is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. A sufficient statistic contains all of the...

unknown quantity and that depends on the data only through a complete, sufficient statistic is the unique best unbiased estimator of that quantity. The Lehmann–Scheffé...

ancillary information. It is closely related to the concept of a sufficient statistic which contains all of the information that the dataset provides about...

variety of desirable properties, most importantly the existence of a sufficient statistic. The concept of exponential families is credited to E. J. G. Pitman...

concept of a complete statistic which contains no ancillary information. It is closely related to the concept of a sufficient statistic which contains all...

a sufficient statistic is the same as that of the sample X. This may be seen by using Neyman's factorization criterion for a sufficient statistic. If...

that determining the MVUE is simply a matter of finding a complete sufficient statistic for the family p θ , θ ∈ Ω {\displaystyle p_{\theta },\theta \in...

algorithmic sufficient statistic. We write `algorithmic' for `Kolmogorov complexity' by convention. The main properties of an algorithmic sufficient statistic are...

then the conditional expectation of g(X) given T(X), where T is a sufficient statistic, is typically a better estimator of θ, and is never worse. Sometimes...

A statistical hypothesis test is a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular...

theorem states that any boundedly complete and sufficient statistic is independent of any ancillary statistic. This is a 1955 result of Debabrata Basu. It...

mean as it is a one-to-one function of the sum) is a complete and sufficient statistic for λ. To prove sufficiency we may use the factorization theorem...

required the existence of a sufficient statistic for the fiducial method to apply. Suppose there is a single sufficient statistic for a single parameter....

Sometimes it is possible to find a sufficient statistic for the nuisance parameters, and conditioning on this statistic results in a likelihood which does...

Common test statistics Descriptive statistics Sample statistics Sufficient statistic Data processing Upton, Graham; Cook, Ian (2 October 2008). "Dictionary...

serves as a sufficient statistic for Z. Furthermore, the above theorems indicate that the propensity score is a minimal sufficient statistic if thinking...

model Sufficient statistic Geisser, S. (2006), Modes of Parametric Statistical Inference, John Wiley & Sons Cox, D. R. (2006), Principles of Statistical Inference...

function (this is usually just gathering the data); Reduce to a sufficient statistic S {\displaystyle S} of the same dimension as θ {\displaystyle \theta...

} does not depend on λ (in the language of statisticians, N is a sufficient statistic for this parametrized family of probability distributions for the...

Further, because T is a sufficient statistic, δ 1 ( X ) {\displaystyle \delta _{1}(X)} does not depend on θ, hence, becomes a statistic. This result is known...

principles, see the derivation in moment-generating function of the sufficient statistic. The noncentral moments (raw moments) of a chi-squared distribution...

coefficient (taken together with the sample mean and variance) is only a sufficient statistic if the data is drawn from a multivariate normal distribution. As...

that the only families of probability distributions that admit a sufficient statistic whose dimension remains bounded as the sample size increases are...

(\theta )T(x))} has a monotone non-decreasing likelihood ratio in the sufficient statistic T ( x ) {\displaystyle T(x)} , provided that η ( θ ) {\displaystyle...

Sufficient statistic, when a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that...

X T Y {\displaystyle \mathbf {X} ^{\rm {T}}\mathbf {Y} } to be a sufficient statistic for β {\displaystyle {\boldsymbol {\beta }}} . Following is a table...

exponential family form with ν + X 2 {\displaystyle \nu +X^{2}} as sufficient statistic. The function A(t | ν) is the integral of Student's probability density...

The consequence is that the raw score for an item or person is the sufficient statistic for the item or person parameter. That is to say, the person total...

of a single parameter and data that can be summarised in a single sufficient statistic, it can be shown that the credible interval and the confidence interval...

integers with one or both bounds unknown has a finite-dimensional sufficient statistic, namely the triple of the sample maximum, sample minimum, and sample...