HAZARD REGRESSION WITH PENALIZED SPLINE:THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.

Cyclic Lattices, Ideal Lattices and Bounds for the Smoothing Parameter

In this article, we introduce the discrete subgroup in ℝn as preliminaries first. Then we provide some theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic lattices in ℝn and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper bound for the smoothing parameter of cyclic lattices.

D_∞-APPROXIMATION OF PRODUCT VARIATIONS OF TWO PARAMETER SMOOTH SEMIMARTINGALES

Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.

Computer vision-based limestone rock-type classification using probabilistic neural network

Proper quality planning of limestone raw materials is an essential job of maintaining desired feed in cement plant. Rock-type identification is an integrated part of quality planning for limestone mine. In this paper, a computer vision-based rock-type classification algorithm is proposed for fast and reliable identification without human intervention. A laboratory scale vision-based model was developed using probabilistic neural network（PNN） where color histogram features are used as input. The color image histogram-based features that include weighted mean, skewness and kurtosis features are extracted for all three color space red, green, and blue. A total nine features are used as input for the PNN classification model. The smoothing parameter for PNN model is selected judicially to develop an optimal or close to the optimum classification model. The developed PPN is validated using the test data set and results reveal that the proposed vision-based model can perform satisfactorily for classifying limestone rocktypes. Overall the error of mis-classification is below 6%. When compared with other three classification algorithms, it is observed that the proposed method performs substantially better than all three classification algorithms.

Decision Bayes Criteria for Optimal Classifier Based on Probabilistic Measures

This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the Bayes classification error probability, we propose to use an iterative algorithm to optimize the dimension reduction for classification with a probabilistic approach to achieve the Bayes classifier. The estimated probabilities of different errors encountered along the different phases of the system are realized by the Kernel estimate which is adjusted in a means of the smoothing parameter. Experiment results suggest that the proposed approach performs well.

New Hybrid EWMA Charts for Efficient Process Dispersion Monitoring with Application in Automobile Industry

The EWMAcharts are thewell-knownmemory-type charts used formonitoring the small-to-intermediate shifts in the process parameters(location and/or dispersion).The hybrid EWMA(HEWMA)charts are enhanced version of the EWMA charts,which effectivelymonitor the process parameters.This paper aims to develop two new uppersided HEWMAcharts for monitoring shifts in process variance,i.e.,HEWMA1 and HEWMA2 charts.The design structures of the proposed HEWMA1 and HEWMA2 charts are based on the concept of integrating the features of two EWMAcharts.TheHEWMA1 and HEWMA2charts plotting statistics are developed using one EWMAstatistic as input for the other EWMAstatistic.AMonte Carlo simulations method is used as a computational technique to determine the numerical results for the performance characteristics,such as average run length(ARL),median run length,and standard deviation run length(SDRL)for assessing the performance of the proposed HEWMA1 and HEWMA2 charts.In addition,to evaluate the overall performance of the proposed HEWMA1 and HEWMA2 charts,other numerical measures consisting of the extra quadratic loss(EQL),relative average run length(RARL),and performance comparison index(PCI)are also computed.The proposed HEWMA1 and HEWMA2 charts are compared to some existing charts,such as CH,CEWMA,HEWMA,AEWMAHHW1,HHW2,AIB-EWMA-I,and AIB-EWMA-II charts,on the basis aforementioned numerical measures.The comparison reveals that the proposed HEWMA1 and HEWMA2 charts achieve better detection ability against the existing charts.In the end,a real-life data application is also provided to enhance the implementation of the proposed HEWMA1 and HEWMA2 charts practically.

Two Parameter Smooth Martingales on the Wiener Space

We prove that two parameter smooth continuous martingales have ∞-modification and establish a Doob’s inequality in terms of(p,r)-capacity for two parameter smooth martingales.

M-Cross-Validation in Local Median Estimation

M-cross-validation criterion is proposed for selecting a smoothing parameter in a nonparametric median regression model in which a uniform weak convergency rate for the M-cross-validated local median estimate, and the upper and lower bounds of the smoothing parameter selected by the proposed criterion are established. The main contribution of this study shows a drastic difference from those encountered in the classical L2-, L1- cross-validation technique, which leads only to the consistency in the sense of the average. Obviously, our results are novel and nontrivial from the point of view of mathematics and statistics, which provides insight and possibility for practitioners substituting maximum deviation for average deviation to evaluate the performance of the data-driven technique.