ASRB NET Small Area Estimation & Model-Based Survey Inference: practice questions

ASRB NET - Agricultural Statistics (and Computer Application / Bioinformatics) · India · Agricultural Scientists Recruitment Board (ICAR)

Original practice questions written to the published syllabus · not past papers

10worked here, free

97written to this exam in this subject

10syllabus units

What this subject covers

Producing district and block estimates that a national sample is too thin to support directly: synthetic and composite estimators, the Fay-Herriot and nested-error models, empirical Bayes and hierarchical Bayes, model-assisted calibration and integration with census and remote-sensing data. A research strength of ICAR-IASRI.

In the exams: Not an explicit unit in AICE-JRF Ag Stat; PhD course and IASRI research area; national statistical offices (applied)

Why direct estimators fail for small domains
Synthetic and composite estimators
Area-level models: Fay-Herriot
Unit-level models: Battese-Harter-Fuller nested-error model
EBLUP and its mean squared error
Empirical Bayes and hierarchical Bayes approaches
Calibration estimation and the GREG estimator
Model-based versus design-based inference
Small area estimation of crop yield, poverty and food insecurity
Combining survey, census and satellite data

What ASRB NET asks from it

ASRB NET / ARS Agricultural Statistics (reported)

Small area estimation methods for crop yield and other agricultural indicators, as an ICAR-IASRI research area.

Where the 97 questions fall

How our questions for ASRB NET spread across the units of Small Area Estimation & Model-Based Survey Inference. Difficulty: 31 easy, 42 medium, 24 hard.

Area-level models: Fay-Herriot	12
Why direct estimators fail for small domains	10
Unit-level models: Battese-Harter-Fuller nested-error model	10
EBLUP and its mean squared error	10
Calibration estimation and the GREG estimator	10
Combining survey, census and satellite data	10
Synthetic and composite estimators	9
Empirical Bayes and hierarchical Bayes approaches	9
Small area estimation of crop yield, poverty and food insecurity	9
Model-based versus design-based inference	8

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Why direct estimators fail for small domains · medium

Why are planned domains the first defence against small samples?

Planned domains remove non-sampling errors
Planned domains make models unnecessary for all areas
Allocation then secures enough units per domain
Planned domains need no sample at all

Answer and working

C. Allocation then secures enough units per domain

Stratifying and allocating by domain ensures minimum samples.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

2 · Synthetic and composite estimators · easy

What is the main weakness of a synthetic estimator?

It needs a large sample from the area itself
It cannot make any use of census counts
Very large variance in every small area
Bias that does not shrink as the sample grows

Answer and working

D. Bias that does not shrink as the sample grows

Bias does not shrink with sample size.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

3 · Synthetic and composite estimators · medium

What does a regression-synthetic estimator do?

Uses neighbouring areas' raw sample data only
Uses only the area's own direct estimate
Averages all areas' direct estimates equally
Predicts from x_d' beta-hat with no direct data

Answer and working

D. Predicts from x_d' beta-hat with no direct data

It ignores the area's own data: shrinkage factor zero.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

4 · Unit-level models: Battese-Harter-Fuller nested-error model · hard

What is the danger of informative sampling for unit-level models?

Bias if weights are ignored
No effect on any estimate
Zero variance in every area
Negative shrinkage factors

Answer and working

A. Bias if weights are ignored

Selection related to the response biases unweighted models.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

5 · Calibration estimation and the GREG estimator · easy

What does calibration do to survey weights?

Removes design weights
Sets them all equal
Matches known totals
Doubles them

Answer and working

C. Matches known totals

Weights close to design weights satisfying sum w x = X.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

6 · Model-based versus design-based inference · medium

How are SAE methods usually compared before adoption?

Choosing the one with most covariates
Design-based simulation studies
Asking users which they prefer
Comparing only national totals

Answer and working

B. Design-based simulation studies

Repeated sampling from realistic populations reveals bias and MSE.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

7 · Small area estimation of crop yield, poverty and food insecurity · hard

How should SAE maps show uncertainty?

Use more colour classes on the same map
Show only national averages beside the map
With companion maps of the CV or relative MSE
Hide uncertainty to avoid confusing users

Answer and working

C. With companion maps of the CV or relative MSE

Users need to see where estimates are reliable.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

8 · Synthetic and composite estimators · easy

A composite estimator is:

A weighted mean of direct and synthetic
The synthetic estimate with no weighting
The direct estimate times a fixed factor
The median of all areas' direct estimates

Answer and working

A. A weighted mean of direct and synthetic

Composite = phi x direct + (1 - phi) x synthetic.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

9 · Unit-level models: Battese-Harter-Fuller nested-error model · easy

Which model works with unit-level survey data?

Sample-size-dependent composite
Basic area-level Fay-Herriot
Simple synthetic ratio method
Nested-error regression

Answer and working

D. Nested-error regression

The Battese-Harter-Fuller nested-error model is fitted to units.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

10 · Calibration estimation and the GREG estimator · easy

Calibration weights satisfy which condition?

Every weight equals one exactly
Weighted sample x equals known X
Weights sum to the sample size
Weighted y equals a census y

Answer and working

B. Weighted sample x equals known X

The calibration equation is sum w_i x_i = X.

Further reading: Rao and Molina, Small Area Estimation; Sarndal, Swensson and Wretman, Model Assisted Survey Sampling

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