Small Area Estimates for Cross-Classifications

Zhang, Li‐Chun; Chambers, Ray

doi:10.1111/j.1369-7412.2004.05266.x

Cited by 40 publications

(37 citation statements)

References 20 publications

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“…IPF or variations thereof of tabular estimates have been used extensively to reconcile row-and column-sums of table entries with fixed marginals (Bishop et al, 1975) (Li and Schreuder, 1985) and fit complex multivariate models that are consistent with known marginals (D'Agostino and Rubin, 2000;Zhang and Chambers, 2004;Cramer, 1998). However, IPF poses two drawbacks in the context of fitting a table to known marginals: i) a lack of analytically tractable estimators of variance of IPF-adjusted estimates, and ii) the frequent failure of IPF to satisfy constraints when a table (matrix) contain one or more zeroes.…”

Section: Discussionmentioning

confidence: 99%

“…Li and Schreuder (Li and Schreuder, 1985) provide a variant of IPF for constraining a table of tree stem volume estimates to pre-specified column and row totals. More recent IPF applications includes, fitting a multivariate Gaussian distribution to known marginals (Cramer, 1998;Fahrmeir et al, 1999), estimation of covariance proportionality factors in grouped normal distributions (Liu and Rubin, 1998;Zhang and Chambers, 2004), block updating of Gibbs sampler (Piccioni, 2000), and adjustments for missing covariates in retrospective studies (D'Agostino and Rubin, 2000). However, variance estimators of IPF constrained estimates have not been forthcoming.…”

Section: Introductionmentioning

confidence: 99%

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A Variance Estimator for Constrained Estimates of Change in Relative Categorical Frequencies

Magnussen

Köhl²

2005

Environ Monit Assess

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Consistent estimators of change and state becomes an issue when sample data come from a mix of permanent and temporary observation units. A joint maximum likelihood estimator of state and change creates estimates of state that depend on antecedent viz. posterior survey results and may differ from estimates of state derived from a single-date analysis of the sample data. A constrained estimator of change in relative categorical frequencies that eliminates this potential inconsistency is proposed and a model based estimator of their sampling variance is developed. The performance of the constrained estimator is quantified against six criteria and a joint maximum likelihood estimator in simulated sampling from 15 populations with three combinations of permanent and temporary samples, four to six categorical class attributes, and constant size between sampling dates. Bias of the constrained estimators was negligible but larger than for joint maximum likelihood estimators. Mean absolute deviations and variances of constrained estimators were generally at par with the joint estimators. Constrained estimators of root mean square errors and achieved coverage of nominal confidence intervals of constrained estimators were occasionally better. A generalized variance function for the constrained estimates of change is provided as a computational shortcut.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Variance Estimator for Constrained Estimates of Change in Relative Categorical Frequencies

Magnussen

Köhl²

2005

Environ Monit Assess

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“…random sampling; e.g. simulated annealing (Kongmuang 2007), linear programming models (Zhang and Chambers 2004), complex combinatorial optimisation methods (Ballas et al 2006)] or deterministic [i.e. rule based – if A then B; e.g.…”

Section: Methodsmentioning

confidence: 99%

Micro‐level analysis of childhood obesity, diet, physical activity, residential socioeconomic and social capital variables: where are the obesogenic environments in Leeds?

Procter

Clarke

Ransley

et al. 2008

Area

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This paper describes global (whole of Leeds) and local (super output area) analyses of the relationship between childhood obesity and many 'obesogenic environment' variables, such as deprivation, urbanisation, access to local amenities, and perceived local safety, as well as dietary and physical activity behaviours. The analyses identify the covariates with the strongest relationships with obesity, and highlight variation in these relationships across Leeds, thus identifying 'at-risk' populations. This paper seeks to demonstrate the importance of analysis at the micro-level in order to provide health planners with additional information with which to tailor interventions and health policies to prevent childhood obesity.

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“…As the search area becomes larger, the procedure of searching for the k th tree around the sample point (Batcheler, Craib 1985) becomes time-consuming. According to Zhang and Chambers (2004), censoring to a maximum search distance requires a likelihood approach to the estimation in order to handle the censoring correctly, and a large sample size is required for an accurate estimate of the proportion of censored samples (Magnussen et al 2011). Such a burden eliminates any practical advantage of this method over sampling with fixed area plots.…”

mentioning

confidence: 99%

Adaptive k-tree sample plot for the estimation of stem density: An empirical approach

Hormoz¹

2018

J. For. Sci.

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Sohrabi H. (2018): Adaptive k-tree sample plot for the estimation of stem density: An empirical approach. J. For. Sci., 64: 17-24.Available budgets for the inventory of non-commercial woodlands are small. Therefore, there has been increased interest in using distance methods, such as k-tree sampling, which are faster than fixed plot sampling. In low-density woodlands, large search areas for k nearest trees contradict any practical advantage over sampling with fixed area plots. Here, a modification of a k-tree sample plot with an empirical approach to estimating the number of trees per unit area in low-density woodlands is presented. The standard and modified k-tree sample plots have been tested in one actual and three simulated forests with different spatial patterns. The modified method was superior to other combinations of methods in terms of relative bias and relative efficiency. Considering statistical and practical aspects of sampling for tree density, the modified method is more promising than is the standard one.

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Small Area Estimates for Cross-Classifications

Cited by 40 publications

References 20 publications

A Variance Estimator for Constrained Estimates of Change in Relative Categorical Frequencies

A Variance Estimator for Constrained Estimates of Change in Relative Categorical Frequencies

Micro‐level analysis of childhood obesity, diet, physical activity, residential socioeconomic and social capital variables: where are the obesogenic environments in Leeds?

Adaptive k-tree sample plot for the estimation of stem density: An empirical approach

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