A New Extrapolation Economy Cascadic Multigrid Method for Image Restoration Problems

In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation operator, which provides more accurate initial values for the fine grid level. An edge preserving denoising operator is constructed to remove noise and preserve image edges. The local smoothing operator reduces the influence of staircase effect. The experiment results show that the new method not only improves the computational efficiency but also ensures good recovery quality.

Improved calibration method for displacement transformation coefficient in optical and visual measurements

Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement transformation coefficient(DTC)of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process,and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view(FFOV).To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands,a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV.First,an image coordinate system,a pixel measurement coordinate system,and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM.In addition,marker spots in the FFOV are selected,and the DTCs at the marker spots are obtained from calibration experiments.Also,a fitting method based on locally weighted scatterplot smoothing(LOWESS)is selected,and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots.Finally,the calibrated distribution functions of the DTCs are applied to the LVDMM,and experiments conducted to verify the displacement measurement accuracies are reported.The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than±15μm and±19μm,respectively,and that for oblique displacement is better than±24μm.Compared with the traditional calibration method,the displacement measurement error in the FFOV is now 90%smaller.This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV,and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.

ESTIMATORS AND SOME BEHAVIORS FORA PARTIALLY LINEAR MODEL WITH CENSORED DATA

This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.

A global perspective on macroprudential policy interaction with systemic risk,real economic activity,and monetary intervention

The study empirically assesses how macroprudential policy interacts with systemic risk,industrial production,and monetary intervention on a global level from January 2006 to December 2018.We adopt the aggregate proxies of these variables,capturing their global effects,and use a novel econometric technique,namely,smooth local projections.The study finds that global macroprudential policy leads the monetary policy,exhibiting a countercyclical pattern concerning industrial production.The latter has an inverse bidirectional linkage with systemic risk.Thus,an ex-ante tight macroprudential policy can indirectly mitigate global systemic risk through its pro-growth effect on industrial production,although no convincing evidence exists for the direct impact of a macroprudential intervention on systemic risk.The study results endure several extensions and a robustness check,which builds on alternative measures of global systemic stress and real economic activity,thereby legitimizing the increased importance attached to the macroprudential policy since the 2007–2009 global financial crisis.

Testing for the parametric parts in a single-index varying-coefficient model

Single-index varying-coefficient models (SIVCMs) are very useful in multivariate nonparametric regression.However,there has less attention focused on inferences of the SIVCMs.Using the local linear method,we propose estimates of the unknowns in the SIVCMs.In this article,our main purpose is to examine whether the generalized likelihood ratio (GLR) tests are applicable to the testing problem for the index parameter in the SIVCMs.Under the null hypothesis our proposed GLR statistic follows the chi-squared distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters or functions,which is called as Wilks' phenomenon (see Fan et al.,2001).A simulation study is conducted to illustrate the proposed methodology.

Statistical Diagnosis for HIV Dynamics Based on Mean Shift Outlier Model

Ordinary differential equation(ODE) are widely used for quantifying HIV viral dynamics.It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. In this study, the authors use the Mean Shift Outlier Model(MSOM) to detect outliers in HIV model based on the two-step estimation of ODE. Approximate formula for shift parameter is derived. Furthermore, a score test statistic is constructed and its approximating distribution is established. The simulation results show that: 1) The boundary points have more impact on the parameter estimation relative to interior points. 2) The proposed procedure can detect the outliers effectively. The authors illustrate the proposed approach using an application example from an HIV clinical trial and find similar pattern to the simulation studies.

Dynamic single-index model for functional data

We propose a new functional single index model, which called dynamic single-index model for functional data, or DSIM, to efficiently perform non-linear and dynamic relationships between functional predictor and functional response. The proposed model naturally allows for some curvature not captured by the ordinary functional linear model. By using the proposed two-step estimating algorithm, we develop the estimates for both the link function and the regression coefficient function, and then provide predictions of new response trajectories. Besides the asymptotic properties for the estimates of the unknown functions, we also establish the consistency of the predictions of new response trajectories under mild conditions. Finally, we show through extensive simulation studies and a real data example that the proposed DSIM can highly outperform existed functional regression methods in most settings.

Pointwise multipliers for Besov spaces of dominating mixed smoothness-Ⅱ

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R^d).

Asymptotic Normality of Estimators in Partially Linear Varying Coefficient Models

Partially linear varying coefficient model is a generalization of partially linear model and varying coefficient model and is frequently used in statistical modeling. In this paper, we construct estimators of the parametric and nonparametric components by Profile least-squares procedure which is based on local linear smoothing. The resulting estimators are shown to be asymptotically normal with heteroscedastic error.