Prediction Error of Small Area Predictors Shrinking Both Means and Variances

Maiti, Tapabrata; Ren, Hao; Sinha, Samiran

doi:10.1111/sjos.12061

Cited by 31 publications

(35 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, g 1i (φ) can be easily calculated 23 by generating a large number of random samples of z 1 and z 2 . On the other hand, the second term g 2i (φ) can be evaluated 24 as the following lemma, where the proof is given in the Appendix.…”

Section: Estimation Of Model Parametersmentioning

confidence: 99%

“…The covariates x i were initially generated from the uniform distribution on (0, 4) and fixed in simulation runs. 23 Concerning sampling variance D i , we divided 30 areas into 5 groups (from G 1 to G 5 ), and areas within the same group 24 have the same D i value. The D i -pattern we considered was (0.2, 0.4, 0.6, 0.8, 1.0).…”

Section: Evaluation Of Prediction Errorsmentioning

confidence: 99%

“…For the degree of splines, we considered three cases: p = 1, 2, 3. 23 We estimated model parameters β 0 , . .…”

Section: Evaluation Of Prediction Errorsmentioning

confidence: 99%

“…Thus, a 23 natural way to solve this problem is using a parametric family of transformations which enables us to select a reasonable 24 transformation based on data. A famous family is the Box-Cox transformation (Box and Cox, 1964) defined as 25 h BC 26 However, it suffers from a truncation problem that the range of the Box-Cox transformation is not the whole real line if 27 λ ̸ = 0, which leads to inconsistency of the maximum likelihood estimator of λ.…”

mentioning

confidence: 99%

“…Since the model parameters φ is unknown in practice, we estimate them by maximizing the marginal likelihood function, 23 and the details are given in the next section. Let  φ be the corresponding estimator of φ.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Transforming response values in small area prediction

Kubokawa

2017

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

a b s t r a c tIn real applications of small area estimation, one often encounters data with positive response values. The use of a parametric transformation for positive response values in the Fay-Herriot model is proposed for such a case. An asymptotically unbiased small area predictor is derived and a second-order unbiased estimator of the mean squared error is established using the parametric bootstrap. Through simulation studies, a finite sample performance of the proposed predictor and the MSE estimator is investigated. The methodology is also successfully applied to Japanese survey data.

show abstract

Section: Estimation Of Model Parametersmentioning

confidence: 99%

Section: Evaluation Of Prediction Errorsmentioning

confidence: 99%

“…For the degree of splines, we considered three cases: p = 1, 2, 3. 23 We estimated model parameters β 0 , . .…”

Section: Evaluation Of Prediction Errorsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Transforming response values in small area prediction

Kubokawa

2017

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

Bayesian Small Area Estimation

Polettini¹,

Arima²

2022

Wiley StatsRef: Statistics Reference Online

View full text Add to dashboard Cite

The wealth of timely and detailed information provided by sample surveys ( see Survey Sampling; Finite Populations, Sampling From ) attracts interest of researchers and analysts, with planned domains ( see Sampling Designs in Surveys) being of primary yet clearly not exclusive inferential interest. Indeed, based on the sample data, a whole variety of subpopulations could be investigated to comprehend local needs and issues, highlight the geography of socioeconomic disparities, drive the planning and evaluation of policies, and so on. We denote by small area any geographical or demographic domain that is not planned for the survey. Counties, municipalities or states, or the groups obtained by cross‐classification of age, sex, ethnicity, and region are examples. In general, we call direct an estimator solely based on the subsample of units belonging to the area of interest. Accurate design‐based inference may be jeopardized by the small (or even zero) sample size of such domains, whence the terminology. Inferential interest concerns area‐specific parameters, usually means, proportions, or percentiles. Typical applications include estimation of mean household income at the municipality level in poverty studies, the number of persons affected by a given disease in a given sex by age by region classification in epidemiological studies, the crop area under vines at the regional level in agricultural economics, and counts and rates for school age children under poverty at the county and school district levels for allocation of funds. To produce reliable estimates of such aggregates, we use indirect estimators that rely on auxiliary information to connect small areas through explicit or implicit models, thus borrowing strength and increasing the effective sample size. Such process is generally referred to as “small area estimation.” The article Small Area Estimation describes the nature of the problem and the different approaches. This article focuses on Bayesian models for small area estimation. We present two basic linear models and briefly discuss a number of different extensions that are easily accommodated under a Bayesian framework.

show abstract

A new robust Bayesian small area estimation via ‐stable model for estimating the proportion of athletic students in California

2021

View full text Add to dashboard Cite

In the last few years, diabetes mellitus and obesity revealed to be one of the fastest‐growing chronic diseases in youth in the United States. The number of new diabetes cases is dramatically increasing, and, for the moment, effective therapy does not exist. Experts believe that one of the causes of this increase is the decline in exercise behavior. The California Education Code requires local educational agencies (LEAs) to administer the FITNESSGRAM, the Physical Fitness Test (PFT), to Californian students of public schools. This test evaluates six fitness areas, and experts defined that a passing result on all six areas of the test represents a fitness level that offers some protection against the diseases associated with physical inactivity. We consider 2015–2016 data provided by the California Department of Education (CDE): for each Californian county (m=57), we aim at estimating the county‐level proportion of students with a score equal to six. To account for the heterogeneity of the phenomenon and the presence of outlying counties, we extend the standard area‐level model by specifying the random effects as a symmetric α‐stable (SαS) distribution that can accommodate different types of outlying observations. The model can accurately estimate the county‐level proportion of students with a score equal to six. Results highlight some interesting relationships with social and economic situations in each county. The performance of the proposed model is also investigated through an extensive simulation study.

show abstract

Prediction Error of Small Area Predictors Shrinking Both Means and Variances

Cited by 31 publications

References 12 publications

Transforming response values in small area prediction

Transforming response values in small area prediction

Bayesian Small Area Estimation

A new robust Bayesian small area estimation via ‐stable model for estimating the proportion of athletic students in California

Contact Info

Product

Resources

About