Can I write estimate $\pm$ its standard error? Suppose I have an MLE estimate $\hat{\theta}$ for a parameter $\theta$, and $\hat{\sigma}$ is the sqrt of the inverse of the negative of the Hessian of the log likelihood at $\hat{\theta}$. Can I write $\hat{\theta} \pm \hat{\sigma}$?
In general, if I have an estimate $\hat{\theta}$ for a parameter $\theta$, and an estimate $\hat{\sigma}$ of the standard deviation of $\hat{\theta}$, can I write $\hat{\theta} \pm \hat{\sigma}$? Will others understand what I mean? Is it also what others write?
 A: It's fairly common, but not standard enough that it needs no explanation. $\hat\theta\pm 1.96 \hat\sigma$ is also common—an (approximate perhaps) 95% confidence interval.
A: I think it depends what you want to convey. 
To report the standard error or your estimate you could just write $\hat{\theta} (\hat{\sigma})$. This notation is quite common in the statistical literature, but for the sake of clarity you might mention that the standard error is in parenthesis/brackets the first time you use this notation.
To provide a confidence interval with your estimate you might want to write $\hat{\theta} \pm z_{\alpha/2}\hat{\sigma}$, where $z_{\alpha/2}$ is the quantile of the standard normal distribution and $1-\alpha$ the confidence level of your choice. A common choice is $\alpha = 0.05$ leading to $\hat{\theta} \pm 1.96\hat{\sigma}$.
The second option is a much stronger statement. In addition of providing the standard error of the estimate, it gives a confidence interval relying on the normality of the MLE, which might be too coarse in finite samples: it might include invalid parameter values (e.g., probabilities larger than one), and/or wrongly imply that the confidence interval is symmetric.
A: There are lots of parameters that are written as $x \pm y$. Off the top of my head, I have seen people use this format to report:


*

*mean and standard error: 

*mean and standard deviation

*mean and confidence interval

*mean and range/tolerance (particularly on blueprints or design documents)

*median and mean absolute deviation.


All of these are fine, as long the values are clearly described Some version of the APA style require explicit labels like "The line's slope was close to unity ($M\pm SE: 1.01 \pm 0.05$). That can be handy, but it can clutter up the text. If you're reporting a lot of values, a simple note ("All data is shown as mean $\pm$ standard errors") can work too.
Obviously, also consider the point you want to make. Standard deviation/MAD/ranges hints at the shape of a distribution, but not about the precision of an estimate. Standard error tells you how precise the estimate is, but does not describe the shape of the distribution.
