Error Distribution Model Research Articles

Volatility Spillovers and Heavy Tails: A Large T-Vector Autoregressive Approach

Volatility is a key measure of risk in financial analysis. The high volatility of one financial asset today could affect the volatility of another asset tomorrow. These lagged effects among volatilities - which we call volatility spillovers - are studied using the Vector AutoRegressive (VAR) model. We account for the possible fat-tailed distribution of the VAR model errors using a VAR model with errors following a multivariate Student t-distribution with unknown degrees of freedom. Moreover, we study volatility spillovers among a large number of assets. To this end, we use penalized estimation of the VAR model with t-distributed errors. We study volatility spillovers among energy, biofuel and agricultural commodities and reveal bidirectional volatility spillovers between energy and biofuel, and between energy and agricultural commodities.

Day-Ahead Probabilistic Load Flow Analysis Considering Wind Power Forecast Error Correlation

Short-term power flow analysis has a significant influence on day-ahead generation schedule. This paper proposes a time series model and prediction error distribution model of wind power output. With the consideration of wind speed and wind power output forecast error’s correlation, the probabilistic distributions of transmission line flows during tomorrow’s 96 time intervals are obtained using cumulants combined Gram-Charlier expansion method. The probability density function and cumulative distribution function of transmission lines on each time interval could provide scheduling planners with more accurate and comprehensive information. Simulation in IEEE 39-bus system demonstrates effectiveness of the proposed model and algorithm.

Robust Least-Squares Support Vector Machine With Minimization of Mean and Variance of Modeling Error.

The least-squares support vector machine (LS-SVM) is a popular data-driven modeling method and has been successfully applied to a wide range of applications. However, it has some disadvantages, including being ineffective at handling non-Gaussian noise as well as being sensitive to outliers. In this paper, a robust LS-SVM method is proposed and is shown to have more reliable performance when modeling a nonlinear system under conditions where Gaussian or non-Gaussian noise is present. The construction of a new objective function allows for a reduction of the mean of the modeling error as well as the minimization of its variance, and it does not constrain the mean of the modeling error to zero. This differs from the traditional LS-SVM, which uses a worst-case scenario approach in order to minimize the modeling error and constrains the mean of the modeling error to zero. In doing so, the proposed method takes the modeling error distribution information into consideration and is thus less conservative and more robust in regards to random noise. A solving method is then developed in order to determine the optimal parameters for the proposed robust LS-SVM. An additional analysis indicates that the proposed LS-SVM gives a smaller weight to a large-error training sample and a larger weight to a small-error training sample, and is thus more robust than the traditional LS-SVM. The effectiveness of the proposed robust LS-SVM is demonstrated using both artificial and real life cases.

A robust cylindrical fitting to point cloud data

ABSTRACTEnvironmental, engineering and industrial modelling of natural features (e.g. trees) and man-made features (e.g. pipelines) requires some form of fitting of geometrical objects such as cylinders, which is commonly undertaken using a least-squares method that—in order to get optimal estimation—assumes normal Gaussian distribution. In the presence of outliers, however, this assumption is violated leading to a Gaussian mixture distribution. This study proposes a robust parameter estimation method, which is an improved and extended form of vector algebraic modelling. The proposed method employs expectation maximisation and maximum likelihood estimation (MLE) to find cylindrical parameters in case of Gaussian mixture distribution. MLE computes the model parameters assuming that the distribution of model errors is a Gaussian mixture corresponding to inlier and outlier points. The parameters of the Gaussian mixture distribution and the membership functions of the inliers and outliers are computed using an expectation maximisation algorithm from the histogram of the model error distribution, and the initial guess values for the model parameters are obtained using total least squares. The method, illustrated by a practical example from a terrestrial laser scanning point cloud, is novel in that it is algebraic (i.e. provides a non-iterative solution to the global maximisation problem of the likelihood function), is practically useful for any type of error distribution model and is capable of separating points of interest and outliers.

STUDY ON MODELING AND VISUALIZING THE POSITIONAL UNCERTAINTY OF REMOTE SENSING IMAGE

It is inevitable to bring about uncertainty during the process of data acquisition. The traditional method to evaluate the geometric positioning accuracy is usually by the statistical method and represented by the root mean square errors (RMSEs) of control points. It is individual and discontinuous, so it is difficult to describe the error spatial distribution. In this paper the error uncertainty of each control point is deduced, and the uncertainty spatial distribution model of each arbitrary point is established. The error model is proposed to evaluate the geometric accuracy of remote sensing image. Then several visualization methods are studied to represent the discrete and continuous data of geometric uncertainties. The experiments show that the proposed evaluation method of error distribution model compared with the traditional method of RMSEs can get the similar results but without requiring the user to collect control points as checkpoints, and error distribution information calculated by the model can be provided to users along with the geometric image data. Additionally, the visualization methods described in this paper can effectively and objectively represents the image geometric quality, and also can help users probe the reasons of bringing the image uncertainties in some extent.

STUDY ON MODELING AND VISUALIZING THE POSITIONAL UNCERTAINTY OF REMOTE SENSING IMAGE

Abstract. It is inevitable to bring about uncertainty during the process of data acquisition. The traditional method to evaluate the geometric positioning accuracy is usually by the statistical method and represented by the root mean square errors (RMSEs) of control points. It is individual and discontinuous, so it is difficult to describe the error spatial distribution. In this paper the error uncertainty of each control point is deduced, and the uncertainty spatial distribution model of each arbitrary point is established. The error model is proposed to evaluate the geometric accuracy of remote sensing image. Then several visualization methods are studied to represent the discrete and continuous data of geometric uncertainties. The experiments show that the proposed evaluation method of error distribution model compared with the traditional method of RMSEs can get the similar results but without requiring the user to collect control points as checkpoints, and error distribution information calculated by the model can be provided to users along with the geometric image data. Additionally, the visualization methods described in this paper can effectively and objectively represents the image geometric quality, and also can help users probe the reasons of bringing the image uncertainties in some extent.

Behavior of R-estimators under measurement errors

As was shown recently, the measurement errors in regressors affect only the power of the rank test, but not its critical region. Noting that, we study the effect of measurement errors on R-estimators in linear model. It is demonstrated that while an R-estimator admits a local asymptotic bias, its bias surprisingly depends only on the precision of measurements and does neither depend on the chosen rank test score-generating function nor on the regression model error distribution. The R-estimators are numerically illustrated and compared with the LSE and $L_1$ estimators in this situation.

Error distribution modelling of satellite soil moisture measurements for hydrological applications

AbstractSatellite‐based soil moisture data accuracies are of important concerns by hydrologists because they could significantly influence hydrological modelling uncertainty. Without proper quantification of their uncertainties, it is difficult to optimize the hydrological modelling system and make robust decisions. Currently, the satellite soil moisture data uncertainty has been limited to summary statistics with the validations mainly from the in situ measurements. This study attempts to build the first error distribution model with additional higher‐order uncertainty modelling for satellite soil moisture observations. The methodology is demonstrated by a case study using the Soil Moisture and Ocean Salinity satellite soil moisture observations. The validation is based on soil moisture estimates from hydrological modelling, which is more relevant to the intended data use than the in situ measurements. Four probability distributions have been explored to find suitable error distribution curves using the statistical tests and bootstrapping resampling technique. General extreme value is identified as the most suitable one among all the curves. The error distribution model is still in its infant stage, which ignores spatial and temporal correlations, and nonstationarity. Further improvements should be carried out by the hydrological community by expanding the methodology to a wide range of satellite soil moisture data using different hydrological models. Copyright © 2016 John Wiley & Sons, Ltd.

An algebraic solution of maximum likelihood function in case of Gaussian mixture distribution

ABSTRACTTraditionally, the least-squares method has been employed as a standard technique for parameter estimation and regression fitting of models to measured points in data sets in many engineering disciplines, geoscience fields as well as in geodesy. If the model errors follow the Gaussian distribution with mean zero in linear models, the least-squares estimate is linear, unbiased and of minimum variance. However, this may not always be the case owing to contaminated data (i.e. the presence of outliers) or data from different sources with varying distributions. This study proposes an algebraic iterative method that approximates the error distribution model using a Gaussian mixture distribution, with the application of maximum likelihood estimation as a possible solution to the problem. The global maximisation of the likelihood function is carried out through the computation of the global solution of a multivariate polynomial system using numerical Groebner basis in order to considerably reduce the running time. The novelty of the proposed method is the application of the total least square (TLS) error model as opposed to ordinary least squares (OLS) and the maximisation of the likelihood function of the Gaussian mixture via an algebraic approach. Use of the TLS error model rather than OLS enables errors in all the three coordinates of the model of a 3D plane (i.e. ) to be considered. The proposed method is illustrated by fitting a plane to real laser-point cloud data containing outliers to test its robustness. Compared with the Random Sample Consensus and Danish robust estimation methods, the results of the proposed algebraic method indicate its efficiency in terms of computational time and its robustness in managing outliers. The proposed approach thus offers an alternative method for solving mixture distribution problems in geodesy.

Minimum Distance Lasso for robust high-dimensional regression

We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. Likelihood-based estimators lack resilience against outliers and model misspecification, a critical issue when dealing with high-dimensional noisy data. Our method, Minimum Distance Lasso (MD-Lasso), combines minimum distance functionals customarily used in nonparametric estimation for robustness, with $\ell_{1}$-regularization. MD-Lasso is governed by a scaling parameter capping the influence of outliers: the loss is locally convex and close to quadratic for small squared residuals, and flattens for squared residuals larger than the scaling parameter. As the parameter approaches infinity the estimator becomes equivalent to least-squares Lasso. MD-Lasso is able to maintain the robustness of minimum distance functionals in sparse high-dimensional regression. The estimator achieves maximum breakdown point and enjoys consistency with fast convergence rates under mild conditions on the model error distribution. These hold for any solution in a convexity region around the true parameter and in certain cases for every solution. We provide an alternative set of results that do not require the solutions to lie within the convexity region but where the $\ell_{2}$-norm of the feasible solutions is constrained within a safety radius. Thanks to this constraint, a first-order optimization method is able to produce local optima that are consistent. A connection is established with re-weighted least-squares that intuitively explains MD-Lasso robustness. The merits of our method are demonstrated through simulation and eQTL analysis.

Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors

Censored quantile regression is an important alternative to the Cox proportional hazards model in survival analysis. In contrast to the usual central covariate effects, quantile regression can effectively characterize the covariate effects at different quantiles of the survival time. When covariates are measured with errors, it is known that naively treating mismeasured covariates as error-free would result in estimation bias. Under censored quantile regression, we propose smoothed and corrected estimating equations to obtain consistent estimators. We establish consistency and asymptotic normality for the proposed estimators of quantile regression coefficients. Compared with the naive estimator, the proposed method can eliminate the estimation bias under various measurement error distributions and model error distributions. We conduct simulation studies to examine the finite-sample properties of the new method and apply it to a lung cancer study. Supplementary materials for this article are available online.

A practical guide and power analysis for GLMMs: detecting among treatment variation in random effects.

In ecology and evolution generalized linear mixed models (GLMMs) are becoming increasingly used to test for differences in variation by treatment at multiple hierarchical levels. Yet, the specific sampling schemes that optimize the power of an experiment to detect differences in random effects by treatment/group remain unknown. In this paper we develop a blueprint for conducting power analyses for GLMMs focusing on detecting differences in variance by treatment. We present parameterization and power analyses for random-intercepts and random-slopes GLMMs because of their generality as focal parameters for most applications and because of their immediate applicability to emerging questions in the field of behavioral ecology. We focus on the extreme case of hierarchically structured binomial data, though the framework presented here generalizes easily to any error distribution model. First, we determine the optimal ratio of individuals to repeated measures within individuals that maximizes power to detect differences by treatment in among-individual variation in intercept, among-individual variation in slope, and within-individual variation in intercept. Second, we explore how power to detect differences in target variance parameters is affected by total variation. Our results indicate heterogeneity in power across ratios of individuals to repeated measures with an optimal ratio determined by both the target variance parameter and total sample size. Additionally, power to detect each variance parameter was low overall (in most cases >1,000 total observations per treatment needed to achieve 80% power) and decreased with increasing variance in non-target random effects. With growing interest in variance as the parameter of inquiry, these power analyses provide a crucial component for designing experiments focused on detecting differences in variance. We hope to inspire novel experimental designs in ecology and evolution investigating the causes and implications of individual-level phenotypic variance, such as the adaptive significance of within-individual variation.

Robust Inertial-Astronomic Attitude Determination Algorithm with Adaptive Star Geometrical Error Model for HCVs

AbstractInertial/astronomic integration is an effective way to improve the accuracy of attitude determination of hypersonic cruise vehicles (HCVs). Compared with common low-dynamic aircraft, the environmental affection during hypersonic flight leads to the non-Gaussian noise character of astronomic observation. Meanwhile, rapid star geometry changing during HCVs’ rapid movement causes redistribution of errors in astronomic measurements and significant variation of its main Gaussian characteristic. A kind of robust inertial/astronomic attitude determination algorithm with adaptive star geometrical error model is proposed. The adaptive star geometrical error distribution model is established for obtaining the main Gaussian model of astronomic measurement misalignment errors in flight. After that, inertial/astronomic integration model–based on misalignment errors is proposed, which avoids Euler angle transformation. On these bases, the improved robust filter algorithm is designed, which utilizes real-time as...

Is China the price taker in soybean futures?

Purpose – The purpose of this paper is to examine whether China is still a passive price taker from the US soybean futures, or instead domestic futures market has developed certain degrees of pricing power through time. The finding helps to identify the importance of China soybean futures in the perspective of portfolio selection for international futures traders. If China soybean futures market is no longer a price taker after the subprime crisis, traders need to include it as a separate category in their portfolio. Design/methodology/approach – This paper uses exponential generalized autoregressive conditional heteroskedasticity-generalized error distribution (EGARCH-GED) and generalized autoregressive conditional heteroskedasticity-generalized error distribution (GARCH-GED) models to test spillover effects between Dalian Commodity Exchange (DCE) and Chicago Board of Trade (CBOT) soybean futures. The authors divide daily samples into three subperiods based on the subprime crisis. Three research questions – whether China is still the price taker, the importance of Chinese soybean futures in international futures portfolio selection, and the influences of subprime crisis on soybean futures volatility relationship – are examined by comparing estimation results through time and different contracts. Findings – The spillover effect from CBOT soybean futures to DCE No. 1 soybean futures becomes weaker through time. China is no longer a soybean futures price taker after the subprime crisis. The authors also find the shocks of bearish news on DCE soybeans are greater than those of bullish news. Potential volatility of DCE in long positions is bigger than that in short positions. Practical implications – China is the largest soybean importer. DCE is a very important futures market for non-genetically modified soybeans. It is necessary for both international and domestic futures traders to understand the changes in international soybean futures price relationship and take corresponding strategies. It is also important for market to realize that DCE soybean futures are to a less degree price taker after the subprime crisis. Originality/value – The paper applies EGARCH-GED and GARCH-GED models to identify changes in spillover effects before, during, and after the subprime crisis. Different from other studies, this paper finds after the subprime crisis, China is no longer the soybean futures price taker. This paper also compares the spillover effects of non-genetically modified soybean futures (No. 1 soybean futures) with genetically modified soybean futures (No. 2 soybean futures).

Estimating individual growth variability in albacore (Thunnus alalunga) from the North Atlantic stock: Aging for assessment purposes

Length-frequency data and derived catch at age matrices are used in north Atlantic albacore (Thunnus alalunga) stock assessment conducted within the International Commission for the Conservation of Atlantic Tunas (ICCAT). Growth is assumed to follow the von Bertalanffy model with the assumption that growth parameters are constant over time and the same for all fish. However, individual growth variability is an important factor not considered and affecting the input into the modelling of the population. This study describes a Bayesian hierarchical model applied to model the individual variability in the parameters asymptotic length (L∞) and growth rate (K) of the von Bertalanffy growth model for North Atlantic albacore. The method assumes that the L∞ and K values for each individual fish are drawn from a random distribution centered on the population mean values, with estimated variances. Multiple observations of spine diameter at age for individual fish were obtained by direct reading of spine sections collected in 2011 and 2012. A suite of back calculation methods were then applied to the measurements of annuli diameters in the aged individuals observed to back-calculate lengths at each age. The von Bertalanffy model was fitted to the measured and back-calculated lengths. Models with and without individual growth variability were compared using the deviance information criterion (DIC) to find the best model. Normal and log-normal error distribution models were used to analyse the data. Additionally, subsamples of the data were used to evaluate whether an unbalanced age-distribution in the data affects estimates of growth parameters. It was found that North Atlantic albacore asymptotic length (L∞) varies significantly between individual fish but not individual rate growth (K), for all back-calculation methods. Furthermore, negatively correlated relationships between von Bertalanffy growth parameters of asymptotic mean (L∞) and growth rate (K) were estimated for North Atlantic albacore with the array of models explored. The overall estimated values of K and population mean L∞ parameters were similar to values estimates in previous north Atlantic albacore growth studies.

Efficient statistical analysis of geometric tolerances using unified error distribution and an analytical variation model

Inaccuracies in conventional tolerance characterization methods, which are based on worst-case and root-square-error methods, as well as inefficiencies in Monte Carlo computational methods of statistical tolerance analysis, require an accurate and efficient method of statistical analysis of geometric tolerances. Here, we describe a unified error distribution model for various types of geometric tolerance to obtain the distribution of the deviations in different directions. The displacement distributions of planes, straight lines, and points are analyzed based on distributions within tolerance zones. The distribution of the displacements of clearance fits is then determined according to the precedence of the assembly constraints. We consider the accumulated assembly variations and displacement distributions, and an analytical model is constructed to calculate the distribution of the deviations of the control points and the process capability index to validate the functional requirements. The efficiency of the method is shown by applying it to the assembly of a single-rod piston cylinder. The results are compared with other statistical methods of tolerance analysis. We find an improvement of approximately 20 % in tolerance analysis, and the process capability index of the assembly procedure was reduced by 10 %.

Integrating hierarchical Bayes with phosphorus loading modelling

The causal linkage between lake productivity and phosphorus loading has provided the basis for a family of models that predict lake total phosphorus concentrations as a function of lake morphometric/hydraulic characteristics, such as the areal phosphorus loading rate, mean lake depth, fractional phosphorus retention and areal hydraulic loading. Most of these empirical models have been derived from “cross-sectional” datasets, comprising multiple point measurements or single averages from a number of lakes, and are typically used to predict changes within a single system at different points in time. This practice implicitly postulates that the large scale (cross-sectional) patterns described in the model are also representative of the dynamics of individual systems. In this study, we relax this assumption using a Bayesian hierarchical strategy that aims to accommodate the role of significant sources of variability (morphology, hydraulic regime). We first examine several hierarchical structures representing different characterizations of model error, parameter covariance, and prior distribution followed by the hyperparameters. Our analysis primarily highlights the robustness of the posterior group-level patterns to the hierarchical formulation developed. We also show that the delineation of homogeneous subsets of lakes with respect to their morphological/hydraulic characteristics and the subsequent integration with hierarchical frameworks may give empirical phosphorus retention/loading models with better predictive ability. We then present a complementary exercise that aims to accommodate the spatial and seasonal total phosphorus variability within individual systems, using a spatially-explicit simple mass-balance model forced with idealized sinusoidal loading. Our study concludes by advocating that the hierarchical Bayes provides a conceptually appealing framework to gradually accommodate different sources of variability and more prudently increase the complexity of simple empirical models.

Dual-Bézier path smoothing and interpolation for five-axis linear tool path in workpiece coordinate system

The tool path composed of consecutive short linear segments (G01 blocks) is still the widespread tool path representation form in five-axis machining. The inherent shortcoming of linear tool path is first-order discontinuity at the corner, which is the bottleneck to achieve high-speed and high-accuracy machining. In this article, a dual-Bézier path smoothing algorithm for five-axis linear tool path in workpiece coordinate system is proposed. There are three steps involved in our method. First, the corner error distribution model is introduced to assign the given tolerance to the smoothing approximation error constraint and the chord error constraint to ensure the interpolation trajectory error within the given tolerance. Second, segment junctions of the linear tool path in workpiece coordinate system are smoothed by double G2 continuous cubic Bézier curves. One cubic Bézier curve is used to round the corner of the tool tip point path, and the other Bézier curve is used to round the corner of the tool axis point path. This algorithm takes the conditions of approximation error constraint, the parameterized synchronization constraint, and continuous curvature constraint into consideration. Hence, the tangency and curvature continuities are both guaranteed in the new path. Third, an adaptive feedrate scheduling method is introduced to interpolate the new path. Simulation and experiment are performed to verify the effectiveness of the proposed method in five-axis tool path smoothing, speed smoothing, and trajectory accuracy controlling.

Bayesian estimation and inference for log-ACD models

This paper adapts Bayesian Markov chain Monte Carlo methods for application to some auto-regressive conditional duration models. Subsequently, the properties of these estimators are examined and assessed across a range of possible conditional error distributions and dynamic specifications, including under error mis-specification. A novel model error distribution, employing a truncated skewed Student-t distribution is proposed and the Bayesian estimator assessed for it. The results of an extensive simulation study reveal that favourable estimation properties are achieved under a range of possible error distributions, but that the generalised gamma distribution assumption is most robust and best preserves these properties, including when it is incorrectly specified. The results indicate that the powerful numerical methods underlying the Bayesian estimator allow more efficiency than the (quasi-) maximum likelihood estimator for the cases considered.

Probabilistic Multiple Linear Regression Modeling for Tropical Cyclone Intensity

Abstract The authors describe the development and verification of a statistical model relating tropical cyclone (TC) intensity to the local large-scale environment. A multiple linear regression framework is used to estimate the expected intensity of a tropical cyclone given the environmental and storm conditions. The uncertainty of the estimate is constructed from the empirical distribution of model errors. NCEP–NCAR reanalysis fields and historical hurricane data from 1981 to 1999 are used for model development, and data from 2000 to 2012 are used to evaluate model performance. Seven predictors are selected: initial storm intensity, the change of storm intensity over the past 12 h, the storm translation speed, the difference between initial storm intensity and its corresponding potential intensity, deep-layer (850–200 hPa) vertical shear, atmospheric stability, and 200-hPa divergence. The system developed here models storm intensity changes in response to changes in the surrounding environment with skill comparable to existing operational forecast tools. Since one application of such a model is to predict changes in TC activity in response to natural or anthropogenic climate change, the authors examine the performance of the model using data that is most readily available from global climate models, that is, monthly averages. It is found that statistical models based on monthly data (as opposed to daily) with only a few essential predictors, for example, the difference between storm intensity and potential intensity, perform nearly as well at short leads as when daily predictors are used.