Point Estimators

What is Point Estimator?

Point estimator is primarily used in statistics where a sample set of data is considered and among it a single best-judged value is chosen which serves as the base of an undescribed or unknown population parameter.

The point estimator technique is a technique that is used in statistics that comes into use to arrive at an estimated value of an unknown parameter of a population. Here from the sample set of data, a single value or estimate is chosen, which is generally considered to be the best guess or the best estimate from the lot. This single statistic represents the best estimate of the unknown parameter of the population.

Point estimates are generally considered to be consistent, unbiased, and most efficient. In other words, the estimate should vary the least from sample to sample.

Point Estimators

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Characteristics of Point Estimators

The characteristics can be the following:

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#1 – Bias

Biasness is defined as the gap between the value expected from the estimator and the value of estimation considered with regards to the parameter. When the value estimated is showing zero bias, the situation is considered unbiased. Also, at times when the estimated value of the parameter and the parameter value being estimated are equal, the estimation is considered to be biased. Closer the expected valueExpected ValueExpected value refers to the anticipation of an investment's for a future period considering the various probabilities. It is evaluated as the product of probability distribution and outcomes.read more of estimation to the parameter value being measured, the lower the level of business.

#2 – Consistency

It states that as the size of the population increases, how close the estimator stays to the value of the parameter. Thus, a large sample size if required to maintain its consistency level. When the expected value moves towards the value of the parameter, we state that the estimation is consistent.

#3 – Most Efficient or Unbiased

The most efficient estimator is considered the one which has the least unbiased and consistent variance among all the estimators considered. The variance here is considered as to how dispersed the estimator is from the estimate. The smallest variance should deviate the least when different samples are brought into place. This also depends on the distribution of the population.

Properties

  • Biasedness is one of the most important properties. This is described as the difference between the point estimator value estimated and the expected value of the parameter. The closer the value of the estimator to the value of the parameter expected, the lesser is the bias.
  • The next property is consistency and sufficiency. Consistency is the measure of how close the estimator is to the value of the parameter. In simple terms, it means as the size of the sample increases, the estimator value should remain close to the value of the parameter, and the lower it deviates, the more it is considered to be consistent.
  • Lastly, mean square error and relative efficiency can also be treated as property. The mean square error is derived as the sum of the variance and the square of its bias. The estimator with the lowest MSE is considered to be the best.

Methods of Finding Point Estimators

There are generally two prime methods which are as follows:

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#1 – Method of Moments

This method was first used and invented by the famous Russian mathematician Pafnuty Chebyshev in 1887. This is generally applied with the process of collecting facts about an entire population and application of the same facts to the sample set obtained from the population. It usually begins by deriving a lot of equations related to the moments prevalent among the population and applying the same to the unknown parameter.

The next step is drawing a random sample from the population where the moments can be estimated, and the equation from the second step is calculated by the use of the mean or average of the population moments. This generally creates the best point estimator of the unknown set of parameters.

#2 – Maximum Likelihood Estimator

Here in this technique, the set of unknown parameters is derived, which can relate the function related to it and also maximize the function. Here a well-known model is selected, and the values present are used further to compare with the data set, which on a trial and error method, helps us to adjourn the most relevant match for the data set, which is called the point estimator.

Point Estimation vs Interval Estimation

  • The prime difference between the two is the usage of the value.
  • In point estimation, a single value is considered, which is the best statistic or the statistic mean, whereas, in interval estimation, a range of numbers is considered to drive information about the sample set.
  • Point estimators are generally estimated by techniques like a method of moments and maximum likelihood, whereas interval estimators are derived by techniques like inverting a test statistic, pivotal quantities, and Bayesian intervals.
  • Point estimator will provide an inference related to a population by means of providing an estimate of value related to an unknown parameter by using a single value or point, whereas interval estimator will provide an inference related to a population by means of providing an estimate of value related to an unknown parameter by the usage of intervals.

Advantages

  • It is considered to be the best-chosen value or the best-guessed value. This generally brings a lot of consistency to the study even if sample changes
  • Here, we are generally focused on a single value, which saves a lot of time doing the study.
  • Point estimators are considered to be less biased and more consistent, and thus, the flexibility it has is generally more than interval estimators when there is a change in the sample set.

Conclusion

Point Estimator solely depends on the researcher who is conducting the study on what method of estimation one needs to apply as both point, and interval estimators have their own pros and cons. It is a bit more efficient because it is considered to be more consistent and less biased, and it can also be used when there is a change in sample sets.

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