We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences of the observations. We show that the variance function estimator is nearly optimally adaptive to the smoothness of both the mean and variance functions. Th...

this paper deals with a globally convergent adaptive and sliding mode control of a cart-pole inverted pendulum for trajectory tracking in the presence of a bounded measurement noise and parameter uncertainty. two kinds of controllers have been used for evaluation of tracking error in presence of a bounded noise; as a result, we want to compare that at what time we can see the convergence of tra...

In practical applications of item response theory (IRT), item parameters are usually estimated first from a calibration sample. After treating these estimates as fixed and known, ability parameters are then estimated. However, the statistical inferences based on the estimated abilities can be misleading if the uncertainty of the item parameter estimates is ignored. Instead, estimated item param...

Suppose we observe an ergodic Markov chain on the real line, with a parametric model for the autoregression function, i.e. the conditional mean of the transition distribution. If one speciies, in addition, a paramet-ric model for the conditional variance, one can deene a simple estimator for the parameter, the maximum quasi-likelihood estimator. It is robust against misspeciication of the condi...

We investigate adaptive methods for optimal control problems with finitely many control parameters. We analyze a-posteriori error estimates based on verification of second-order sufficient optimality conditions. Reliability and efficiency of the error estimator is shown. The estimator is used in numerical tests to guide adaptive mesh refinement.

However, feedback linearization control does not guarantee robustness in the presence of modeling errors. In [3], ∞ H control and sliding mode control was proposed. ∞ H control is a computation expensive method that presents good disturbance attenuation performance. In [4], sliding mode control and PID controller was discussed. In [5], the PID controller was discussed. The PID controller is a s...

We present a new method for simulating and predicting hydrologic variables with uncertainty assessment provide example applications to river flows. The is identified the acronym “Bluecat” based on use of deterministic model which subsequently converted stochastic formulation. latter provides an adjustment statistical basis prediction along its confidence limits. distinguishing features proposed...

In this paper, we study a generalized Kalman--Bucy filtering problem under uncertainty. The drift uncertainty for both signal process and observation is considered, the attitude to characterized by convex operator (convex risk measure). optimal filter or minimum mean square estimator (MMSE) calculated solving estimation operator. first part of studied $g$-expectation which special For case, pro...

In this paper, we study the control of chaotic systems with unknown parameters. A stable adaptive control scheme is used to guarantee that the parameter estimator converges to stabilizing values such that the controlled chaotic system asymptotically approaches a reference point. A Lyapunov function approach is used to prove a global result which guarantees the stability of both controlled chaot...