Properties of Good Estimator
A good point estimator should possess several desirable
properties. Here are some important properties of a good point estimator:
- Unbiasedness:
An estimator is said to be unbiased if, on
average, it gives the correct value of the parameter it is estimating. In other
words, the expected value of the estimator equals the true value of the
parameter. An unbiased estimator does not systematically overestimate or
underestimate the parameter.
- Efficiency:
An efficient estimator is one that
has the smallest possible variance among all unbiased estimators. In other
words, it provides the most precise estimate of the parameter compared to other
estimators. Efficiency is a desirable property because it reduces the
variability or uncertainty in the estimation.
- Consistency:
A consistent estimator is one that
approaches the true value of the parameter as the sample size increases. As the
sample size grows larger, a consistent estimator should converge to the true
value of the parameter. Consistency ensures that the estimator becomes more
reliable as more data becomes available.
- Sufficiency:
A sufficient estimator captures
all the information about the parameter contained in the data. It means that
once you know the value of the estimator, there is no additional information in
the sample that would provide further insight into the parameter. Sufficiency
helps in reducing the dimensionality of the data while retaining the essential
information.
- Robustness:
A robust estimator is resistant to outliers or
departures from the assumed model. It means that the estimator's performance is
not unduly affected by extreme or atypical observations. Robust estimators are
desirable when dealing with data that may contain outliers or when the
underlying assumptions of the model are violated.
- Low
variance:
A good estimator should have a low variance,
indicating that it produces estimates that are relatively close to the true
value of the parameter. A low-variance estimator is desirable because it
reduces the spread or uncertainty around the estimated value.
- Computational
feasibility:
An estimator should be computationally
feasible, meaning that it can be calculated efficiently and in a reasonable
amount of time. The estimator should not require excessive computational
resources or be overly complex to implement.
These properties collectively help determine the quality and
reliability of a point estimator. However, it's important to note that not all
estimators can possess all these properties simultaneously. The choice of
estimator depends on the specific requirements of the problem at hand and the
underlying assumptions of the statistical model
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