Formulae to Measure Point Estimators

Formulae used to measure point estimators depend on the specific estimator and parameter being estimated. However, in general, a point estimator can be represented as a function of the sample data, denoted by a symbol such as [Tex]\hat{θ}[/Tex].

For example, the sample mean (x̄) is a point estimator for the population mean (μ), and its formula is:

x̄ = (Σx_i) / n

where,

• x_i represents Each Individual Observation in Sample
• n is Sample Size

Similarly, the sample variance (s²) is a point estimator for the population variance (σ²), and its formula is:

s² = Σ (x_i – x̄)² / (n – 1)

Other point estimators, such as the sample proportion or the sample median, have their own specific formulae based on the sample data and the parameter being estimated.

What are Values Needed to Calculate Point Estimators?

To calculate point estimators, you typically need sample data from the population of interest. The specific values needed depend on the estimator being used.

For example, to calculate the sample mean, you need the individual observations from the sample. To calculate the sample variance, you need both the individual observations and the sample mean.

Similarly, other estimators require different types of sample data, such as counts for proportions or ordered data for medians. Additionally, the sample size is often a crucial factor in calculating point estimators, as it determines the precision and reliability of the estimates.

Some Common Point Estimators Used in Statistics

Common point estimators include:

• Sample Mean (x̄) for estimating Population Mean (μ)
• Sample Variance (s²) for estimating Population Variance (σ²)
• Sample Proportion (p̂) for estimating Population Proportions

Method of Moments (MoM) in Point Estimation

• Method of moments is an approach in point estimation where population moments are equated with sample moments to derive estimators.

• It involves setting the sample moments equal to the theoretical moments of the population distribution.

Maximum Likelihood Estimation (MLE)

• Maximum likelihood estimation is a method used to estimate the parameters of a statistical model by maximizing the likelihood function.

• It seeks the parameter values that make the observed data most probable under the assumed model.

Read More,

• Mean
• Mode
• Difference Between Variance and Standard Deviation

Point estimation is a fundamental concept in statistics providing a method for estimating population parameters based on sample data. In this article, we will discuss point estimation, its techniques and its significance in detail.