Uniform convergence of the empirical cumulative distribution function under informative selection from a finite population

Bonnéry, Daniel; Breidt, F. Jay; Coquet, François

doi:10.3150/11-bej369

Cited by 12 publications

(11 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As in Bonnéry, Breidt and Coquet (2012), the conditions we propose are verifiable for various sample schemes, commonly encountered in real problems in surveys, and involve computing conditional versions of first and second-order inclusion probabilities.…”

Section: Introductionmentioning

confidence: 90%

“…The weight ρ(x, y; θ, ξ) is the expected inclusion probability of an element given its covariate is x and response is y, divided by the expected inclusion probability given its covariate is x. (This definition can be extended for random sample sizes and withreplacement sampling, replacing expected inclusion probability by expected number of selections (Bonnéry, Breidt and Coquet (2012).) As shown by Landsman and Graubard (2013), the Breslow and Cain (1988) approach is a special case of sample likelihood estimation.…”

Section: Introductionmentioning

confidence: 99%

“…In Bonnéry, Breidt and Coquet (2012), a precise asymptotic framework for informative selection is given and weak conditions on the informative selection mechanism are stated under which the (unweighted) empirical cumulative distribution function (cdf) converges uniformly to the cdf associated with the limiting sample pdf. That is, the classical Glivenko-Cantelli theorem holds in the case of a weak dependence among the draws, perhaps suggestive of good behavior for the sample likelihood approach.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotics for the maximum sample likelihood estimator under informative selection from a finite population

Bonnéry¹,

Breidt²,

Coquet³

2018

Bernoulli

Self Cite

View full text Add to dashboard Cite

International audienceInference for the parametric distribution of a response given covariates is considered under informative selection of a sample from a finite population. Under this selection, the conditional distribution of a response in the sample, given the covariates and given that it was selected for observation, is not the same as the conditional distribution of the response in the finite population, given only the covariates. It is instead a weighted version of the conditional distribution of interest. Inference must be modified to account for this informative selection. An established approach in this context is maximum “sample likelihood”, developing a weight function that reflects the informative sampling design, then treating the observations as if they were independently distributed according to the weighted distribution. While the sample likelihood methodology has been widely applied, its theoretical foundation has been less developed. A precise asymptotic description of a wide range of informative selection mechanisms is proposed. Under this framework, consistency and asymptotic normality of the maximum sample likelihood estimators are established. The theory allows for the possibility of nuisance parameters that describe the selection mechanism. The proposed regularity conditions are verifiable for various sample schemes, motivated by real problems in surveys. Simulation results for these examples illustrate the quality of the asymptotic approximations, and demonstrate a practical approach to variance estimation that combines aspects of model-based information theory and design-based variance estimation

show abstract

Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotics for the maximum sample likelihood estimator under informative selection from a finite population

Bonnéry¹,

Breidt²,

Coquet³

2018

Bernoulli

Self Cite

View full text Add to dashboard Cite

show abstract

“…In many situations, statisticians have at their disposal not only data but also weights arising from some survey sampling plan. Ignoring the method used to form the database can often result in a significant bias, thereby completely jeopardizing the estimation, see Bonnéry et al () or Gelman (). To avoid such drawbacks, variants of the estimators can be adopted, which incorporate the underlying sampling design through the use of the inclusion probabilities.…”

Section: Introductionmentioning

confidence: 99%

Empirical Processes in Survey Sampling with (Conditional) Poisson Designs

Bertail

Chautru

Clémençon

2016

Scandinavian J Statistics

View full text Add to dashboard Cite

International audienceIt is the main purpose of this paper to study the asymptotics of certain variants of the empirical process in the context of survey data. Precisely, Functional Central Limit Theorems are established under usual conditions when the sample is drawn from a Poisson or a rejective sampling design. The framework we develop encompasses sampling designs with non-uniform first order inclusion probabilities, which can be chosen so as to optimize estimation accuracy. Applications to Hadamard differentiable functionals are considered

show abstract

“…( ) is a cumulative distribution function of the normal distribution [20]. Using equal step size Δ to subdivide the probability curve, the area summation of every closed figure = ( ) − ( −1 ), = Δ ⋅ + 0 , = exp( ) and longitudinal strata thickness of each layer ℎ = ℎ ⋅ .…”

Section: Research On Whether the Inverse Problem Model Of Formation Pmentioning

confidence: 99%

An Estimation Method of Water Drive Displacement Based on Formation Permeability Distribution and Inverse Problem Modeling

Huang

Wang

et al. 2014

Advances in Mechanical Engineering

View full text Add to dashboard Cite

Formation permeability distribution is important in the oil industry since it is a key tool in forecasting oil production performance, a matter of primary concern to oilfield operators. However, the direct problems of reservoir analysis are limited in practice by a lack of input parameters such as reservoir vertical heterogeneity. Therefore, inverse problem modeling is important to achieve reservoir vertical heterogeneity using production profiles, which are always known for existing reservoirs. In this way, what has occurred inside a reservoir can be understood by applying reservoir output in the reverse model. Because formation permeability can frequently be represented by a normal distribution and can describe heterogeneity and water production capability, an inverse problem of formation permeability was modeled to study reservoir vertical heterogeneity and reservoir production performance based on oil-water two-fluid flow theory and optimization problems. Moreover, through establishing an objective function, we obtained an optimal solution for water production rate. Finally, one case is simulated by this model and good results achieved, which are compatible with production and experimental data.

show abstract

Uniform convergence of the empirical cumulative distribution function under informative selection from a finite population

Cited by 12 publications

References 32 publications

Asymptotics for the maximum sample likelihood estimator under informative selection from a finite population

Asymptotics for the maximum sample likelihood estimator under informative selection from a finite population

Empirical Processes in Survey Sampling with (Conditional) Poisson Designs

An Estimation Method of Water Drive Displacement Based on Formation Permeability Distribution and Inverse Problem Modeling

Contact Info

Product

Resources

About