Convergence of the Best Linear Predictor of a Weakly Stationary Random Field

2018 ◽  
Vol 25 (3) ◽  
pp. 937-958
Author(s):  
Raymond Cheng
Keyword(s):  
Random Field ◽  
Linear Predictor ◽  
Best Linear Predictor ◽  
Stationary Random Field

On dispersion of stable random vectors and its application in the prediction of multivariate stable processes

1994 ◽  
Vol 31 (3) ◽  
pp. 691-699 ◽  
Author(s):  
A. Reza Soltani ◽  
R. Moeanaddin
Keyword(s):  
Stable Process ◽  
Stable Processes ◽  
Random Vectors ◽  
Linear Predictor ◽  
Error Vector ◽  
Best Linear Predictor ◽  
Definition Of ◽  
Stable Random Vectors

Our aim in this article is to derive an expression for the best linear predictor of a multivariate symmetric α stable process based on many past values. For this purpose we introduce a definition of dispersion for symmetric α stable random vectors and choose the linear predictor which minimizes the dispersion of the error vector.

Probabilistic failure envelopes of strip foundations on soils with non-stationary characteristics of undrained shear strength

Géotechnique ◽  
2021 ◽  
pp. 1-44
Author(s):  
Zhichao Shen ◽  
Qiujing Pan ◽  
Siau Chen Chian ◽  
Susan Gourvenec ◽  
Yinghui Tian
Keyword(s):  
Shear Strength ◽  
Random Field ◽  
Numerical Models ◽  
Undrained Shear Strength ◽  
Considerable Effect ◽  
Failure Envelopes ◽  
Autocorrelation Distance ◽  
Stationary Random Field ◽  
Constant Coefficient Of Variation ◽  
Undrained Shear

This paper investigates probabilistic failure envelopes of strip foundations on spatially variable soils with profiles of undrained shear strength su linearly increasing with depth using the lower bound random finite element limit analysis. The spatially variable su is characterised by a non-stationary random field with linearly increasing mean and constant coefficient of variation (COV) with depth. The deterministic uniaxial capacities and failure envelopes are firstly derived to validate numerical models and provide a reference for the subsequent probabilistic analysis. Results indicate that the random field parameters COVsu (COV of su) and Δ (dimensionless autocorrelation distance) have a considerable effect on the probabilistic normalised uniaxial capacities which alters the size of probabilistic failure envelopes. However, COVsu and Δ have an insignificant effect on the shape of probabilistic failure envelopes is observed in the V-H, V-M and H-M loading spaces, such that failure envelopes for different soil variabilities can be simply scaled by the uniaxial capacities. In contrast to COVsu and Δ, the soil strength heterogeneity index κ = μkB/μsu0 has the lowest effect on the probabilistic normalised uniaxial capacity factors but the highest effect on the shape of the probabilistic failure envelopes. A series of expressions are proposed to describe the shape of deterministic and probabilistic failure envelopes for strip foundations under combined vertical, horizontal and moment (V-H-M) loading.

The asymptotic theory of linear time-series models

1973 ◽  
Vol 10 (01) ◽  
pp. 130-145 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Time Series ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Asymptotic Theory ◽  
Linear Time ◽  
Stationary Time Series ◽  
Linear Predictor ◽  
The Central Limit Theorem ◽  
Best Linear Predictor

A linear time-series model is considered to be one for which a stationary time series, which is purely non-deterministic, has the best linear predictor equal to the best predictor. A general inferential theory is constructed for such models and various estimation procedures are shown to be equivalent. The treatment is considerably more general than previous treatments. The case where the series has mean which is a linear function of very general kinds of regressor variables is also discussed and a rather general form of central limit theorem for regression is proved. The central limit results depend upon forms of the central limit theorem for martingales.

Random walk in a random environment with correlated sites

2001 ◽  
Vol 38 (4) ◽  
pp. 1018-1032 ◽  
Author(s):  
T. Komorowski ◽  
G. Krupa
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Field ◽  
Random Environment ◽  
Law Of Large Numbers ◽  
Transition Probabilities ◽  
Direct Application ◽  
Random Environments ◽  
Large Numbers ◽  
Stationary Random Field

We prove the law of large numbers for random walks in random environments on the d-dimensional integer lattice Zd. The environment is described in terms of a stationary random field of transition probabilities on the lattice, possessing a certain drift property, modeled on the Kalikov condition. In contrast to the previously considered models, we admit possible correlation of transition probabilities at different sites, assuming however that they become independent at finite distances. The possible dependence of sites makes impossible a direct application of the renewal times technique of Sznitman and Zerner.

Linear Prediction of a True Score From a Direct Estimate and Several Derived Estimates

2007 ◽  
Vol 32 (1) ◽  
pp. 6-23 ◽  
Author(s):  
Shelby J. Haberman ◽  
Jiahe Qian
Keyword(s):  
Linear Prediction ◽  
Mean Squared Error ◽  
Weighted Average ◽  
Statistical Prediction ◽  
True Score ◽  
Direct Estimate ◽  
Linear Predictor ◽  
Squared Error ◽  
Best Linear Predictor ◽  
Prediction Problems

Statistical prediction problems often involve both a direct estimate of a true score and covariates of this true score. Given the criterion of mean squared error, this study determines the best linear predictor of the true score given the direct estimate and the covariates. Results yield an extension of Kelley’s formula for estimation of the true score to cases in which covariates are present. The best linear predictor is a weighted average of the direct estimate and of the linear regression of the direct estimate onto the covariates. The weights depend on the reliability of the direct estimate and on the multiple correlation of the true score with the covariates. One application of the best linear predictor is to use essay features provided by computer analysis and an observed holistic score of an essay provided by a human rater to approximate the true score corresponding to the holistic score.

scholarly journals Stochastic Nonlinear Ground Response Analysis Considering Existing Boreholes Locations by the Geostatistical Method

2021 ◽  
Author(s):  
A.H. Amjadi ◽  
Ali johari
Keyword(s):  
Random Field ◽  
Mean Value ◽  
Response Analysis ◽  
Soil Parameters ◽  
Seismic Responses ◽  
Ground Response ◽  
Ground Response Analysis ◽  
Ground Acceleration ◽  
Geostatistical Method ◽  
Stationary Random Field

Abstract The field and laboratory evidence of nonlinear soil behavior, even at small strains, emphasizes the ‎importance of employing nonlinear methods in seismic ground response analysis. Additionally, ‎determination of dynamic characteristics of soil layers always includes some degree of uncertainty. Most of ‎previous stochastic studies of ground response analysis have focused only on uncertainties of soil ‎parameters, and the effect of soil sample location has been mostly ignored. This study attempts to couple ‎nonlinear time-domain ground response analysis with uncertainty of soil parameters considering existing ‎boreholes’ ‎location through a geostatistical method using a program written in MATLAB. To evaluate ‎the efficiency of the proposed method, stochastic seismic ground responses at construction location were compared with those of the non-stationary random ‎field method‎ through real site data. The ‎results demonstrate that applying the boreholes’ ‎location significantly affects not only the ground ‎responses but also their Coefficient Of Variation (COV). Furthermore, the mean value of the seismic ‎responses is affected more considerably by the values of soil parameters at the vicinity of the construction location. It is also inferred that considering boreholes’ location may reduce the COV of the seismic ‎responses. Among the surface responses in the studied site, the values of Peak Ground Displacement (PGD) ‎and Peak Ground Acceleration (PGA) reflect the highest and ‎lowest dispersion due to uncertainties of soil ‎properties through both non-stationary random field and geostatistical methods.

scholarly journals Effect of Septoria brown spot on soybean yield in Illinois

2019 ◽  
Author(s):  
Heng-An Lin ◽  
María B. Villamil ◽  
Santiago X. Mideros
Keyword(s):  
Disease Severity ◽  
Critical Factor ◽  
Brown Spot ◽  
Linear Predictor ◽  
Soybean Yield ◽  
Best Linear Predictor ◽  
Effect On Yield ◽  
Yield Responses ◽  
Production Areas ◽  
Different Levels

AbstractBrown spot caused by Septoria glycines is a prevalent foliar disease in all soybean production areas. Application of foliar fungicides after bloom reduces the disease severity, yet yield responses are not consistent among locations and years. Our research goal was to determine the effect of different levels of Septoria brown spot on yield. Different levels of disease severity were effectively obtained in the field by weekly application of chlorothalonil for three, six, and nine times after disease inoculation at V3/V4 stage. Fungicide treatments had a significant effect on vertical progress and chlorotic area with no statistically significant effect on yield. Soybean yield was negatively correlated with vertical progress of the disease (r = −0.36). The vertical progress was the best linear predictor of yield. Based on this model, when the vertical progress of brown spot at R6 increased by 10%, the yield decreased by 142.13 kg/ha (3.4%). A variance component analyses of our data showed that location was the most critical factor, illustrating the significant effect of local environmental conditions on the disease. Power analyses indicated that at least eight locations are needed to detect an effect of 269 kg/ha. Our results provide useful information to improve the experimental design for future experiments addressing the yield constrain by late season diseases of soybean.

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