An arbitration proceeding is best described as a quasi-judicial proceeding.
It is not a purely judicial proceeding because it is not conducted by a court of law but by a private tribunal chosen by the parties.
It is not a purely administrative proceeding because the arbitrator is required to act judicially: they must hear both sides, consider evidence, and deliver a binding decision (an award) that determines the rights and obligations of the parties.
Because it has some characteristics of a judicial proceeding (adjudication of a dispute) but is not conducted by a formal court, it is termed 'quasi-judicial'.