Questions tagged [statistical-inference]

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

1,035 questions
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How easy is it to create false evidence for a biased coin?

I have a biased coin which comes up heads with probability $p$. I know the value of $p$, but I want to falsely claim that the coin has a different probability of heads, $q$, where $q > p$. To ...
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single variable is significant but overall test is not

I do a multiple regression with 3 independent variables $X_1$, $X_2$ and $X_3$. The correlation between $Y$ and $X_1$, $Y$ and $X_2$, and $Y$ and $X_3$, are each large and statistically significant. ...
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Divergence based robust inference

The term 'divergence' means a function $D$ which takes two probability distributions $g,f$ as input and puts out a non-negative real number $D(g,f)$. I have learnt that the inference based on ...
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Sampling error of correlation coefficient (Phi coefficient) for binary variables

Suppose I have two correlated binary variables (A and B) with known probabilities ($p_a$ and $p_b$) and correlation (Phi) coefficient in population - $\rho$ . Is there any analytic function for ...
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Equivalent defintions of minimal sufficient statistics

Wikipedia claims that the statistic $S(X)$ is minimal sufficient if and only if $f_{\theta}(x)/f_{\theta}(y)$ is independent of $\theta$ $\iff$ $S(x) = S(y)$. It is also claimed that this is a ...
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I am learning Gaussian Process reading GPML. I am a bit confused with understanding the Bayesian analysis. Let consider the standard linear regression model with "Gaussian noise", i.e, $$f(\textbf{x}... 0answers 374 views UMVUE of \sqrt{a}/b for Gamma distribution Suppose (X_1,X_2,\ldots,X_n)\sim \operatorname{Gamma}(a,b), independent and identically distributed with pdf:$$f(x)=\frac{b^a}{\Gamma(a)}x^{a-1}e^{-bx},\quad x>0$$Find the UMVUE of \frac{\... 0answers 56 views Can a weakly consistent estimator beat a strongly consistent one? Suppose we have two estimators \hat{\theta}_1 and \hat{\theta}_2 of \theta, both with the same bias. If we have$$ \begin{align} &\hat{\theta}_1 \xrightarrow{a.s.}\ \theta \\ &\hat{\...
This is from Casella and Berger's Statistical Inference: Definition: A statistic $T(\mathbf{X})$ is a sufficient statistic for $\theta$ if the conditional distribution of the sample $\mathbf{X}$ ...
I'm trying to understand a proof of Cochran's theorem Let $X_1, X_2, \ldots, X_n$ be a random sample from an $N(0,1)$ distribution and let $x$ represent the vector of these observations. ...