What is Point Estimator?

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, a single value or estimate is chosen from the sample set of data, which is generally considered the best guess or estimate from the lot. This single statistic represents the best estimate of the unknown parameter of the population.

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

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Characteristics of Point Estimators

The characteristics can be the following:

#1 – Bias

Biasness is the gap between the value expected from the estimator and the value of estimation considered regarding the parameter. When the estimated value shows zero bias, the situation is considered unbiased. Also, when the estimated value of the parameter and the parameter value estimate is equal, the estimation is considered biased. The 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 measured parameter value, the lower the business level.

#2 – Consistency

It states that the estimator stays close to the parameter’s value as the population’s size increases. Thus, a large sample size is required to maintain its consistency level. When the expected value moves towards the parameter’s value, 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 considers how dispersed the estimator is from the estimate. The smallest variance should deviate the least when different samples are brought into place. But, of course, this also depends on the distribution of the population.

Properties

  • Biasedness is one of the most important properties. This is the difference between the estimated point estimator value and the parameter’s expected value. The closer the value of the estimator to the expected parameter value, the lesser the bias.The next property is consistency and sufficiency. Consistency measures how close the estimator is to the parameter’s value. As the sample size increases, the estimator value should remain close to the parameter’s value. The lower it deviates, the more it is considered to be consistent.Lastly, mean square error and relative efficiency can be treated as properties. 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:

#1 – Method of Moments

This method was first used and invented by the famous Russian mathematician Pafnuty Chebyshev in 1887. It generally applies to collecting facts about an entire population and applying the same facts to the sample set obtained from the population. It usually begins by deriving many 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 one can estimate the moments. Then, the second step equation one can calculate using the mean or average of the population moments. It generally creates the best point estimator of the unknown set of parameters.

#2 – Maximum Likelihood Estimator

Here, the set of unknown parameters is derived in this technique, which can relate the related function and 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 value used.In point estimation, a single value is considered: the best statistic or the statistic means. In interval estimation, a range of numbers is considered to drive information about the sample set.Point estimators are generally estimated by moments and maximum likelihood, whereas interval estimators derive by techniques like inverting a test statistic, pivotal quantities, and Bayesian intervals.A point estimator will provide an inference related to a population by estimating a value related to an unknown parameter using a single value or point. In contrast, an interval estimator will provide an inference related to a population by estimating a value related to an unknown parameter using intervals.

Advantages

  • It is considered the best-chosen or the best-guessed value. It generally brings a lot of consistency to the study, even if the sample changes.Here, we generally focus on a single value, saving much study time.Point estimators are considered less biased and more consistent. Thus, its flexibility is generally more than interval estimators when there is a change in the sample set.

Conclusion

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

This article is a guide to Point Estimators and its definition. Here, we discuss point estimators’ characteristics, properties, methods, and advantages. You may learn more about financing from the following articles: –

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