Building hand-object models for dexterous in-hand manipulation remains a crucial and open problem. Major challenges include the difficulty of obtaining the geometric and dynamical models of the hand, object, and time-varying contacts, as well as the inevitable physical and perception uncertainties. Instead of building accurate models to map between the actuation inputs and the object motions, this work proposes to enable the hand-object systems to continuously approximate their local models via a self-identification process where an underlying manipulation model is estimated through a small number of exploratory actions and non-parametric learning. With a very small number of data points, as opposed to most data-driven methods, our system self-identifies the underlying manipulation models online through exploratory actions and non-parametric learning. By integrating the self-identified hand-object model into a model predictive control framework, the proposed system closes the control loop to provide high accuracy in-hand manipulation. Furthermore, the proposed self-identification is able to adaptively trigger online updates through additional exploratory actions, as soon as the self-identified local models render large discrepancies against the observed manipulation outcomes. We implemented the proposed approach on a sensorless underactuated Yale Model O hand with a single external camera to observe the object's motion. With extensive experiments, we show that the proposed self-identification approach can enable accurate and robust dexterous manipulation without requiring an accurate system model nor a large amount of data for offline training.