ESTIMATORS AND THE ESTIMATION 

PROCESS 

by Charles R. Perry, Jr. 

The objective of any survey is to provide information on the characteristics of the population 

by examining a subset of the population. By analyzing the data from that subset - called a 

sample - we try to estimate population parameters such as means, totals, ratios, regression 

coefficients, etc. The goal of estimation is to wring from the sample all possible clues about 

the characteristics of the population while recognizing that the sample has limits to what 

it can tell us. 

What factors limit the information that the sample can provide? There are two primary 

limiting factors. The first is sampling error. Sampling error is controlled mostly through 

the sample design, especially the sample size. The second limiting factor is the nonsampling 

error, or bias, that affects the data. Nonsampling error actually causes a sample to 

misrepresent the true characteristics of the population. The sum of the sampling error and 

the nonsampling error defines the total error associated with a particular sample. This total 

error limits how much useful information can be obtained from the sample about the 

population. 

The estimation process has two components. The estimator, which is usually a formula or 

set of formulas, dictates how to calculate the estimate from the sample data. In other words, 

the formula(s) is the estimator and the actual number produced from the sample data is the 

estimate. NASS has created a variation on this terminology by using indication to refer to 

the number produced from the data and letting estimate refer only to the Agricultural Statistics 

Board estimate - the official number that is set after reviewing all the indications. 

There are two types of indications in general use - point indications and interval indications. 

A point indication is simply a single number calculated from the sample data. An interval 

indication has two numbers to provide upper and lower bounds on the population parameter. 

A confidence interval is an example of an interval indication. Although interval indications 

are a more sophisticated tool, NASS uses point indications for most of its work. However, 

whenever someone starts discussing CV's, that person is edging toward the interval concept 

rather than the point concept. 

It is possible to have several estimators even with the same sample design. For example, 

with our area sample we can have a tract estimator, an entire farm estimator, and a 

weighted estimator. How does one determine the best estimator? Statistical theory has 

developed a large amount of literature concerning the qualities that make a" good" estimator. 

Statistical properties such as variance, bias, mean square error, efficiency, sufficiency, and 

consistency as well as practical considerations such as cost have received a great deal of 

attention. It is difficult to discuss those issues without using a great many formulas. However, I 

should point out that different estimators may be "best" in different situations. For example, a 
tract estimator of total hogs may perform fairly well, but a tract estimator of pig deaths may 

perform poorly. Thus, to choose one "best" estimator for all situations becomes very difficult. 

The Board process is a tool used by NASS to evaluate multiple indications along with any 

other available information in order to produce an official estimate. Therefore, in the Board 

process, even if nowhere else, the relative strengths and weaknesses of each indication must 

be taken into account. 

NASS research has devoted considerable effort toward the investigation of analytic procedures 

that integrate or partially integrate survey estimates, control data, and other information. The 

aim is not to have analytic techniques replace the Board process but to provide the Board with 

more reliable inputs. 

A joint effort between the Research and Development Division and the Livestock Branch 

investigated the use of composite estimators for the June hog series. The aim of this 

work was to develop analytic procedures for combining farm, tract, weighted, and multiple 

frame indications in a single indication for use by the Board. Procedures were developed and 

tested using historical data for eight of the major hog producing States. These composite 

hog indications were used operationally with satisfactory results in June 1988. NASS has 

also implemented the use of composite indications for some crop variables. 

Estimation is the final step of the survey process - the final fruit of a carefully cultivated 

tree. During estimation NASS must decide what information has been learned about the 

agricultural situation. With precise, accurate, and relevant information, we can begin to 

interpret and understand the ever changing world of agriculture.