The choice of distribution is often made on the basis of how well the data appear to be fitted by the distribution. The inverse Gaussian distribution is one of the basic models for describing positively skewed data which arise in a variety of applications. In this paper, the problem of interest is simultaneously parameter estimation and variable selection for joint mean and dispersion models of the inverse Gaussian distribution. We propose a unified procedure which can simultaneously select significant variables in mean and dispersion model. With appropriate selection of the tuning parameters, we establish the consistency of this procedure and the oracle property of the regularized estimators. Simulation studies and a real example are used to illustrate the proposed methodologies.

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Summary This article studies the problem of practical prescribed‐time tracking for pure‐feedback nonlinear systems, where the transient behavior, steady‐state precision, settling time as well as the rate of convergence can be preset irrespective of initial conditions. With the help of a time‐dependent function and a state‐dependent function, a simple coordinate transformation is established to construct a neuro‐adaptive controller to achieve the tracking purpose. In particular, the proposed controller does not need to update the design parameters in accordance with different initial conditions, which makes the controller more versatile. The effectiveness of the proposed method is illustrated through two practical systems, namely, a continuous stirred tank reactor (CSTR), and a robotic system.