Parameter Estimation Procedure Research Articles

Adaptive forecasting and financial risk estimation

The study is directed towards development of an adaptive decision support system for modeling and forecasting nonlinear nonstationary processes in economy, finances and other areas of human activities. The structure and parameter adaptation procedures for the regression and probabilistic models are proposed as well as the respective information system architecture and functional layout are developed. The system development is based on the system analysis principles such as adaptive model structure estimation, optimization of model parameter estimation procedures, identification and taking into consideration of possible uncertainties met in the process of data processing and mathematical model development. The uncertainties are inherent to data collecting, model constructing and forecasting procedures and play a role of negative influence factors to the information system computational procedures. Reduction of their influence is favourable for enhancing the quality of intermediate and final results of computations. The illustrative examples of practical application of the system developed proving the system functionality are provided.

Markov-Modulated Linear Regression Parameter Estimation Using a Convolution of Exponential Densities

Markov-modulated linear regression model is a special case of the Markov-additive process (𝒀, 𝑱) = {(𝒀(𝒕), 𝑱(𝒕)), 𝒕 ≥ 𝟎}, where component J is called Markov, and component Y is additive and described by a linear regression. The component J is a continuous-time homogeneous irreducible Markov chain with the known transition intensities between the states. Usually this Markov component is called the external environment or background process. Unknown regression coefficients depend on external environment state, but regressors remain constant. This research considers the case, when the Markov property is not satisfied, namely, the sojourn time in each state is not exponentially distributed. Estimation procedure for unknown model parameters is described when it’s possible to represent transition intensities as a convolution of exponential densities. An efficiency of such an approach is evaluated by a simulation.

Modeling and monitoring unweighted networks with directed interactions

Networks have been widely employed to represent interactive relationships among individual units in complex systems such as the Internet of Things. Assignable causes in systems can lead to abrupt increased or decreased frequency of communications within the corresponding network, which allows us to detect such assignable causes by monitoring the communication level of the network. However, existing statistical process control methods for unweighted networks have scarcely incorporated either the network sparsity or the direction of interactions between two network nodes, i.e., dyadic interaction. Regarding this, we establish a matrix-form model to characterize directional dyadic interactions in time-independent unweighted networks. With inactive dyadic interactions excluded, the proposed procedure of parameter estimation achieves higher consistency with less computational cost than its alternative when networks are large-scale and sparse. Using the generalized likelihood ratio test, the work derives two schemes for monitoring directed unweighted networks. The first can be used in general cases whereas the second incorporates a priori shift information to improve change detection efficiency in some cases and estimate the location of a single shifted parameter. Simulation study and a real application are provided to demonstrate the advantages and effectiveness of proposed schemes.

Modal non‐linear regression in the presence of Laplace measurement error

SummaryIn this paper, we propose a robust estimation procedure for a class of non‐linear regression models when the covariates are contaminated with Laplace measurement error, aiming at constructing an estimation procedure for the regression parameters which are less affected by the possible outliers, and heavy‐tailed underlying distribution, as well as reducing the bias introduced by the measurement error. Starting with the modal regression procedure developed for the measurement error‐free case, a non‐trivial modification is made so that the modified version can effectively correct the potential bias caused by measurement error. Large sample properties of the proposed estimate, such as the convergence rate and the asymptotic normality, are thoroughly investigated. A simulation study and real data application are conducted to illustrate the satisfying finite sample performance of the proposed estimation procedure.

Multivariate Gamma Regression: Parameter Estimation, Hypothesis Testing, and Its Application

Gamma distribution is a general type of statistical distribution that can be applied in various fields, mainly when the distribution of data is not symmetrical. When predictor variables also affect positive outcome, then gamma regression plays a role. In many cases, the predictor variables give effect to several responses simultaneously. In this article, we develop a multivariate gamma regression (MGR), which is one type of non-linear regression with response variables that follow a multivariate gamma (MG) distribution. This work also provides the parameter estimation procedure, test statistics, and hypothesis testing for the significance of the parameter, partially and simultaneously. The parameter estimators are obtained using the maximum likelihood estimation (MLE) that is optimized by numerical iteration using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The simultaneous test for the model’s significance is derived using the maximum likelihood ratio test (MLRT), whereas the partial test uses the Wald test. The proposed MGR model is applied to model the three dimensions of the human development index (HDI) with five predictor variables. The unit of observation is regency/municipality in Java, Indonesia, in 2018. The empirical results show that modeling using multiple predictors makes more sense compared to the model when it only employs a single predictor.

What Matters When Developing Oil Price Volatility Forecasting Frameworks?

Forecasting oil price volatility is considered of major importance for numerous stakeholders, including, policy makers, industries and investors. This paper examines and evaluates the main factors that oil price volatility forecasters should take before constructing their forecasting models. Such factors are related to: i) direct vs iterated forecasts, ii) the incorporation of continuous and jump components, iii) the importance of semi variance volatility measures, and iv) OLS vs time-varying parameter (TVP) estimation procedures. Even more, we evaluate the performance of these factors for both realized and implied volatility measures, based on statistical loss functions, as well as, their economic use. The results show that depending on whether end-users are interested in forecasting the realized or the implied volatility, the factors influencing the accuracy of forecasts are different. In particular, for the realized volatility, direct forecasting based on TVP estimation procedure, as well as, using the information obtained in the semi variance measures are capable of producing significantly superior forecasts. By contrast, separating the continuous and the jump components of the realized volatility does not provide any added value to these forecasts. Turning to the OVX, based on the economic evaluation of our forecasts, the TVP estimation procedure seems to performbetter. In addition, we find evidence that the continuous component and the semi variance measures of the realized volatility also yield better OVX forecasts in the longer run horizons.

Bivariate flood distribution analysis under parametric copula framework: a case study for Kelantan River basin in Malaysia

Flood is becoming an intensive hydro-climatic issue at the Kelantan River basin in Malaysia. Univariate frequency analysis would be unreliable due to multidimensional behaviour of flood, which often demands multivariate flow exceedance probabilities. The joint distribution analysis of multiple interacting flood characteristics, i.e. flood peak, volume and duration, is very useful for understanding critical hydrologic behaviour at a river basin scale. In this paper, a copula-based methodology is incorporated for multivariate flood frequency analysis for the 50-year annual basis flood characteristics of Kelantan River basin at Guillemard bridge station in Malaysia. Investigation reveals that the Lognormal (2P), Johnson SB-4P and Gamma-3P are selected as marginal distributions for the flood peak flow, volume and duration series. Several bivariate families such as mono-parametric, bi-parametric (i.e. mixed version) and rotated version of Archimedean copulas and also the elliptical copula are introduced to cover a large dependence pattern of flood characteristics. The dependence parameter of bivariate copulas is estimated by the method of moments (MOM) based on the inversion of Kendall’s tau and maximum pseudo-likelihood estimator. To analytically validate and recognize most parsimonious copulas, GOF test and Cramer–von Mises distance statistics (Sn) with the parametric bootstrap method are employed. The Gaussian copula is identified as the most justifiable model for joint modelling of the flood peak–volume and peak–duration combination for MOM-based parameter estimation procedure. Similarly, the Frank copula is selected as the best-fitted structure for modelling peak–duration combination based on MPL estimators, but the MOM estimator recognized Gaussian copula as most suitable for peak–volume pair. Furthermore, the best-fitted copulas are used for obtaining the joint and conditional return periods of the flood characteristics.

A Fractal Projection and Markovian Segmentation-Based Approach for Multimodal Change Detection

Change detection in heterogeneous bitemporal satellite images has become an emerging, important, and challenging research topic in remote sensing for rapid damage assessment. In this article, we explore a new parametric mapping strategy based on a modified geometric fractal decomposition and a contractive mapping approach allowing us to project the before image on any after imaging modality type. This projection exploits the fact that any satellite image data can be approximatively encoded in terms of spatial self-similarities at different scales and this property remains quite invariant to a given imaging modality type. Once the projection is performed and that a pixelwise difference map between the two images (presented in the same imaging modality) is then binarized in the unsupervised Bayesian framework. At this stage, we will test several parameter estimation procedures combined with several segmentation strategies based on different Bayesian cost functions. The experiments for change detection, with real images showing different multimodalities and changed events, indicate that this new fractal-based projection method, which is entirely based on a series of structural and spatial information, is an interesting alternative to classical regression-based projection methods (based only on luminance transformation). Besides, the experiments also show that the difference map, resulting in this novel projection strategy, is also particularly amenable for an unsupervised Markovian binarization approach.

An online Bayesian approach to change-point detection for categorical data

Change-point detection for categorical data has wide applications in many fields. Existing methods either are distribution-free, not utilizing categorical information sufficiently, or have limited performance when there exists “rare events” (events that occur with low frequency). In this paper, we propose a Bayesian change-point detection model for categorical data based on Dirichlet-multinomial mixtures. Because of the introduction of prior information, our method performs well for the existence of “rare events”. An online parameter estimation procedure and an online detection strategy are then designed to adapt to data streams. Monte Carlo simulations discuss the power of the proposed method and show advantages compared with existing algorithms. Applications in biomedical research, document analysis, health news case study and location monitoring indicate practical values of our method.

ADAPTIVE MODELING AND FORECASTING OF NONLINEAR NONSTATIONARY PROCESSES

The study is directed towards development of adaptive decision support system for modeling and forecasting nonlinear nonstationary processes in economy, finances and other areas of human activities. The structure and parameter adaptation procedures for the regression and probabilistic models are proposed as well as respective information system architecture and functional layout are developed. The system development is based on the system analysis principles such as adaptive model structure estimation, optimization of model parameter estimation procedures, identification and taking into consideration of possible uncertainties met in the process of data processing and mathematical model development. The uncertainties are inherent to data collecting, model constructing and forecasting procedures and play a role of negative influence factors to the information system computational procedures. Reduction of their influence is favorable for enhancing the quality of intermediate and final results of computations. The illustrative examples of practical application of the system developed proving the system functionality are provided.

Predicting post-natal energy intake of lesser black-backed gull chicks by Dynamic Energy Budget modeling

The standard Dynamic Energy Budget (DEB) model is widely used to describe the physiology of individual animals. Here we parametrized the DEB model for the lesser black-backed gull Larus fuscus mainly on the basis of literature data. Next we performed an inverse modeling approach to predict the food intake rate of gull chicks (model input) on the basis of their growth trajectory from hatching to fledging (model output). Food intake rate and growth were also measured for this period in an aviary experiment, where three different diet treatments resulted in a large range in overall intake rate. These measured food intake rate data were not used in the parameter estimation procedure, but rather to validate model results. Model predictions of food intake rate were systematically only about 10% below the observations, but predictions and observations correlated strongly. The DEB model might be used to predict food provisioning rates in the field, which are difficult to obtain, on the basis of growth data, which are much easier to get.

The coupled two-step parameter estimation procedure for borehole thermal resistance in thermal response test

The ground thermal properties and borehole thermal resistance are the essential parameters for the design of borehole heat exchanger (BHE) field, and they are usually estimated using the experimental inlet/outlet fluid temperatures of BHE in thermal response test (TRT). This paper proposes the coupled two-step parameter estimation procedure (TSPEP) for estimating ground thermal conductivity and borehole thermal resistance of BHE by evaluating the actual averaged–over-the –depth mean fluid temperature (MFT) using the quasi-three-dimensional model inside the borehole. The simulated annealing algorithm (SAA) is used to iteratively find the minimum values of the two objective functions to obtain the optimal estimated results. In TSPEP, the estimated ground volumetric heat capacity and weighted factor f in the 1st step are transferred to calculate MFT using the experimental data in the 2nd step, which guarantees the direct approach based on the infinite line source model (ILSM)applied to improve the accuracy of the estimated borehole thermal resistance. For 50 m depth BHE, the estimated borehole thermal resistance is increased by 12.1% using TSPEP than the effective borehole thermal resistance evaluated by the arithmetic average fluid temperature (AFT). The estimated ground thermal conductivity in TSPEP is almost same with that from the direct approach based on ILSM, and the maximum relative error between them is only 0.91% even though borehole depth of BHE changes from 50 m to 200 m.

Mathematical modeling and parameter estimation of levodopa motor response in patients with parkinson disease

Parkinson disease (PD) is characterized by a clear beneficial motor response to levodopa (LD) treatment. However, with disease progression and longer LD exposure, drug-related motor fluctuations usually occur. Recognition of the individual relationship between LD concentration and its effect may be difficult, due to the complexity and variability of the mechanisms involved. This work proposes an innovative procedure for the automatic estimation of LD pharmacokinetics and pharmacodynamics parameters, by a biologically-inspired mathematical model. An original issue, compared with previous similar studies, is that the model comprises not only a compartmental description of LD pharmacokinetics in plasma and its effect on the striatal neurons, but also a neurocomputational model of basal ganglia action selection. Parameter estimation was achieved on 26 patients (13 with stable and 13 with fluctuating LD response) to mimic plasma LD concentration and alternate finger tapping frequency along four hours after LD administration, automatically minimizing a cost function of the difference between simulated and clinical data points. Results show that individual data can be satisfactorily simulated in all patients and that significant differences exist in the estimated parameters between the two groups. Specifically, the drug removal rate from the effect compartment, and the Hill coefficient of the concentration-effect relationship were significantly higher in the fluctuating than in the stable group. The model, with individualized parameters, may be used to reach a deeper comprehension of the PD mechanisms, mimic the effect of medication, and, based on the predicted neural responses, plan the correct management and design innovative therapeutic procedures.

A NEW MULTILEVEL MODELING APPROACH FOR CLUSTERED SURVIVAL DATA

In multilevel modeling of clustered survival data, to account for the differences among different clusters, a commonly used approach is to introduce cluster effects, either random or fixed, into the model. Modeling with random effects may lead to difficulties in the implementation of the estimation procedure for the unknown parameters of interest because the numerical computation of multiple integrals may become unavoidable when the cluster effects are not scalars. On the other hand, if fixed effects are used, there is a danger of having estimators with large variances because there are too many nuisance parameters involved in the model. In this article, using the idea of the homogeneity pursuit, we propose a new multilevel modeling approach for clustered survival data. The proposed modeling approach does not have the potential computational problem as modeling with random effects, and it also involves far fewer unknown parameters than modeling with fixed effects. We also establish asymptotic properties to show the advantages of the proposed model and conduct intensive simulation studies to demonstrate the performance of the proposed method. Finally, the proposed method is applied to analyze a dataset on the second-birth interval in Bangladesh. The most interesting finding is the impact of some important factors on the length of the second-birth interval variation over clusters and its homogeneous structure.

Robust M estimation for 3D correlated vector observations based on modified bifactor weight reduction model

This paper develops a robust M estimation approach applied for three-dimensional (3D) correlated vector observations. A modified bifactor reduction model is constructed, where the weight shrinking factor of the 3D vector observation is determined by a new test statistic that coincides with the estimated direction of the outlier vector and thus is more sensitive to vector-type outliers than the standardized residual used for most conventional robust M methods. With the proposed bifactor reduction model, the outlying vector observation is down-weighted directly along a specific direction, rather than separately at the three components. The new equivalent weight matrix derived from the proposed bifactor model still keeps symmetry, based on which the parameter estimation procedure is developed. A real 3D control network of GNSS vector observations is processed by simulating outliers with different types, sizes and locations. The results show the effectiveness of the proposed approach by comparing with other four conventional robust M method (IGGIII, Danish, Huber and Hampel).

Document-level emotion detection using graph-based margin regularization

Sentiment analysis aims to automatically detect the underlying attitudes that users express. For the documents with complex unstructured data, such as reviews, emojis and surveys, it is usually hard to precisely identify the real emotion. Thus, it becomes urgent, yet challenging, to develop a technique that can process and make use of the unstructured information. In this article, we consider sentiment classification for those unstructured features extracted from texts. We propose a regularization-based framework to pursue better classification performance by (1) introducing polarity shifters assembled with sentiment words to create novel bigram features and (2) simultaneously constructing a constraint graph to encode the relative polarity among unstructured features to improve the parameter estimation procedure. Under these settings, our approach can uncover the intrinsic semantic information from the unstructured text data. Theoretically, we justify its underlying equivalent connection with the standard Bayes classifier, which is ideally optimal when the sample distribution is known. Moreover, we show that our new method yields better generalization ability due to the reduced solution search space and the appealing asymptotic consistency. The superior performance from real data experiments demonstrates the robustness and effectiveness of the proposed method.

Inference of Historical Population-Size Changes with Allele-Frequency Data.

With up to millions of nearly neutral polymorphisms now being routinely sampled in population-genomic surveys, it is possible to estimate the site-frequency spectrum of such sites with high precision. Each frequency class reflects a mixture of potentially unique demographic histories, which can be revealed using theory for the probability distributions of the starting and ending points of branch segments over all possible coalescence trees. Such distributions are completely independent of past population history, which only influences the segment lengths, providing the basis for estimating average population sizes separating tree-wide coalescence events. The history of population-size change experienced by a sample of polymorphisms can then be dissected in a model-flexible fashion, and extension of this theory allows estimation of the mean and full distribution of long-term effective population sizes and ages of alleles of specific frequencies. Here, we outline the basic theory underlying the conceptual approach, develop and test an efficient statistical procedure for parameter estimation, and apply this to multiple population-genomic datasets for the microcrustacean Daphnia pulex.

Improving the Predictive Skill of a Distributed Hydrological Model by Calibration on Spatial Patterns With Multiple Satellite Data Sets

AbstractHydrological model calibration combining Earth observations and in situ measurements is a promising solution to overcome the limitations of the traditional streamflow‐only calibration. However, combining multiple data sources in model calibration requires a meaningful integration of the data sets, which should harness their most reliable contents to avoid accumulation of their uncertainties and mislead the parameter estimation procedure. This study analyzes the improvement of model parameter selection by using only the spatial patterns of satellite remote sensing data, thereby ignoring their absolute values. Although satellite products are characterized by uncertainties, their most reliable key feature is the representation of spatial patterns, which is a unique and relevant source of information for distributed hydrological models. We propose a novel multivariate calibration framework exploiting spatial patterns and simultaneously incorporating streamflow and three satellite products (i.e., Global Land Evaporation Amsterdam Model [GLEAM] evaporation, European Space Agency Climate Change Initiative [ESA CCI] soil moisture, and Gravity Recovery and Climate Experiment [GRACE] terrestrial water storage). The Moderate Resolution Imaging Spectroradiometer (MODIS) land surface temperature data set is used for model evaluation. A bias‐insensitive and multicomponent spatial pattern matching metric is developed to formulate a multiobjective function. The proposed multivariate calibration framework is tested with the mesoscale Hydrologic Model (mHM) and applied to the poorly gauged Volta River basin located in a predominantly semiarid climate in West Africa. Results of the multivariate calibration show that the decrease in performance for streamflow (−7%) and terrestrial water storage (−6%) is counterbalanced with an increase in performance for soil moisture (+105%) and evaporation (+26%). These results demonstrate that there are benefits in using satellite data sets, when suitably integrated in a robust model parametrization scheme.

Estimation of Physical Parameters Using a New Discrete-time Derivative Algorithm

The paper presents a parameters estimation procedure for physical systems modeled using the POG (Power-Oriented Graphs) technique. The coefficients defining the constitutive relation for both static and dynamic physical elements within the system can be estimated, as well as the coefficients describing energy conversions taking place either within the same energetic domain or between two different energetic domains. The evolution of the state vector over time is supposed to be known, whereas its first derivative is supposed to be unknown and is obtained by using a new algorithm for computing the discrete-time derivative of a sampled signal, which is effective even in presence of disturbances affecting the signal samples. As long as the unknown parameters appear linearly within the system differential equations, the system is allowed to exhibit any nonlinear function of the state vector and its first derivative. The procedure is finally applied to two different case studies: a linear one and a nonlinear one.

Identification of fractional-order models for condition monitoring of solid-oxide fuel cell systems

With rising market deployment the condition monitoring of solid oxide fuel cell systems is gaining particular importance. The conventional approaches mainly use electrochemical impedance spectroscopy based on the repeated sinusoidal perturbation over a range of frequencies. One of the notable weaknesses of the approach is excessively long perturbation time needed to properly evaluate the impedance curve. In this paper, we propose a time-efficient approach in which, a short, persistently exciting and small-amplitude perturbation is used to excite all the relevant system eigenmodes. A model structure from a class of linear fractional order models is selected to describe the perturbed dynamics and to account for anomalous diffusion processes in the cells. Then, the model parameters are estimated directly from measured input and output records. The paper presents a computationally efficient parameter estimation procedure in which the numerical issues of differentiation of noisy signals are alleviated by using modulating functions. In practice, that means a combination of filtering and application of conventional least squares. The approach is applied on a case of health assessment of solid oxide fuel cells.