a group of equal proportions - the definition of quantile is one of a class of values of a variate that divides the total frequency of a sample or population into a given number of equal proportions

A quantile.

Yes.

Usually the value of the lower quantile, median, and upper quantile are in ascending order, how if for the particular set of data, if all values are the same, then these three measures can be the same.

Victor Chernozhukov has written:

'Quantile regression with censoring and endogeneity'

'An IV model of quantile treatment effects' -- subject(s): Accessible book

'Rearranging Edgeworth-Cornish-Fisher expansions'

'L1-Penalized Quantile Regression in High Dimensional Sparse Models' -- subject(s): Regression analysis

'Instrumental variable quantile regression' -- subject(s): Accessible book

'Extremal quantities and value-at-risk' -- subject(s): Accessible book

'Estimation and confidence regions for parameter sets in econometric models' -- subject(s): Accessible book