# Numerical Prediction Task

A numerical prediction task is a prediction task that produces a point estimate of a population parameter based on a population sample.

**AKA:**Population Parameter Estimation.**Context:****input:**a Numerically Labeled Dataset.**output:**a Point Estimate, such as:- an Average Estimate (of an Average Point/Average Value)
- a Minimum Estimate (of a Minimum Point/Minimum Value).
- a Maximum Estimate (of a Maximum Point/Maximum Value).
- a Median Estimate (of a Median Point/Median Value).
- a Square Sum Estimate (of a Sum Square Value).
- a Standard Deviation Estimate (of a Standard Deviation Value).
- a Maximum Likelihood Estimate (e.g. by an MLE Task)
- a Maximum a Posteriori Estimate (e.g. by a MAP Task)
- optional: a Point Estimation Function (by a point estimation function creation task).

**measure**a Point Estimation Performance Measure, such as RMS.- It can be solved by a Point Estimation System (that implements a point estimation algorithm).
- It can range from being a Univariate Point Estimation Task, to being a Bivariate Point Estimation Task, to being a Multivariate Point Estimation Task.
- It can range from (typically) being a Data-Driven Point Estimation Task to being a Heuristic Point Estimation Task.
- It can range from being an Interpolation Task to being an Extrapolation Task.

**Example(s):****Counter-Example(s):****See:**Statistical Inference, Estimation Theory, Parametric Estimation Model.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/point_estimation Retrieved:2015-6-15.
- In statistics,
**point estimation**involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" or "best estimate" of an unknown (fixed or random) population parameter.More formally, it is the application of a point estimator to the data.

In general, point estimation should be contrasted with interval estimation: such interval estimates are typically either confidence intervals in the case of frequentist inference, or credible intervals in the case of Bayesian inference.

- In statistics,

### 2013

- http://stats.stackexchange.com/questions/65212/example-of-maximum-a-posteriori-estimation
- QUOTE: both ML and MAP are point estimators (they return an optimal set of weights, rather than a distribution of optimal weights).

### 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.
- QUOTE: … 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.

### 2005

- (Walker & Nees, 2005) ⇒ Bruce N. Walker, and Michael A. Nees. (2005). “Brief Training for Performance of a Point Estimation Sonification Task.” In: Proceedings of 11th International Conference on Auditory Display (ICAD2005)
- QUOTE: This study examined different types of brief training for a point estimation task with auditory graphs. … Forty Georgia Tech undergraduates completed a pre-test, an experimental training session, and a post-test for the point estimation task.

### 1999

- (Hollander & Wolfe) ⇒ Myles Hollander, Douglas A. Wolfe. (1999). “Nonparametric Statistical Methods, 2nd Edition." Wiley. ISBN:0471190454
- QUOTE: An estimator is a decision rule (strategy, recipe) which, on the basis of the sample observations, estimates the value of a parameter. The specific value (on the basis of a particular set of data) which the estimator assigns is called the estimate.