Wednesday, August 11, 2010

[Statistics] Point Estimation

6103_chap01.pdf (399 KB)

From Wiki:

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" for 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.
Point estimation should be contrasted with general Bayesian methods of estimation, where the goal is usually to compute (perhaps to an approximation) the posterior distributions of parameters and other quantities of interest. The contrast here is between estimating a single point (point estimation), versus estimating a weighted set of points (a probability density function). However, where appropriate, Bayesian methodology can include the calculation of point estimates, either as the expectation or median of the posterior distribution or as the mode of this distribution.
In a purely frequentist context (as opposed to Bayesian), point estimation should be contrasted with the specific interval estimation calculation of confidence intervals.

From other resources:

For a population whose distribution is known but depends on one or more unknown parameters, point estimation predicts the value of the unknown parameter and interval estimation determines the range of the unknown parameter.

In summarization, point estimation is used to estimate mean, variance, standard deviation, or any other statistical parameter for describing the data.

In time-series prediction, point estimation is used to predict one or more values appearing later in the sequence by calculating parameters for a sample.

Methods to obtain point estimates:
1) moments
2) maximum likelihood estimation
3) Bayes estimators
4) EM
5) robust estimation
...

Criteria to assess estimators:
1) bias
2) mean squared error
3) standard error
4) efficiency
5) consistency
...

1 comment:

1. Great thoughts you got there, believe I may possibly try just some of it throughout my daily life.

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