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Statistical tests when sample size is 1

Meta-Analysis could be performed with sample size n=0 :). Quoting Wikipedia: A meta-analysis is a statistical analysis that combines the results of multiple scientific studies (especially randomised ...
user's user avatar
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1 vote

Can I estimate the mean of a dataset if I have its standard deviation and a portion of the full data that is higher than some threshold?

Given an iid sample $(X_1,\ldots,X_n)$, with density $f_\theta$, the sub-vector of order statistics $V=(X_{(\alpha n)},\ldots,X_{(n)})$ [where $0<\alpha<1$ and $\alpha n\in\mathbb N^*$] has ...
Xi'an's user avatar
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1 vote

Is this a typo on P.75, Theorem 5.52 of the book "Asymptotic Statistics" by Van der Vaart?

First point: Since $d(\theta, \theta_0)<\delta$ it should be possible to select $\theta = \theta_0$ which gives $\sup=0>-C\cdot0^\alpha$. Without being specific for this problem, if $x^*=\arg\...
Hunaphu's user avatar
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0 votes

Estimating the Joint and Conditional probability distributions for discrete variables

There are many estimators that can be used to estimate a discrete probability distribution with known range. The empirical distribution (simply taking the observed proportions of occurrences of the ...
Ben's user avatar
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1 vote

Unable to estimate AR(p) coefficients and $\sigma^2$

The trick is to re-label the time units so that the unit of time equals 2. Then things become easier. Let `$X^{*}_{t} = X_{2t}$ and $W^{*}_t = W_{2t} ~\forall~t = 0,1,2,3, \ldots \infty$, Then, you ...
mlofton's user avatar
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2 votes

What standard references discuss the differences between hypothesis testing, estimation and prediction?

One reference is Shmueli 2010. To Explain or to Predict? From the introduction: My main premise is that the two are often conflated, yet the causal versus predictive distinction has a large impact on ...
3 votes

Cramer-Rao bound for biased estimators

The thing about unbiased estimators is that they are not always the best estimator in terms of minimized error. Often, you should choose to use a biased estimator. Nonetheless, one should still care ...
Davey's user avatar
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5 votes

Cramer-Rao bound for biased estimators

how does the bound help us for biased estimators since if the estimator is biased then it's variance is not equal to its mean squared error If you are using the squared error loss then we may use the ...
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