Wage rate established by collective bargaining or by government regulation, specifying the lowest rate at which workers may be employed. A legal minimum wage is one mandated by government for all workers in an economy, with few exceptions. Privately negotiated minimum wages determined by collective bargaining apply to a specific group of workers in the economy, usually in specific trades or industries. The modern minimum wage, combined with compulsory arbitration of labour disputes, first appeared in Australia and New Zealand in the 1890s. In 1909 Britain established trade boards to set minimum wage rates in certain trades and industries. The first minimum wage in the U.S. (which applied only to women) was enacted by Massachusetts in 1912. Minimum wage laws or agreements now exist in most nations.
Learn more about minimum wage with a free trial on Britannica.com.
In mathematics, a point at which the value of a function is lowest. If the value is less than or equal to all other function values, it is an absolute minimum. If it is merely less than at any nearby point, it is a relative, or local, minimum. In calculus, the derivative equals zero or does not exist at a function's minimum point. Seealso maximum, optimization.
Learn more about minimum with a free trial on Britannica.com.
for any other unbiased estimator
If an unbiased estimator of exists, then one can prove there is an essentially unique MVUE estimator. Using the Rao-Blackwell theorem one can also prove that determining the MVUE estimator is simply a matter of finding a complete sufficient statistic for the family and conditioning any unbiased estimator on it. Put formally, suppose is unbiased for , and that is a complete sufficient statistic for the family of densities. Then
is the MVUE estimator for
the MVUE minimizes MSE among unbiased estimators. In some cases biased estimators have lower MSE; see estimator bias.
and we wish to find the UMVU estimator of
First we recognize that the density can be written as
Which is an exponential family with sufficient statistic . In fact this is a full rank exponential family, and therefore is complete sufficient. See exponential family for a derivation which shows
Clearly is unbiased, thus the UMVU estimator is
This example illustrates that an unbiased function of the complete sufficient statistic will be UMVU.