They only exist, in the way that you have put it, as mental experiences. There is no doubt of sense-data experienced directy in the mind, there can be none, as the experience is immediate and direct. This is the Idealist answer to sceptical worries brought about by Representative Realism.
But to speculate about the external existence of real objects on the basis that i have mental experiences is unjustified metaphysical speculation, unverifiable emprically. To talk of objets exiting irrespective of the perciever is speculatory.