The modified information criterion (MIC) is applied to detect multiple change points in a sequence of independent random variables. We find that the method is consistent in selecting the correct model, and the resulting test statistic has a simple limiting distribution. We show that the estimators for locations of change points achieve the best convergence rate, and their limiting distribution ...

Mean Squared Error (MSE) has been the most widely used tool to solve the linear filter estimation or system identification problem. However, MSE gives biased results when the input signals are noisy. This paper presents a novel Error Whitening Criterion (EWC) to tackle the problem of linear system identification in the presence of additive white disturbances. We will motivate the theory behind ...

This paper proposes an affine projection algorithm (APA) with variable projection order using the mean-square error (MSE) criterion. The proposed algorithm determines the projection order at every iteration to use it in the update equation of the proposed APA. The MSE criterion is employed to decide the projection order reasonably. Moreover, this algorithm checks the steady-state condition to c...

Namyong Kim 155 In this paper, we introduce an escalator (ESC) algorithm based on the least squares (LS) criterion. The proposed algorithm is relatively insensitive to the eigenvalue spread ratio (ESR) of an input signal and has a faster convergence speed than the conventional ESC algorithms. This algorithm exploits the fast adaptation ability of least squares methods and the orthogonalization ...

The solution of convergence problems involving sequences of positive functionals defined on certain function-spaces led the author to investigate a different form of this convergence criterion which seems to have a more direct practical application in some special cases of importance. The development hinges on the fact that from a certain point of view every linear operation has domains over wh...

The aim of this paper is to present a Stancu type Kantorovich modification of q−BernsteinSchurer operators introduced by Muraru [22] and modified by Ren and Zeng [29]. Here, we obtain a convergence theorem by using the well known Bohman-Korovkin criterion and find the estimate of the rate of convergence by means of modulus of continuity and Lipschitz function for these operators. Also, we estab...

This paper is concerned with solving Cauchy problem for parabolic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to an adapted stopping criterion depending on noise rate for the minimization process. Numerical...

In this paper we develop a discrete-time adaptive stabilization algorithm based on a one-step backwardhorizon cost criterion. By optimizing the cost with respect to the update step size, we obtain a gain update law that guarantees convergence of the plant states. The convergence proof is based on a modified Lyapunov technique. We extend the algorithm to include integral control for rejecting co...