Calculation of Scale of Fluctuation and Variance Reduction Function

The scale of fluctuation is one of the vital parameters for the application of random field theory to the reliability analysis of geotechnical engineering. In the present study, the fluctuation function method and weighted curve fitting method were presented to make the calculation more simple and accurate. The vertical scales of fluctuation of typical layers of Tianjin Port were calculated based on a number of engineering geotechnical investigation data, which can be guidance to other projects in this area. Meanwhile, the influences of sample interval and type of soil index on the scale of fluctuation were analyzed, according to which, the principle of determining the scale of fluctuation when the sample interval changes was defined. It can be obtained that the scale of fluctuation is the basic attribute reflecting spatial variability of soil, therefore, the scales of fluctuation calculated according to different soil indexes should be basically the same. The non-correlation distance method was improved, and the principle of determining the variance reduction function was also discussed.

LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION

This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.

Heteroscedasticity check in nonlinear semiparametric models based on nonparametric variance function

The assumption of homoscedasticity has received much attention in classical analysis of regression. Heteroscedasticity tests have been well studied in parametric and nonparametric regressions. The aim of this paper is to present a test of heteroscedasticity for nonlinear semiparametric regression models with nonparametric variance function. The validity of the proposed test is illustrated by two simulated examples and a real data example.

Additive predictions of aboveground stand biomass in commercial logs and harvest residues for rotation age Pinus radiata plantations in New South Wales,Australia

Two systems of additive equations were developed to predict aboveground stand level biomass in log products and harvest residue from routinely measured or predicted stand variables for Pinus radiata plantations in New South Wales,Australia.These plantations were managed under three thinning regimes or stand types before clear-felling at rotation age by cut-to-length harvesters to produce sawlogs and pulpwood.The residue material following a clear-fell operation mainly consisted of stumps,branches and treetops,short off-cut and waste sections due to stem deformity,defects,damage and breakage.One system of equations did not include dummy variables for stand types in the model specification and was intended for more general use in plantations where stand density management regimes were not the same as the stand types in our study.The other system that incorporated dummy variables was for stand type-specific applications.Both systems of equations were estimated using 61 plot-based estimates of biomass in commercial logs and residue components that were derived from systems of equations developed in situ for predicting the product and residue biomass of individual trees.To cater for all practical applications,two sets of parameters were estimated for each system of equations for predicting component and total aboveground stand biomass in fresh and dry weight respectively.The two sets of parameters for the system of equations without dummy variables were jointly estimated to improve statistical efficiency in parameter estimation.The predictive performances of the two systems of equations were benchmarked through a leave-one-plot-out cross validation procedure.They were generally superior to the performance of an alternative two-stage approach that combined an additive system for major components with an allocative system for sub-components.As using forest harvest residue biomass for bioenergy has increasingly become an integrated part of forestry,reliable estimates of product and residue biomass will assist harvest and management planning for clear-fell operations that integrate cut-to-length log production with residue harvesting.

Bootstrap inference of the skew-normal two-way classification random effects model with interaction

In this paper,we consider the statistical inference problems for the fixed effect and variance component functions in the two-way classification random effects model with skewnormal errors.Firstly,the exact test statistic for the fixed effect is constructed.Secondly,using the Bootstrap approach and generalized approach,the one-sided hypothesis testing and interval estimation problems for the single variance component,the sum and ratio of variance components are discussed respectively.Further,the Monte Carlo simulation results indicate that the exact test statistic performs well in the one-sided hypothesis testing problem for the fixed effect.And the Bootstrap approach is better than the generalized approach in the one-sided hypothesis testing problems for variance component functions in most cases.Finally,the above approaches are applied to the real data examples of the consumer price index and value-added index of three industries to verify their rationality and effectiveness.

Bootstrap Inference on the Variance Component Functions in the Two-Way Random Effects Model with Interaction

In this paper,using the Bootstrap approach and generalized approach,the authors consider the one-sided hypothesis testing problems for variance component functions in the two-way random effects model.Firstly,the test statistics and confidence intervals for the sum of variance components are constructed.Next,the one-sided hypothesis testing problems for the ratio of variance components are also discussed.The Monte Carlo simulation results indicate that the Bootstrap approach is better than the generalized approach in most cases.Finally,the above approaches are applied to the real data examples of mice blood p H and molded plastic part’s dimensions.

Generalised variance functions for longitudinal survey data

In this research, we propose longitudinal generalised variance functions (LGVFs) to produceconvenient estimates of variances by incorporating time effect into modelling. Asymptoticproperties of some certain type of estimators are investigated. Simulation studies and implementation of the proposed methods to Current Population Survey (CPS) data show that LGVFswork well in producing standard error estimates.

Confidence Intervals of Variance Functions in Generalized Linear Model

In this paper we introduce an appealing nonparametric method for estimating variance and conditional variance functions in generalized linear models （GLMs）, when designs are fixed points and random variables respectively, Bias-corrected confidence bands are proposed for the （conditional） variance by local linear smoothers. Nonparametric techniques are developed in deriving the bias-corrected confidence intervals of the （conditional） variance. The asymptotic distribution of the proposed estimator is established and show that the bias-corrected confidence bands asymptotically have the correct coverage properties. A small simulation is performed when unknown regression parameter is estimated by nonparametric quasi-likelihood. The results are also applicable to nonparamctric autoregressive times series model with heteroscedastic conditional variance.

A Complete Characterization of Multivariate Normal Stable Tweedie Models through a Monge Ampere Property

Extending normal gamma and normal inverse Gaussian models,multivariate normal stable Tweedie(NST)models are composed by a fixed univariate stable Tweedie variable having a positive value domain,and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component.Within the framework of multivariate exponential families,the NST models are recently classified by their covariance matrices V(m)depending on the mean vector m.In this paper,we prove the characterization of all the NST models through their determinants of V(m),also called generalized variance functions,which are power of only one component of m.This result is established under the NST assumptions of Monge-Ampere property and steepness.It completes the two special cases of NST,namely normal Poisson and normal gamma models.As a matter of fact,it provides explicit solutions of particular Monge-Ampere equations in differential geometry.

A Stochastic Level-Value Estimation Method for Global Optimization

In this paper,we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem.For this purpose,we first derive a generalized variance function associated with the considered problem and prove that the largest root of the function is the global minimal value.Then,Newton’s method is applied to find the root.The convergence of the proposed method is established under some suitable conditions.Based on the main idea of the cross-entropy method to update the sampling density function,an important sampling technique is proposed in the implementation.Preliminary numerical experiments indicate the validity of the proposed method.

A K-Means Clustering-Based Multiple Importance Sampling Algorithm for Integral Global Optimization

In this paper, we propose a K-means clustering-based integral level-value estimation algorithm to solve a kind of box-constrained global optimization problem. For this purpose, we introduce the generalized variance function associated with the level-value of the objective function to be minimized. The variance function has a good property when Newton’s method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation is equal to the global minimum value of the corresponding optimization problem. Based on the K-means clustering algorithm, the multiple importance sampling technique is proposed in the implementable algorithm. The main idea of the cross-entropy method is used to update the parameters of sampling density function. The asymptotic convergence of the algorithm is proved, and the validity of the algorithm is verified by numerical experiments.