Estimation of the distribution function with calibration methods

Rueda, María del Mar; Martínez, S.; Martínez, Helena Martínez; Caruz, Antonio

doi:10.1016/j.jspi.2005.12.011

Cited by 56 publications

(61 citation statements)

References 6 publications

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“…The proposed class of estimators can be easily extended to use multiauxiliary information as presented by Ahmed and Abu-Dayyeh [1] and Rueda et al [37].…”

Section: Resultsmentioning

confidence: 99%

A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information

Singh

Singh²,

Kozak

2008

Acta Appl Math

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This paper considers the problem of estimating the finite-population distribution function and quantiles with the use of auxiliary information at the estimation stage of a survey. We propose the families of estimators of the distribution function of the study variate y using the knowledge of the distribution function of the auxiliary variate x. In addition to ratio, product and difference type estimators, many other estimators are identified as members of the proposed families. For these families the approximate variances are derived, and in addition, the optimum estimator is identified along with its approximate variance. Estimators based on the estimated optimum values of the unknown parameters used to minimize the variance are also given with their properties. Further, the family of estimators of a finitepopulation distribution function using two-phase sampling is given, and its properties are investigated.

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“…The proposed class of estimators can be easily extended to use multiauxiliary information as presented by Ahmed and Abu-Dayyeh [1] and Rueda et al [37].…”

Section: Resultsmentioning

confidence: 99%

A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information

Singh

Singh²,

Kozak

2008

Acta Appl Math

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“…Rueda et al [11] assume that the relationship between y and x can be described by a linear superpopulation model ξ : y i = β x i + ε i , i = 1, . .…”

Section: The Calibration Methods In the Estimation Of The Distributionmentioning

confidence: 99%

“…Calibration was introduced by Deville and Särndal [4] to estimate the population total, but this approach is readily adapted to the estimation of more complex parameters than a population total [14]. Harms and Duchesne [6] and Rueda et al [11] used different ways to implement the calibration approach in the estimation of the distribution function. Both methods give nearly design unbiased estimation and compare favourably with earlier estimation methods for the distribution function, which were not based on calibration thinking but on the auxiliary information itself (see [13]).…”

Section: Introductionmentioning

confidence: 99%

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On determining the calibration equations to construct model-calibration estimators of the distribution function

Martínez¹,

Rueda²,

Caruz³

et al. 2011

Rev Mat Complut

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The calibration approach to estimating the finite population distribution function was proposed by Rueda et al. (J. Stat. Plan. Inference 137(2):435-448, 2007). The proposed estimator is built by means of constraints that require the use of a set of fixed values. Assuming a linear regression working model, Rueda et al. (Metrika 71:33-44, 2010) considered a single fixed value for the calibration and determine the optimum value in the sense of minimum variance. Assuming more complex models, we now study the problem of determining two optimal values to achieve the best estimation under simple random sampling without replacement.

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“…Chambers and Dunstan (1986) and Dorfman and Hall (1993) proposed parametric model-based distribution function estimators. Rueda et al (2007) use the calibration method (see Deville and Särndal 1992) to obtain an estimator of the distribution function assuming a linear relationship between the interest and auxiliary variables. It is an interesting fact that the first use of nonparametric regression in survey sampling was for the purpose of estimating the distribution function.…”

Section: Estimation Of the Population Distribution Functionmentioning

confidence: 99%

Nonparametric methods in sample surveys. Application to the estimation of cancer prevalence

2010

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We address the problem of the estimation of the population mean and the distribution function using nonparametric regression. These methods are being used in a wide range of settings and areas of research. In particular, they are a good alternative to other classical methods in the survey sampling context, since they work under the assumption that the underlying regression function is smooth. Some relevant nonparametric regression methods in survey sampling are presented. Data on breast cancer prevalence derived from 40 European countries are used to study the application of the nonparametric estimators to the estimation of cancer prevalence. Result derived from an empirical study show that nonparametric estimators have a good empirical performance in this study on cancer prevalence.

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Estimation of the distribution function with calibration methods

Cited by 56 publications

References 6 publications

A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information

A Family of Estimators of Finite-Population Distribution Function Using Auxiliary Information

On determining the calibration equations to construct model-calibration estimators of the distribution function

Nonparametric methods in sample surveys. Application to the estimation of cancer prevalence

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