This paper considers k-monotone estimation and the related asymptotic performance analysis over a suitable Hölder class for general k. A novel two stage k-monotone B-spline estimator is proposed: in the first stage, an unconstrained estimator with optimal asymptotic performance is considered; in the second stage, a k-monotone B-spline estimator is constructed by projecting the unconstrained est...

Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of convergence are established for a range of matrix norm losses. A fully data driven estimator based on adaptive constrained `1 minimization is proposed and its rate o...

The optimal value of the smoothing parameter of the Kernel estimator can be obtained by the well known Plug-in algorithm. The optimality is realised in the sense of Mean Integrated Square Error (MISE). In this paper, we propose to generalise this algorithm to the case of the difficult problem of the estimation of a distribution which has a bounded support. The proposed algorithm consists in sea...

Abstract. This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in wh...

The problems on the estimations in communication constrained networks have attracted considerable attentions in recent years. In such networks, the estimator shows a poor performance due to the less transmissions, compared with the Linear Minimum Variance Estimator(LMVE). In this paper, a new method is proposed to obtain a better estimator with respect to unbounded noises. According to our prop...

Thin fibers of cross-linked polyacrylate gel were prepared by inducing polymerization reaction inside long glass or Tygon tubings. By immersing these gel fibers in salt solutions containing both Ca(2+) and Na(+) at varying ratios, a discontinuous transition from the swollen state to the shrunken was demonstrated. A very sharp boundary was observed between the swollen and shrunken portions of th...

We derive a local linear estimator of generalized impulse response (GIR) functions for nonlinear conditional heteroskedastic autoregressive processes and show its asymptotic normality. We suggest a plug-in bandwidth based on the derived asymptotically optimal bandwidth. A local linear estimator for the conditional variance function is proposed which has simpler bias than the standard estimator....

Estimation of the time-average variance constant (TAVC) of a stationary process plays a fundamental role in statistical inference for the mean of a stochastic process. Wu (2009) proposed an efficient algorithm to recursively compute the TAVC with O(1) memory and computational complexity. In this paper, we propose two new recursive TAVC estimators that can compute TAVC estimate with O(1) computa...

In this paper we study optimal estimation design for sampled linear systems where the sensors measurements are transmitted to the estimator site via a generic digital communication network. Sensor measurements are subject to random delay or might even be completely lost. We show that the minimum error covariance estimator is timevarying, stochastic, and it does not converge to a steady state. M...