query: If $T(\bf{X})$ is a sufficient statistic for $\theta$, why does the conditional distribution of $\bf{X}$ given $T(\bf{X})$ doesn't depend on $\theta$?
positive_passages.docid: 151835
positive_passages.text: Intutitive meaning behind the formal definition of sufficient statistic?
negative_passages.docid: 35454
negative_passages.text: Is it correct to write $\Bbb E[X]$ or $\Bbb E_{\theta}[X]$?
negative_passages.docid: 66104
negative_passages.text: Showing that something is a sufficient statistic
negative_passages.docid: 32509
negative_passages.text: Proving a statistic is ancillary
negative_passages.docid: 116689
negative_passages.text: Joint distribution of range $(R=X_n-X_1)$ and mid-range $(V=\frac{1}{2}(X_1+X_n)$order statistics
negative_passages.docid: 100173
negative_passages.text: Maximum likelihood estimation when the density is $f(x;\theta) = \theta x^{\theta -1} $
negative_passages.docid: 56453
negative_passages.text: Sufficient statistics for Uniform $(-\theta,\theta)$
negative_passages.docid: 123844
negative_passages.text: conditional expectation: an implication
negative_passages.docid: 83464
negative_passages.text: Conditional expectation of $\mathbb{E}(X - Y | (X, Y)\in\mathcal{A})$
negative_passages.docid: 33785
negative_passages.text: Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom
negative_passages.docid: 116898
negative_passages.text: Find the maximum likelihood estimator for $\theta$ when $f(x)=2\theta^{-2}x, 0\leq x \leq \theta$
negative_passages.docid: 61712
negative_passages.text: A sufficient statistic for Laplace distribution
negative_passages.docid: 109945
negative_passages.text: What is the distribution of the difference of two-t-distributions
negative_passages.docid: 15561
negative_passages.text: Obtaining a level-$\alpha$ likelihood ratio test for $H_0: \theta = \theta_0$ vs. $H_1: \theta \neq \theta_0$ for $f_\theta (x) = \theta x^{\theta-1}$
negative_passages.docid: 115068
negative_passages.text: If the dimension of a sufficient statistic $T(X)$ equals the dimension of parameter space, $T(X)$ is minimal sufficient?
negative_passages.docid: 139123
negative_passages.text: Is $\bar X$ a minimum variance unbiased estimator of $\theta$ in an exponential distribution?
negative_passages.docid: 133266
negative_passages.text: If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis