Interval Estimation Task
An Interval Estimation Task is an estimation task that requires an interval estimate.
- AKA: Range Prediction.
- Context:
- output: Interval Estimate.
- It can be associated to a Range Estimation Performance Measure.
- It can be solved by an Interval Estimation System (that implements an Interval Estimation Algorithm).
- …
- Example(s):
- Counter-Example(s):
- See: Confidence Interval, Probabilistic Classification, Decision Theory, Sampling (Statistics), Interval (Mathematics), Population Parameter.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/interval_estimation Retrieved:2015-2-13.
- In statistics, interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter, in contrast to point estimation, which is a single number. Jerzy Neyman (1937) identified interval estimation ("estimation by interval") as distinct from point estimation ("estimation by unique estimate"). In doing so, he recognised that then-recent work quoting results in the form of an estimate plus-or-minus a standard deviation indicated that interval estimation was actually the problem statisticians really had in mind.
The most prevalent forms of interval estimation are:
- Other common approaches to interval estimation, which are encompassed by statistical theory, are:
- Tolerance intervals.
- Prediction intervals - used mainly in Regression Analysis.
- Likelihood intervals.
- There is a third approach to statistical inference, namely fiducial inference, that also considers interval estimation. Non-statistical methods that can lead to interval estimates include fuzzy logic.
An interval estimate is one type of outcome of a statistical analysis. Some other types of outcome are point estimates and decisions.
- In statistics, interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter, in contrast to point estimation, which is a single number. Jerzy Neyman (1937) identified interval estimation ("estimation by interval") as distinct from point estimation ("estimation by unique estimate"). In doing so, he recognised that then-recent work quoting results in the form of an estimate plus-or-minus a standard deviation indicated that interval estimation was actually the problem statisticians really had in mind.
2006
- (Shieh, 2006) ⇒ Gwowen Shieh. (2006). “Exact Interval Estimation, Power Calculation, and Sample Size Determination in Normal Correlation Analysis.” Psychometrika 71, no. 3
- ABSTRACT: This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple correlation coefficients. The inversion principle and monotonicity property of the proposed formulations are used to describe alternative approaches to the exact interval estimation, power calculation, and sample size determination for correlation coefficients.
2006
- (Dubnicka, 2006k) ⇒ Suzanne R. Dubnicka. (2006). “Introduction to Statistics - Handout 11." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
- … Estimation and hypothesis testing are the two common forms of statistical inference. … In estimation, we are trying to answer the question, “What is the value of the population parameter?” An estimate is our “best guess” of the value of the population parameter and is based on the sample. Therefore, an estimate is a statistic. Two types of estimates are considered: point estimates and interval estimates. A point estimate is a single value (point) which represents our best guess of a parameter value. As our point estimate is not likely to be exactly the same value as the parameter, we often given a measure of variability associated with our point estimate. This value is called the standard error of the estimate and gives us an idea of how far off our estimate can potentially be. An interval estimate, commonly called a confidence interval, is a range of values within which we “strongly” believe the parameter value lies. A confidence interval incorporates the point estimate and standard error. … There may be more than one sensible point estimate of a parameter, depending on the criteria used.