What do you call a jointly sufficient statistic?

What do you call a jointly sufficient statistic?

In such a case, the sufficient statistic may be a set of functions, called a jointly sufficient statistic. Typically, there are as many functions as there are parameters.

When is an unknown parameter a sufficient statistic?

More generally, the “unknown parameter” may represent a vector of unknown quantities or may represent everything about the model that is unknown or not fully specified. In such a case, the sufficient statistic may be a set of functions, called a jointly sufficient statistic.

Which is the best definition of sufficiency in statistics?

Sufficiency is the kind of topic in which it is probably best to just jump right in and state its definition. Let’s do that! Let X 1, X 2, …, X n be a random sample from a probability distribution with unknown parameter θ. Then, the statistic:

When is y a sufficient statistic for P?

The definition of sufficiency tells us that if the conditional distribution of X 1, X 2, …, X n, given the statistic Y, does not depend on p, then Y is a sufficient statistic for p. The conditional distribution of X 1, X 2, …, X n, given Y, is by definition:

Why is the exponential family special in statistics?

mal, Poisson, Binomial, exponential, Gamma, multivariate normal, etc. The reason for the special status of the Exponential family is that a number of important and useful calculations in statistics

When is a statistic sufficient for a family of probability distributions?

Sufficient statistic. In particular, a statistic is sufficient for a family of probability distributions if the sample from which it is calculated gives no additional information than does the statistic, as to which of those probability distributions is that of the population from which the sample was taken.

Is there such a thing as a minimal sufficient statistic?

If there exists a minimal sufficient statistic, and this is usually the case, then every complete sufficient statistic is necessarily minimal sufficient (note that this statement does not exclude the option of a pathological case in which a complete sufficient exists while there is no minimal sufficient statistic).

Which is an example of a sufficiently sufficient statistic?

For example, for a Gaussian distribution with unknown mean and variance, the jointly sufficient statistic, from which maximum likelihood estimates of both parameters can be estimated, consists of two functions, the sum of all data points and the sum of all squared data points (or equivalently, the sample mean and sample variance ).

Which is a sufficient statistic for the parameter θ?

A statistic t = T ( X) is sufficient for underlying parameter θ precisely if the conditional probability distribution of the data X, given the statistic t = T ( X ), does not depend on the parameter θ. As an example, the sample mean is sufficient for the mean ( μ) of a normal distribution with known variance.