# Presentation: 589861

## Federica Piersimoni
ISTAT - Italian National Institute of Statistics
Roberto Benedetti
University “G.d’Annunzio” of Chieti-Pescara, Italy
Giuseppe Espa
Universy of Trento, Italy

**ISTAT - Italian National Institute of Statistics**
***Roberto Benedetti***
**University “G.d’Annunzio” of Chieti-Pescara, Italy**
***Giuseppe Espa***
**Universy of Trento, Italy**

- On the use of auxiliary variables in agricultural surveys design

## Contents

**Actual situation**
**Proposal**
**Estimators**
**Sampling designs**
**Data description**
**Simulation**
**Analysis of the results**
**Conclusions**

## Actual situation

**Population units**

**Sample units**

**Actual situation**

## in sample surveys

## 2001 scatter plot matrix

**2001 scatter plot matrix**
**tc1**= cattle slaughterings 2001
**tc2**= sheep and goats
-         slaughterings 2001
**tc3**= pigs slaughterings 2001
**tc4**= equines slaughterings 2001

## 2000 scatter plot matrix

**2000 scatter plot matrix**
**tc10**= cattle slaughterings 2000
**tc20**= sheep and goats
-           slaughterings 2000
**tc30**= pigs slaughterings 2000
**tc40**= equines slaughterings 2000

## 1999 scatter plot matrix

**1999 scatter plot matrix**
**tc19**= cattle slaughterings 1999
**tc29**= sheep and goats
-           slaughterings 1999
**tc39**= pigs slaughterings 1999
**tc49**= equines slaughterings 1999

## SCATTER PLOTS

**SCATTER PLOTS**

- tc1: cattle slaughterings 2001
- tc2: sheep and goats slaughterings 2001
- tc3: pigs slaughterings 2001
- tc4: equines slaughterings 2001

- tc10: cattle slaughterings 2000
- tc20: sheep and goats slaughterings 2000
- tc30: pigs slaughterings 2000
- tc40: equines slaughterings 2000

- tc19: cattle slaughterings 1999
- tc29: sheep and goats slaughterings 1999
- tc39: pigs slaughterings 1999
- tc49: equines slaughterings 1999

## Year 2001

**Year 2001**

**Year 2000**

**Year 1999**

## Sampling frame: N = 2.211 units (enterprises) and 

**Sampling frame**: *N* = 2.211 units (enterprises) and
- 12 variables:
- 	number of:
- cattle,
- pigs,
- sheep and goats,
- equines
- 	slaughtered at the census surveys of 1999, 		2000 e 2001.
****

## 

****
- 2000 samples of size *n* = 200...
- ...using as auxiliary information* the complete frame *at 1999 and at 2000 to obtain estimates at 2001!
- Estimates obtained through the HorvitzThompson expansion estimator and the calibration estimator (*PV*) by Deville and Särndal (1992):

**Distance function**

**Vector of the totals of**
** ****the auxiliary variables**

## Samples selection

**Samples selection**
**simple random sampling (SRS)**
**stratified sampling (ST)**
**ranked set sampling (RSS)**
**probability proportional to size (********PS)**
**balanced sampling**
******PS****  + ****balanced sampling****   **

## SRS: direct estimate doesn’t use                   auxiliary information

***SRS*****:***** *****direct estimate doesn’t use                   auxiliary information**
** **
***ST*****:**** auxiliary information is used **_***ex ante***_** the strata setting up;**
**  ****five planned strata;**
**  ****multivariate allocation model by Bethel (1989).****   **

## RSS: original formulation: 

***RSS*****: ****original formulation: **
** **
**Selection *****SRS *****without reinsertion of a first sample of *****n***** units;**
**Ranking in increasing order of the *****n***** units of the sample with respect to an auxiliary variable *****x***** known for every population unit; **
**The interest variable  *****y *****is measured on the first unit only; **
**A second *****SRS***** is drawn and ranked; **
**The interest variable  *****y *****is measured on the second unit only; **
**...****.and so on till *****n***** replications.**** **

## Ranking variable:

***Ranking *****variable:**
***with k *****=1,...,*****N*****,***** i *****=1,4 and *****t*****=1999, 2000. **
**For the units *****k*****: ****	****	****	******

## PS:

*********PS*****:**
**If *****y***** ******** positive auxiliary variable *****x***** ******** selection with probability ******** *****x*****. **
**Such *****ex ante***** probability is **

## BALANCED SAMPLING and PS + BALANCED SAMPLING:

***BALANCED SAMPLING and ************PS + BALANCED SAMPLING*****:**
**The balance constraint**
**has been imposed for the four variables to be estimated. **
**The difference between the two criteria:**
**in the second case the constraint is imposed *****ex post***** to ***********PS***** samples**

## Slide 18

## Slide 19

## Slide 20

## Slide 21

## Slide 22

## TOTAL

**TOTAL**

## Conclusions

**Conclusions**

** ****It is better to impose the balance constraints in **
**design phase, than in *****ex post***
** ****(cf. RMSE SRS - RMSE BAL)**

**Best performances: balanced ***********PS *****selections and ***********PS***** with calibration**

** ****a joint use of complex estimators together**
** ****with efficient sampling designs may reduce**
**considerably the variability of the estimates**

**but......**

## but......

*********PS *****and ***********PS***** with calibration selection criteria**

**but......**

**more efficient**

**less robust of the others when**
** ****outliers are present**

-  **bad performance of *****RSS***** method**

-  **forced univariate use of the auxiliary information**
** ****for the ranking setting up when linear independence is present**

## Simulated sampling distribution of the tc2 estimates in the case of ps, with calibration estimator based on auxiliary variables of 2000

- Simulated sampling distribution of the tc2 estimates in the case of ps, with calibration estimator based on auxiliary variables of 2000

**TRUE VALUE**

## Simulated sampling distribution of the tc3 estimates in the case of ps, with calibration estimator based on auxiliary variables of 1999

- Simulated sampling distribution of the tc3 estimates in the case of ps, with calibration estimator based on auxiliary variables of 1999

**TRUE VALUE**

## Simulated sampling distribution of the tc4 direct estimates in the case of balanced ps, based on auxiliary variables of 1999

- Simulated sampling distribution of the tc4 direct estimates in the case of balanced ps, based on auxiliary variables of 1999

**TRUE VALUE**

## Simulated sampling distribution of the tc2 direct estimates in the case of balanced ps, based on auxiliary variables of 2000

- Simulated sampling distribution of the tc2 direct estimates in the case of balanced ps, based on auxiliary variables of 2000

**TRUE VALUE**

## References

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