Design-based ranked set sampling using auxiliary variables

Barabesi, Lucio; Marcheselli, Marzia

doi:10.1007/s10651-004-4187-8

Cited by 7 publications

(7 citation statements)

References 20 publications

(15 reference statements)

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“…There have been many attempts to improve distance methods (for examples, Barabesi and Marcheselli 2004;Byth 1982;Cox et al 1997;Kendall and Moran 1963;Kleinn and Vilčko 2006b;Lewis 1975;Parker 1979;Patil et al 1982;Persson 1964;Picard et al 2005;Pollard 1971;Pollard et al 2002;Prodan 1968). Recently, Kronenfeld (2009) has suggested to exploit the commonly observed trend of a decline in bias as k increases to obtain an asymptotic estimate of density from a non-linear model fitted to a set of ordered distances.…”

Section: Introductionmentioning

confidence: 99%

An adaptive composite density estimator for k-tree sampling

2011

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Density estimators for k-tree distance sampling are sensitive to the amount of extra Poisson variance in distances to the kth tree. To lessen this sensitivity, we propose an adaptive composite estimator (COM). In simulated sampling from 16 test populations, a three-component composite density estimator (COM)-with weights determined by a multinomial logistic function of four readily available ancillary variables-was identified as superior in terms of average relative absolute bias. Results from a different set of nine validation populations-with widely different stem densities and spatial patterns of tree locations-confirmed that relative root mean squared errors (RRMSE) of COM were, on average, considerably lower than those obtained with the three-component k-tree density estimators. The RRMSE performance of COM improved with increasing values of k. With k = 6 and sample sizes of 10, 20, and 30, the average relative bias of COM was between -5 and 5% in seven validation populations but in an open low-density savanna-like population bias reached -12% (1979 data) and 7% (1996 data). For k = 6 and n = 10, the RRMSE of COM was, in six of the nine validation populations, within 3.3 percentage points of the RRMSE for sampling with fixed-area plots. Jackknife estimates of the precision of COM estimates of density were negatively biased, leading to under-coverage (7%) of computed 95% confidence intervals.

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Section: Introductionmentioning

confidence: 99%

An adaptive composite density estimator for k-tree sampling

2011

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“…Therefore, φ(μ 1 , ...,μ l ) displays a surprising O(n −3/2 ) variance rate. Finally, the simulation carried out in [3] shows that suggested ranked estimators outperform their usual counterparts even in a small-sample setting.…”

Section: Applications To Designs With Auxiliary Variablementioning

confidence: 92%

“…where Φ = 1 − S is the cumulative distribution function of N (0, 1) and c = 1/ (pq) 3 . In a similar way, for any k ∈]i n , j n ], it turns out that…”

Section: Preliminariesmentioning

confidence: 99%

“…However, when an auxiliary variable induces the ranking on the target variable, a large n may be chosen and may be set r = 1. As an example, this framework is considered for the estimation of a population mean μ in the design-based approach (see [3]) where the asymptotic results on μ n have to be developed for n → ∞. Since, the variance of μ n turns out to be n −2 σ 2 n , with σ…”

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confidence: 99%

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Some asymptotic results on the sum of variances of order statistics

Marcheselli

Pratelli

Navale³

et al. 2007

ijcms

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“…Bouza (2002a,b) studied an application of the RSS technique, with replacement, to estimate the population mean in the presence of non-responses. Further studies related to the theory and application of RSS designs in finite populations are provided in Barabesi and Marcheselli (2004), Ozturk et al (2005), Deshpande et al (2006), and Bouza (2009). Al-Saleh and Samawi (2007) studied the inclusion probabilities in RSS and some of its variation when the set size is k = 2 or k = 3 and, later on, Özdemir and Gökpınar (2007) extended this result to a more general set size and compared the inclusion probability for an RSS technique with that of a SRS with the same sample size.…”

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confidence: 99%

Design based estimation for ranked set sampling in finite populations

Jozani

Johnson

2010

Environ Ecol Stat

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In this paper, we consider design-based estimation using ranked set sampling (RSS) in finite populations. We first derive the first and second-order inclusion probabilities for an RSS design and present two Horvitz-Thompson type estimators using these inclusion probabilities. We also develop an alternate Hansen-Hurwitz type estimator and investigate its properties. In particular, we show that this alternate estimator always outperforms the usual Hansen-Hurwitz type estimator in the simple random sampling with replacement design with comparable sample size. We also develop formulae for ratio estimator for all three developed estimators. The theoretical results are augmented by numerical and simulation studies as well as a case study using a well known data set. These show that RSS design can yield a substantial improvement in efficiency over the usual simple random sampling design in finite populations.

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Design-based ranked set sampling using auxiliary variables

Cited by 7 publications

References 20 publications

An adaptive composite density estimator for k-tree sampling

An adaptive composite density estimator for k-tree sampling

Some asymptotic results on the sum of variances of order statistics

Design based estimation for ranked set sampling in finite populations

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