* "variance of the estimator" means "variance of

**the sampling distribution of**the estimator". AFAICT, this is unambiguous, and the only reasonable interpretation is for "estimator" to mean the random variable. To make this even more explicit: the estimator(RV) is the result of applying the estimator(function) to the random data.

* "estimate the parameters" means "estimate

**the values of**the parameters"; more confusingly, "choose the parameters" can mean "choose

**the values of**the parameters". This may just be the econometricians I've been reading.

* "distribution" to mean "family of distributions". Very standard. No one blinks an eye at "the Gaussian distribution". I think "family" is typically only used to describe families for which mean and variance are not sufficient statistics.

* "sample" to mean "data point". One should be careful here: in standard usage, a "sample" is a

**collection**of data points. Sometimes, though, one samples just one point, and metonymically calls it "the sample".

* using "correlated" to mean "dependent". This is incorrect, except in special circumstances, such as multivariate Gaussian models.

* using "sufficient statistics" to mean "summary statistics" (e.g. in the context of mean-field approximations). This is incorrect.

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UPDATE: I should write a SigBovik paper titled "Introduction to Statistical Pedantics".