A statistic is sufficient for $\theta$ if the conditional distribution of X given T does not depend on $ \theta $. You're right in that $\theta$ is not a random variable.

In this lesson, we'll learn how to find statistics that summarize all of the information in a sample about the desired parameter. Such statistics are called sufficient statistics, and hence the …

In this lesson, we'll learn how to find statistics that summarize all of the information in a sample about the desired parameter. Such statistics are called sufficient statistics, and hence the …

Aug 29, 2023 · Sufficiency is a central concept in statistics that allows us to focus on the essential aspects of the data set while ignoring details that are irrelevant to the inference problem.

Jun 6, 2020 · A sufficient statistic is known as minimal or necessary if it is a function of any other sufficient statistic. A necessary sufficient statistic realizes the utmost possible reduction of a …

Dec 8, 2024 · In statistical theory, a "statistic" is a well-behaved (i.e., "measurable") function of the data, which is what's actually used in calculations or inferences, rather than the full data set. …

Jan 1, 2014 · A statistic T is called complete sufficient for θ if and only if (1) T is sufficient for θ and (2) T is complete. A complete sufficient statistic, if it exists, is also a minimal sufficient statistic. …

Apr 23, 2022 · A sufficient statistic contains all available information about the parameter; an ancillary statistic contains no information about the parameter. The following result, known as …

A statistic T is called a sufficient statistic for the parameter Θ (in the Bayesian sense) if, for every prior µ Θ , there exist versions of the posterior distributions µ Θ|X and µ Θ|T such that, for …

Sufficient statistics are many, even based on the same sample and for the same parameter (e.g., the ordered sample is such). A sufficient statistic ismin-imal if it is the function of any other …

If you have $n$ random variables that are iid with density $\frac{1}{p}e^{-x/p}$, how do you show that the sum of the $x_i$'s is a sufficient statistic? Attempt: Take likelihood function and …

n, the statistic T, is called a sufficient statistic if equation (1) is a function of the values, t, of the statistic and does not depend on the value of the parameter θ. Thus, by the law of total …

Mar 12, 2015 · A sufficient statistic need not estimate anything. For example, if $X_1, \ldots, X_n$ are iid samples drawn from an exponential distribution with unknown mean $\theta$, then …

Feb 10, 2018 · A statistic T = T ⁢ (𝑿) of 𝑿 for the parameter θ is called a sufficient statistic, or a sufficient estimator, if the conditional probability distribution of 𝑿 given T ⁢ (𝑿) = t is not a function …

Oct 4, 2015 · The "normal" definition of a sufficient statistics is via independence of the pdf (conditional on the statistic) of the parameter θ. The Fisher-Neyman theorem gives a nice …

1 day ago · Celebrating Math and Statistics Awareness Month at home is a great way to nurture critical thinking and confidence—skills that will benefit kids in school and beyond. So, grab a …

May 23, 2023 · The big picture is that, for a specific family of distribution, a sufficient statistic contains all the information about a corresponding parameter the observed data provides. …

22 hours ago · Existing ‘official’ multi-regional input-output (MRIO) databases lack sufficient sectoral detail and extensions for calculating accurate environmental and social footprints. …

Jan 25, 2025 · It can be checked that $T = \mathbb{1}_{\{Red door \cup blue door\}}$ is a sufficient statistic. But if we assume $p$ to be something like $\frac{1}{1000}$ , the conditional …