Delaunay三角剖分插值用于超分辨成像

微变焦超分辨成像在插值重建方面比较困难,目前基于最小二乘估计的频域模型和空域模型也都存在一些局限性。为了兼顾超分辨成像的实时性和精确性,该文在图像重建过程中,借鉴Delaunay三角剖分的数学概念,采用随机增量算法,定义了基于Delaunay三角剖分的插值算法。该算法可以提高分辨率,降低运算量。仿真实验结果表明,该算法在图像重建的时间和均方误差方面,均优于共轭梯度最小二乘法,其中基于Delaunay三角剖分的三次方插值算法的优越性更为突出。     

Central Limit Theorems of Local Polynomial Threshold Estimator for Diffusion Processes with Jumps

Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the non‐parametric local polynomial threshold estimator, especially local linear case, is employed to estimate the diffusion coefficients of diffusion processes, the adaptive and predictable structure of the estimator conditionally on the σ ‐field generated by diffusion processes is destroyed, so the classical central limit theorem for martingale difference sequences cannot work. In high‐frequency data, we proved the central limit theorems of local polynomial threshold estimators for the volatility function in diffusion processes with jumps by Jacod's stable convergence theorem. We believe that our proof procedure for local polynomial threshold estimators provides a new method in this field, especially in the local linear case.     

More efficient local polynomial regression with random-effects panel data models

We propose a modification on the local polynomial estimation procedure to account for the “within-subject” correlation presented in panel data. The proposed procedure is rather simple to compute and has a closed-form expression. We study the asymptotic bias and variance of the proposed procedure and show that it outperforms the working independence estimator uniformly up to the first order. Simulation study shows that the gains in efficiency with the proposed method in the presence of “within-subject” correlation can be significant in small samples. For illustration purposes, the procedure is applied to explore the impact of market concentration on airfare.     

广义Genocchi多项式的一组恒等式

用初等的方法研究了一个广义Genocchi多项式的性质,并得到了一组恒等式.     

Stieltjes-Thiele型有理插值公式

通过定义偏逆差商和混合逆差商,在Thiele型有理插值的基础上通过与Stieltjes型连分式相结合而构造了方形网格上的Stieltjes-Thiele有理插值公式.该插值算法满足所给的插值条件,同时给出了其特征定理和误差估计.最后用数值例子验证了本文插值算法的有效性.     

Fusing point and areal level space–time data with application to wet deposition

Summary.  Motivated by the problem of predicting chemical deposition in eastern USA at weekly, seasonal and annual scales, the paper develops a framework for joint modelling of point- and grid-referenced spatiotemporal data in this context. The hierarchical model proposed can provide accurate spatial interpolation and temporal aggregation by combining information from observed point-referenced monitoring data and gridded output from a numerical simulation model known as the 'community multi-scale air quality model'. The technique avoids the change-of-support problem which arises in other hierarchical models for data fusion settings to combine point- and grid-referenced data. The hierarchical space–time model is fitted to weekly wet sulphate and nitrate deposition data over eastern USA. The model is validated with set-aside data from a number of monitoring sites. Predictive Bayesian methods are developed and illustrated for inference on aggregated summaries such as quarterly and annual sulphate and nitrate deposition maps. The highest wet sulphate deposition occurs near major emissions sources such as fossil-fuelled power plants whereas lower values occur near background monitoring sites.     

Estimating crop yield via Gaussian quadrature

The present study proposes a method to estimate the yield of a crop. The proposed Gaussian quadrature (GQ) method makes it possible to estimate the crop yield from a smaller subsample. Identification of plots and corresponding weights to be assigned to the yield of plots comprising a subsample is done with the help of information about the full sample on certain auxiliary variables relating to biometrical characteristics of the plant. Computational experience reveals that the proposed method leads to about 78% reduction in sample size with absolute percentage error of 2.7%. Performance of the proposed method has been compared with that of random sampling on the basis of the values of average absolute percentage error and standard deviation of yield estimates obtained from 40 samples of comparable size. Interestingly, average absolute percentage error as well as standard deviation is considerably smaller for the GQ estimates than for the random sample estimates. The proposed method is quite general and can be applied for other crops as well-provided information on auxiliary variables relating to yield contributing biometrical characteristics is available.     

Model selection in regression based on pre-smoothing

In this paper, we investigate the effect of pre-smoothing on model selection. Christóbal et al 6 Christóbal Christóbal, J. A., Faraldo Roca, P. and González Manteiga, W. 1987. A class of linear regression parameter estimators constructed by nonparametric estimation. Ann. Statist.,, 15: 603–609. [Crossref], [Web of Science ®] [Google Scholar] showed the beneficial effect of pre-smoothing on estimating the parameters in a linear regression model. Here, in a regression setting, we show that smoothing the response data prior to model selection by Akaike's information criterion can lead to an improved selection procedure. The bootstrap is used to control the magnitude of the random error structure in the smoothed data. The effect of pre-smoothing on model selection is shown in simulations. The method is illustrated in a variety of settings, including the selection of the best fractional polynomial in a generalized linear model.