Explaining Estimation Terms Used & What is Estimator ?

 

What is an Estimator // Types of Estimates // General terms in Estimation

 

 

What is an Estimator // Types of Estimates // General terms in Estimation

An estimator in the context of estimation refers to a person, algorithm, or method used to calculate or approximate certain quantities or parameters based on available information or data. Estimators are used in various fields, including economics, statistics, and project management, engineering, to make predictions or estimate unknown values.

Types of Estimates:

Point Estimate: 

It is a single value that is used to estimate an unknown parameter or quantity. It provides a best guess or approximation of the true value based on the available data.

Interval Estimate: 

It provides a range of values within which the true value of a parameter is expected to fall & also includes a lower bound and an upper bound, representing the level of uncertainty in the estimation.

Confidence Interval: 

It is a type of interval estimate that quantifies the uncertainty associated with a point estimate & also provides a range of values within which the true value of a parameter is expected to fall with a specified level of confidence.

Prediction Interval: 

A prediction interval is an estimate of a future value or observation. It provides a range of values within which a future data point is expected to fall with a specified level of confidence.

General Terms in Estimation:

Population: 

In estimation, a population refers to the entire set of individuals, items, or units of interest from which a sample is drawn or data is collected. The goal of estimation is often to make inferences or estimates about population parameters based on sample data.

Sample:

A sample is a subset of individuals, items, or units selected from a population. Estimation is often performed using sample data to make inferences about the entire population.

Parameter: 

A parameter is a characteristic or quantity that describes a population. It is often unknown and estimated using sample data. For example, the population means or population proportion is common parameters of interest.

Statistic: 

A statistic is a characteristic or quantity calculated from sample data. It is used as an estimate or approximation of the corresponding population parameter. For example, the sample mean or sample proportion is common statistics used to estimate population parameters.

Bias: 

Bias refers to the systematic error or tendency of an estimator to consistently deviate from the true value of the parameter being estimated. A biased estimator may consistently overestimate or underestimate the true value.

Variance: 

Variance measures the variability or spread of the estimates around their mean. A smaller variance indicates more precise or reliable estimates, while a larger variance indicates greater variability or uncertainty in the estimates.

Mean Square Error (MSE): 

MSE is a measure of the average squared difference between the estimated values and the true values. It takes into account both bias and variance and is commonly used to assess the accuracy and precision of an estimator.

Efficiency: 

Efficiency compares the precision of different estimators by measuring how much information they utilize to achieve a given level of accuracy. An efficient estimator achieves smaller variances and, therefore, requires a smaller sample size to achieve a desired level of precision.

Consistency: 

Consistency refers to the property of an estimator that it converges to the true value of the parameter as the sample size increases & also produces increasingly accurate estimates as more data becomes available.

Unbiasedness: 

Unbiasedness refers to the property of an estimator that its expected value is equal to the true value of the parameter being estimated. An unbiased estimator, on average, provides estimates that are not systematically too high or too low.

FAQ on Estimation

Q: What is estimation? 

A: Estimation is the process of calculating or approximating unknown values or parameters based on available information or data. It involves using known information to make educated guesses or predictions about unknown quantities.

Q: Why is estimation important? 

A: Estimation is important because it allows us to make informed predictions, decisions, and plans when precise or exact values are not available. It helps in understanding and analyzing data, managing projects, forecasting future outcomes, conducting research, and making financial and business decisions.

Q: How is estimation different from measurement? 

A: Estimation involves making educated guesses or approximations of unknown values based on available information, while measurement involves obtaining precise or exact values using standardized tools or techniques. Estimation is often used when direct measurement is not feasible or practical.

Q: What are the main types of estimation? 

A: The main types of estimation are confidence interval estimation, point estimation, interval estimation, and prediction interval estimation. 

Q: What is a parameter in estimation? 

A: In estimation, a parameter refers to a characteristic or quantity that describes a population. It is often an unknown value of interest, such as the population mean or population proportion. Estimation involves using sample data to estimate or approximate these population parameters.

Q: What is a statistic in estimation? 

A: In estimation, a statistic refers to a characteristic or quantity calculated from sample data. It is used as an estimate or approximation of the corresponding population parameter. Common statistics used in estimation include the sample mean, sample proportion, or sample standard deviation.

Q: Evaluating the quality of an estimator?

 A: The quality of an estimator is evaluated based on various criteria, variance, efficiency, including bias, consistency, and mean square error (MSE). A good estimator should have low bias (not consistently over or underestimating), low variance (not highly variable), high efficiency (utilizing available information effectively), consistency (converging to the true value as sample size increases), and low MSE (small average squared difference from the true value).

Q: What is variance in estimation? 

A: Variance measures the variability or spread of the estimates around their mean. It quantifies the amount of uncertainty or variability in the estimation process. A smaller variance indicates more precise or reliable estimates, while a larger variance indicates greater variability or uncertainty in the estimates.

Q: What is the difference between confidence interval and prediction interval? 

A: A confidence interval is an estimate of the range of values within which the true value of a parameter is expected to fall with a specified level of confidence. It provides an interval estimate for the population parameter. On the other hand, a prediction interval is an estimate of the range of values within which a future data point or observation is expected to fall with a specified level of confidence.

Q: How can we improve the accuracy of my estimates? 

A: To improve the accuracy of estimates, we can consider using larger sample sizes, improving data quality and reliability, employing more precise measurement techniques, using sophisticated estimation methods or algorithms, and incorporating expert judgment or domain knowledge. Additionally, understanding the underlying assumptions and limitations of the estimation process can help in making more accurate estimates.

These frequently asked questions provide a basic understanding of estimation and its key concepts. Remember that estimation methods and techniques may vary depending on the specific field or context of application.