: 99%

“…a Huber-type function) then this algorithm is guaranteed to converge to a unique solution. 29 M-quantile regression models allow to trade robustness for efficiency by properly tuning such constant c: robustness is increased as c decreases, while efficiency is increased as c increases with expectile regression in the limit as c ! 1.…”

Section: Notation and Background Informationmentioning

confidence: 99%

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Semiparametric M-quantile regression for count data

Dreassi

Ranalli

Salvati

2014

Stat Methods Med Res

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Lung cancer incidence over 2005-2010 for 326 Local Authority Districts in England is investigated by ecological regression. Motivated from mis-specification of a Negative Binomial additive model, a semiparametric Negative Binomial M-quantile regression model is introduced. The additive part relates to those univariate or bivariate smoothing components, which are included in the model to capture nonlinearities in the predictor or to account for spatial dependence. All such components are estimated using penalized splines. The results show the capability of the semiparametric Negative Binomial M-quantile regression model to handle data with a strong spatial structure.

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Section: Resultsmentioning

confidence: 99%

Section: Disease Mapping Via Spnbmqmentioning

confidence: 99%

Section: Notation and Background Informationmentioning

confidence: 99%

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Semiparametric M-quantile regression for count data

Dreassi

Ranalli

Salvati

2014

Stat Methods Med Res

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“…Once q and ψ are specified, parameter estimates can be obtained by using an iterative reweighted least squares algorithm (IRLS; Kokic et al, 1997).…”

Section: Notation and Background Informationmentioning

confidence: 99%

Semiparametric M‐quantile regression for estimating the proportion of acidic lakes in 8‐digit HUCs of the Northeastern US

2008

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SUMMARYBetween 1991 and 1995, the Environmental Monitoring and Assessment Program of the US Environmental Protection Agency conducted a survey of lakes in the Northeastern states of the US to determine the ecological condition of these waters. Here, to this end, we want to obtain estimates of the proportion of lakes at (high) risk of acidification or acidified already for each 8-digit hydrologic unit code (HUC) within the region of interest. Sample sizes for the 113 HUCs are very small and 27 HUCs are not even observed. Therefore, small area estimation techniques should be invoked for the estimation of the distribution function of acid neutralizing capacity (ANC) for each HUC. The procedure is based on a semiparametric M-quantile regression model in which ANC depends on elevation and the year of the survey linearly, and on the geographical position of the lake through an unknown smooth bivariate function estimated by low-rank thin plate splines.

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“…The method of M-quantile regression is based on a "quantilelike" generalization of regression and influence function for M-estimation and as such provides a robust alternative to standard regression models. Indeed, this was proven on a small number of applications (Kokic & Chambers, 1997;Chambers & Tzavidis, 2006). In this paper, we extend both the model and the range of applications of this methodology.…”

Section: Introductionmentioning

confidence: 99%

M-quantile Regression Analysis of Temporal Gene Expression Data

Vinciotti¹,

Yu²

2009

Statistical Applications in Genetics and Molecular Biology

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In this paper, we explore the use of M-regression and M-quantile coefficients to detect statistical differences between temporal curves that belong to different experimental conditions. In particular, we consider the application of temporal gene expression data. Here, the aim is to detect genes whose temporal expression is significantly different across a number of biological conditions. We present a new method to approach this problem. Firstly, the temporal profiles of the genes are modelled by a parametric M-quantile regression model. This model is particularly appealing to small-sample gene expression data, as it is very robust against outliers and it does not make any assumption on the error distribution. Secondly, we further increase the robustness of the method by summarising the M-quantile regression models for a large range of quantile values into an M-quantile coefficient. Finally, we employ a Hotelling T 2 -test to detect significant differences of the temporal M-quantile profiles across conditions. Simulated data shows the increased robustness of M-quantile regression methods over standard regression methods. We conclude by using the method to detect differentially expressed genes from time-course microarray data on muscular dystrophy.

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A Measure of Production Performance

Cited by 34 publications

References 15 publications

Semiparametric M-quantile regression for count data

Semiparametric M-quantile regression for count data

Semiparametric M‐quantile regression for estimating the proportion of acidic lakes in 8‐digit HUCs of the Northeastern US

M-quantile Regression Analysis of Temporal Gene Expression Data

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