scholarly journals LÉVY-BASED ERROR PREDICTION IN CIRCULAR SYSTEMATIC SAMPLING

2013 ◽  
Vol 32 (2) ◽  
pp. 117 ◽  
Author(s):  
Kristjana Ýr Jónsdóttir ◽  
Eva B. Vedel Jensen
Keyword(s):  
Stochastic Process ◽  
Statistical Inference ◽  
Covariance Function ◽  
Kernel Smoothing ◽  
Stationary Stochastic Process ◽  
Systematic Sampling ◽  
Error Prediction ◽  
Model Parameters ◽  
Covariance Model ◽  
Measurement Function

In the present paper, Lévy-based error prediction in circular systematic sampling is developed. A model-based statistical setting as in Hobolth and Jensen (2002) is used, but the assumption that the measurement function is Gaussian is relaxed. The measurement function is represented as a periodic stationary stochastic process X obtained by a kernel smoothing of a Lévy basis. The process X may have an arbitrary covariance function. The distribution of the error predictor, based on measurements in n systematic directions is derived. Statistical inference is developed for the model parameters in the case where the covariance function follows the celebrated p-order covariance model.

scholarly journals Sample Properties of Weakly Stationary Processes

1970 ◽  
Vol 39 ◽  
pp. 7-21 ◽  
Author(s):  
T. Kawata ◽  
I. Kubo
Keyword(s):  
Stochastic Process ◽  
Distribution Function ◽  
Spectral Distribution ◽  
Covariance Function ◽  
Stationary Stochastic Process ◽  
Stationary Processes ◽  
Spectral Distribution Function

Let X(t) = X(t,ω), – ∞ < t < ∞, be a stationary stochastic process withand the continuous covariance functionwhere F(x) is the spectral distribution function.

scholarly journals Discussion on Competition for Spatial Statistics for Large Datasets

2021 ◽  
Author(s):  
Roman Flury ◽  
Reinhard Furrer
Keyword(s):  
Spatial Statistics ◽  
Covariance Function ◽  
Likelihood Function ◽  
Large Datasets ◽  
Missing Observations ◽  
Covariance Model ◽  
Compactly Supported ◽  
Covariance Tapering ◽  
Simple Kriging ◽  
Estimated Parameters

AbstractWe discuss the experiences and results of the AppStatUZH team’s participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each of the different sub-competitions, we estimated parameters of the covariance model based on a likelihood function and predicted missing observations with simple kriging. We approximated the covariance model either with covariance tapering or a compactly supported Wendland covariance function.

scholarly journals Maximum Likelihood Estimation of the VAR(1) Model Parameters with Missing Observations

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Helena Mouriño ◽  
Maria Isabel Barão
Keyword(s):  
Stochastic Process ◽  
Missing Data ◽  
Maximum Likelihood ◽  
Moving Average ◽  
Practical Importance ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Missing Observations ◽  
Data Set ◽  
The Impact

Missing-data problems are extremely common in practice. To achieve reliable inferential results, we need to take into account this feature of the data. Suppose that the univariate data set under analysis has missing observations. This paper examines the impact of selecting an auxiliary complete data set—whose underlying stochastic process is to some extent interdependent with the former—to improve the efficiency of the estimators for the relevant parameters of the model. The Vector AutoRegressive (VAR) Model has revealed to be an extremely useful tool in capturing the dynamics of bivariate time series. We propose maximum likelihood estimators for the parameters of the VAR(1) Model based on monotone missing data pattern. Estimators’ precision is also derived. Afterwards, we compare the bivariate modelling scheme with its univariate counterpart. More precisely, the univariate data set with missing observations will be modelled by an AutoRegressive Moving Average (ARMA(2,1)) Model. We will also analyse the behaviour of the AutoRegressive Model of order one, AR(1), due to its practical importance. We focus on the mean value of the main stochastic process. By simulation studies, we conclude that the estimator based on the VAR(1) Model is preferable to those derived from the univariate context.

scholarly journals Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 449 ◽  
Author(s):  
Abdullah M. Almarashi ◽  
Majdah M. Badr ◽  
Mohammed Elgarhy ◽  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Statistical Inference ◽  
Goodness Of Fit ◽  
Stochastic Ordering ◽  
Linear Representation ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
New Model ◽  
Entropy Measures ◽  
Lifetime Studies

The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.

Stochastic Kriging for Crashworthiness Optimization Accounting for Simulation Noise

2020 ◽  
Author(s):  
Seyed Saeed Ahmadisoleymani ◽  
Samy Missoum
Keyword(s):  
Stochastic Process ◽  
Optimization Algorithm ◽  
Stationary Stochastic Process ◽  
Expected Improvement ◽  
Restraint System ◽  
Stochastic Kriging ◽  
Occupant Restraint System ◽  
Crashworthiness Optimization ◽  
Surrogate Based Optimization ◽  
Available Information

Abstract Vehicle crash simulations are notoriously costly and noisy. When performing crashworthiness optimization, it is therefore important to include available information to quantify the noise in the optimization. For this purpose, a stochastic kriging can be used to account for the uncertainty due to the simulation noise. It is done through the addition of a non-stationary stochastic process to the deterministic kriging formulation. This stochastic kriging, which can also be used to include the effect of random non-controllable parameters, can then be used for surrogate-based optimization. In this work, a stochastic kriging-based optimization algorithm is proposed with an infill criterion referred to as the Augmented Expected Improvement, which, unlike its deterministic counterpart the Expect Improvement, accounts for the presence of irreducible aleatory variance due to noise. One of the key novelty of the proposed algorithm stems from the approximation of the aleatory variance and its update during the optimization. The proposed approach is applied to the optimization of two problems including an analytical function and a crashwor-thiness problem where the components of an occupant restraint system of a vehicle are optimized.

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