Constant Variance Research Articles

An Application of Damped Diffusion for Modeling Volatility Dynamics

Abstract This paper proposes a damped constant elasticity variance (CEV) stochastic volatility (DCEV) model, which remedies the possible explosive behavior of the CEV model and also accommodates the mean-reverting dynamics more appropriately than the nonlinear drift (NLD) stochastic volatility model. As the DCEV model maintains the linear drift, an analytic formula is available to efficiently infer latent variances from VIX levels, after which both its physical and risk-neutral parameters can be simultaneously estimated with the maximum-likelihood approach given S&P 500 returns and inferred variances. The DCEV model outperforms the CEV and NLD models in in-sample fitting performance and in out-of-sample variance forecasting under the physical measure. It also exhibits superior ability in out-of-sample option pricing over the CEV and Heston’s (1993) models under the risk-neutral measure. This satisfactory performance demonstrates the suitability of describing volatility dynamics with the DCEV model and the potential of applying this to study other issues.

Augmented truncation approximations to the solution of Poisson’s equation for Markov chains

Poisson’s equation has a lot of applications in various areas, such as Markov decision theory, perturbation theory, central limit theorems (CLTs), etc. Usually it is hard to derive the explicit expression of the solution of Poisson’s equation for a Markov chain on an infinitely many state space. Here we will present a computational framework for the solution for both discrete-time Markov chains (DTMCs) and continuous-time Markov chains (CTMCs), by developing the technique of augmented truncation approximations. The censored Markov chain and the linear augmentation to some columns are shown to be effective truncation approximation schemes. Moreover, the convergence to the variance constant in CLTs are also considered. Finally the results obtained are applied to discrete-time single-birth processes and continuous-time single-death processes.

Predictors for Screen Time Exposure among Children between 3 and 5 Years Old in Southern Brazil.

The use of technology is an increasingly common practice among preschoolers. Little is known about the relationship between screen time exposure (STE) and aspects related to family and the environment. The aim is to characterize STE in Brazilian children aged between 3 and 5 years. Furthermore, the objective of this study is to associate the STE of children and of their parents with sociodemographic variables. Children aged between 3 and 5 years from southern Brazil and their parents participated in this study. To investigate STE, the researchers developed a specific questionnaire. To compare STE between age groups, the Kruskal-Wallis test was performed, followed by Dunn's post hoc test. Spearman's correlation and linear regression were used to correlate the variables. Children (n = 237) spend an average of 3.7 ± 0.8 h/day in front of screens. The STE of children had a moderately positive correlation with the STE of their parents (r = 0.4; p-value < 0.001). Only the variables of the children's and parents' STE had a significant and positive association. The model is significant (F = 6164, p-value < 0.001) and the residuals of the model met the necessary assumptions, with normal distribution, constant variance and without the presence of outliers. Children in southern Brazil remain in front of screens four times longer than the recommended amount of time. It was also found that the STE of parents directly influences that of their children.

Genetic evaluation of growth using random regression models

The variability in growth traits provides enormous scope for improvement through selection and breeding. However, growth is a longitudinal trait measured repeatedly on the animal and random regression models (RRM) have been found to be suitable for modeling the trait as a growth curve. RRM accommodate repeated records for traits which change gradually and continually, over time, and do not require stringent assumptions about constancy of variances and correlations. RRM has the advantage that, variance components can be estimated for any point in the trajectory of the growth curve and genetic parameters could be estimated for any age class within the range of ages included in the study. RRM is suitable for group breeding schemes and field performance recording systems where the growth data will be uneven and for varying age points. Worldwide, several studies on use of the tool, RRM in growth of various livestock species are available, but literature on such studies is scanty from India. The methodology used, data requirement, assumptions, validity, software available and application of RRM in the field are discussed based on the earlier reports.

Statistical detection of synergy: New methods and a comparative study.

Combination therapies are increasingly adopted as the standard of care for various diseases to improve treatment response, minimise the development of resistance and/or minimise adverse events. Therefore, synergistic combinations are screened early in the drug discovery process, in which their potential is evaluated by comparing the observed combination effect to that expected under a null model. Such methodology is implemented in the BIGL R-package which allows for a quick screening of drug combinations. We extend the meanR and maxR tests from this package by allowing non-constant variance of the responses and by extending the list of null models (Loewe, Loewe2, HSA, Bliss). These new tests are evaluated in a comprehensive simulation study under various models for additivity and synergy, various monotherapeutic dose-response models (complete, partial and incomplete responders) and various types of deviation from the constant variance assumption. In addition, the BIGL package is extended with bootstrap confidence intervals for the individual off-axis points and for the overall synergy strength, which were demonstrated to have reliable coverage and can complement the existing tests. We conclude that the differences in performance between the different null models are small and depend on the simulation scenario. As a result, the choice of null model should be driven by expert knowledge on the particular problem. Finally, we demonstrate the new features of the BIGL package and the difference between the synergy models on a real dataset from drug discovery. The BIGL package is available at CRAN (https://CRAN.R-project.org/package=BIGL) and as a Shiny app (https://synergy.openanalytics.eu/app).

Implementing an Enhanced Procurement Management System Using Decision Support Techniques

Modeling procurement management system is important for quality decision making regarding business capacity planning, supply and scheduling. In the Procurement Services Department (PSD), most commonly used indicators to measuring performance include supply period, products rating, ranking recommendations, resource scheduling and number of goods supplied and delivered. In this paper, a Decision Support Service (DSS) technique was proposed to optimize procurement services in business and public organization. First, a study of a typical public and private organization was conducted to gain insights into the operations of the procurement department and the contributions of important system parameters to procurement management. Second, a product and supplier collaborative filtering technique were investigated to obtain transformed data for model training and testing for implementation using Partial Correlation Coefficient (PCC). The Partial Correlation Coefficient (PCC) for a particular product or supplier was utilized for generating the outcomes with tuned values which were compared with actual observed outcomes. The residuals were evaluated in terms of linearity, normality, independence and constant variance. The visualized system plots indicate a good performance as the quality and accuracy of the decision support model was evaluated using some basic metrics. The overall system implementation and performance results demonstrated the importance of Decision Support Services in assessing the performance of procurement management systems. A robust tool for this assessment and a model for procurement and supply planning indicates that the system framework offered Quality of Service (QoS) provisioning.

Using Observed Residual Error Structure Yields the Best Estimates of Individual Growth Parameters

Obtaining the best possible estimates of individual growth parameters is essential in studies of physiology, fisheries management, and conservation of natural resources since growth is a key component of population dynamics. In the present work, we use data of an endangered fish species to demonstrate the importance of selecting the right data error structure when fitting growth models in multimodel inference. The totoaba (Totoaba macdonaldi) is a fish species endemic to the Gulf of California increasingly studied in recent times due to a perceived threat of extinction. Previous works estimated individual growth using the von Bertalanffy model assuming a constant variance of length-at-age. Here, we reanalyze the same data under five different variance assumptions to fit the von Bertalanffy and Gompertz models. We found consistent significant differences between the constant and nonconstant error structure scenarios and provide an example of the consequences using the growth performance index ϕ′ to show how using the wrong error structure can produce growth parameter values that can lead to biased conclusions. Based on these results, for totoaba and other related species, we recommend using the observed error structure to obtain the individual growth parameters.

Particle Filter Reinforcement via Context-Sensing for Smartphone-Based Pedestrian Dead Reckoning

Pedestrian dead reckoning based on particle filter is commonly used for enabling seamless smartphone-based indoor positioning. However, compass directions indoor are heavily distorted due to the presence of ferromagnetic materials. Conventional particle filters convert the raw compass direction to a distribution adding a constant variance noise and leveraging a particle swarm to simulate the distribution. Finally, the selection of eligible directions is performed applying external constraints mainly imposed from the indoor map. However, the choice of a constant parameter decreases the positioning performances because the variance of nearby context, including topography, ferromagnetic materials, and particle distribution, is not represented. Therefore, we propose the particle filter reinforcement able to adaptively learn and adjust the variance of the direction observing the context in real-time. Experiments in real-world scenarios show that the proposed method improves the positioning accuracy by more than 20% at the 80% probability compared with state-of-the-art methods.

Bivariate change point detection: Joint detection of changes in expectation and variance

AbstractA method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect change points in both expectation and variance. For that, we propose a statistical test for the null hypothesis of no change points and an algorithm for change point detection. Both are based on a bivariate moving sum approach that jointly evaluates the mean and the empirical variance. The joint consideration helps improve inference compared with separate univariate approaches. We infer on the strength and the type of changes with confidence. Nonparametric methodology supports the analysis of diverse data. Additionally, a multiscale approach addresses complex patterns in change points and effects. We demonstrate the performance through theoretical results and simulation studies. A companion R‐package jcp (available on CRAN) is discussed.

A Weighted-Least-Squares Estimation Approach to Comparing Trends in Age-Adjusted Cancer Rates Across Overlapping Regions

Li and Tiwari (2008) recently developed a corrected Z-test statistic for comparing the trends in cancer age-adjusted mortality and incidence rates across overlapping geographic regions, by properly adjusting for the correlation between the slopes of the fitted simple linear regression equations. One of their key assumptions is that the error variances have unknown but common variance. However, since the age-adjusted rates are linear combinations of mortality or incidence counts, arising naturally from an underlying Poisson process, this constant variance assumption may be violated. This paper develops a weighted-least-squares based test that incorporates heteroscedastic error variances, and thus significantly extends the work of Li and Tiwari. The proposed test generally outperforms the aforementioned test through simulations and through application to the age-adjusted mortality data from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute.

ANALYSIS OF ELECTRICAL LOAD SCHEDULES OF 10/0.4 KV TRANSFORMER SUBSTATIONS OF RESIDENTIAL AREAS FOR THE IDENTIFICATION OF STATIONARITY PLOTS

It is proposed on the electrical load graphs of transformer substations 10/0.4 kV in residential areas to allocate the stationarity areas for further modelling of load schedules and the implementation of controlling influences on the modes of consumers-regulators in order to align the overall graph of the electrical load. The relevance and complexity of the problem under consideration is caused by the fact that the load variation of transformer substations 10/0.4 kV in residential areas occurs randomly. This is due to the significant number, nomenclature and diversity of types of connected consumers, as well as the lack of deterministic connections between consumers of electricity, in addition, the random load function in the daily interval is non-stationary. In this regard, there was a need to develop the stages of selecting the areas of stationarity on the electrical load graphs of transformer substations 10/0.4 kV of residential areas. A measurement of the load graphs of 10/0,4 kV transformer substations is carried out, according to the results of which the distribution law of active and reactive power measurements is investigated. After confirming the hypothesis of normal distribution law, parametric tests are performed. Fisher's F-criterion is used to confirm the hypothesis of a constant variance, and Student's t-criterion is used to confirm the hypothesis of a constant mathematical expectation. The next stage, based on constancy of the variance and mathematical expectation, is the determination of autocorrelation coefficients of the studied random function and plotting of the autocorrelation function. To approximate the function the autocorrelation coefficients are determined by the least squares method and the autocorrelation function attenuation analysis is performed. The implementation of the defined stages allows to identify the areas of stationarity on the load graphs of transformer substations 10/0.4 kV. For a reliable description of the process of changing the load of transformer substations 10/0.4 kV the use of probabilistic-statistical method of modelling is justified that takes into account the stochastic nature of the load changes on the selected areas of stationarity.

Modeling water consumption in multifamily buildings: a case study in Southern Brazil

ABSTRACT Urban water consumption can be analyzed by means of applied research to help promote the development of environmentally sustainable cities. In this study, water consumption models are established for multifamily residential buildings in Southern Brazil using multiple linear regression analysis and cross-validation techniques. Sociodemographic and building characteristics were analyzed in a sample of 78 buildings for a period of 25 months. Six forecast models were obtained which met the assumptions of constant error variance, multicollinearity, autocorrelation, residual diagnosis, and generalization ability, explaining the variations in up to 90.61% of the building monthly water consumption and 68.72% of the per capita daily water consumption. The most significant variables were building age, number of stories, total area per floor and per person, dwellers per room and per apartment, number of bedrooms, type of metering system, presence of swimming pools and presence of alternative water-supply systems.

Two penalized estimators based on variance stabilization transforms for sparse compressive recovery with Poisson measurement noise

In this paper, we consider compressive inversion of a signal/image that is sparse in typical orthonormal bases used in image processing, given its measurements that have been corrupted by Poisson noise. The square-root operation is known to convert a Poisson random variable into one that is approximately Gaussian distributed with a constant variance. We present two different computationally tractable, penalized estimators with a data-fidelity term based on the aforementioned square-root based ‘variance stabilization transform’. The first estimator has been proposed earlier in the literature, but this is the first paper to analyze its theoretical performance in compressed sensing. Our second estimator is completely novel, and also has the interesting statistical property of being an approximately pivotal estimator. For both estimators, we specifically consider the case of a physically realistic sensing matrix in our analysis. We present detailed performance bounds on the ℓ2 recovery error for purely sparse signals for both estimators, making use of many different Poisson concentration inequalities. Several numerical results are presented, showing the practicality of the proposed estimators.

A novel Nested Stochastic Kriging model for response noise quantification and reliability analysis

Surrogate models and adaptive methods can release the huge computational burden of structural reliability analysis. However, it is very difficult to guarantee the accuracy of uncertainty quantification, especially when noises are contained in samples, which may greatly reduce the confidence of reliability analysis. In this study, we propose a novel Nested Stochastic Kriging (NSK) model method with response noise parameters decoupled from other surrogate model parameters, which can significantly improve the accuracy of uncertainty quantification and modeling efficiency. The proposed NSK is for deterministic data with response noise, aiming at reliability analysis. Various types of uncertainty can be identified by the NSK, including the conditions of known and unknown, constant and variable variances. Moreover, a local sample verification method is established to improve the accuracy of uncertainty quantification. To further improve the accuracy of reliability analysis, an adaptive NSK framework is established with new samples added, and then reliability analysis can be conducted. Through several numerical examples, it can be seen that the NSK always provides the most accurate results with the fewest analysis calls.

Effect of Probability Distribution of the Response Variable in Optimal Experimental Design with Applications in Medicine

In optimal experimental design theory it is usually assumed that the response variable follows a normal distribution with constant variance. However, some works assume other probability distributions based on additional information or practitioner’s prior experience. The main goal of this paper is to study the effect, in terms of efficiency, when misspecification in the probability distribution of the response variable occurs. The elemental information matrix, which includes information on the probability distribution of the response variable, provides a generalized Fisher information matrix. This study is performed from a practical perspective, comparing a normal distribution with the Poisson or gamma distribution. First, analytical results are obtained, including results for the linear quadratic model, and these are applied to some real illustrative examples. The nonlinear 4-parameter Hill model is next considered to study the influence of misspecification in a dose-response model. This analysis shows the behavior of the efficiency of the designs obtained in the presence of misspecification, by assuming heteroscedastic normal distributions with respect to the D-optimal designs for the gamma, or Poisson, distribution, as the true one.

Neural Network for Vocational Guidance Based on The Applicant's Profile For Admission To A Study Program

The vocational orientation tests are currently oriented to established principles and methods, where the applicant identifies his competencies to choose his professional career, the model of university accreditation in its standard 18 reference on the admission to the program of studies and that must be in accordance with the profile of income raised by each program of studies. Artificial intelligence has become necessary through its techniques in the solution of some problems of human behavior simulated through electronic and digital media, so the objective of this research was to develop a neural network based on vocational guidance from the profile of income to ensure that the applicant knows his competencies towards a study program. For this case, it is considered the knowledge, skills and attitudes raised by the program of studies. This neural network considered in 3 incoming axons, 6 hidden layers and one outgoing axon, each nucleus considers sigmoidal activation functions while, for the backpropagation algorithm, functional derivatives of second level have been used, obtaining results with an accuracy of 0.996 correlation with respect to the real data and a constant variance between the tests of 0.01, guaranteeing its use to automate01, guaranteeing its use for automation. Data collection has been done through surveys based on a transversal non-experimental research design and using the applied correlational research level.

LASSO type penalized spline regression for binary data

BackgroundGeneralized linear mixed models (GLMMs), typically used for analyzing correlated data, can also be used for smoothing by considering the knot coefficients from a regression spline as random effects. The resulting models are called semiparametric mixed models (SPMMs). Allowing the random knot coefficients to follow a normal distribution with mean zero and a constant variance is equivalent to using a penalized spline with a ridge regression type penalty. We introduce the least absolute shrinkage and selection operator (LASSO) type penalty in the SPMM setting by considering the coefficients at the knots to follow a Laplace double exponential distribution with mean zero.MethodsWe adopt a Bayesian approach and use the Markov Chain Monte Carlo (MCMC) algorithm for model fitting. Through simulations, we compare the performance of curve fitting in a SPMM using a LASSO type penalty to that of using ridge penalty for binary data. We apply the proposed method to obtain smooth curves from data on the relationship between the amount of pack years of smoking and the risk of developing chronic obstructive pulmonary disease (COPD).ResultsThe LASSO penalty performs as well as ridge penalty for simple shapes of association and outperforms the ridge penalty when the shape of association is complex or linear.ConclusionWe demonstrated that LASSO penalty captured complex dose-response association better than the Ridge penalty in a SPMM.

Free-Radical Polymerization of Styrene: Kinetic Study in a Spinning Disc Reactor (SDR)

Free-radical polymerization of styrene conducted in a spinning disc reactor (SDR) results in significant increases in conversion in one disc pass, equivalent to a few seconds of residence time, with little change in the number average and weight average molecular weights and polydispersity compared to a SDR feed pre-polymerized in a batch reactor. Results of our experimental studies are presented in this paper and a rationale, based on simulation studies, is offered to explain these observations. It is shown that phenomena such as large increases in conversion that do not impact on molecular weights and molecular weight distribution is a result of a simultaneous increase in both the initiator decomposition rate and the propagation rate. The increases in these rate constants, predicted by our modeling studies, provide the driving forces that characterize a polymerization process in a SDR reactor, with the centrifugal force having different degrees of influence on individual reaction steps. This is attributed to different molecular sizes being involved in each of the polymerization reaction steps. The highest impact is observed on the initiator decomposition rate constant, as this reaction step involves a small molecule. Lesser impact is observed on the propagation rate constant, as this reaction step involves interaction of one small molecule and one large reactive species, whilst no or very small effect is seen in the case of the termination rate constant as large reactive species are involved. Developed constant variance model was used to estimate reaction parameters at different temperatures (i.e., initiator efficiency f, rate constants kd, kp, and kt) from the acquired experimental data in order to estimate activation energy (Ea) and pre-exponential factor (A) in a SDR. Data analysis at various SDR operating temperatures suggested activation energy for the styrene polymerization in the SDR as 40.59 ± 1.11 kJ mol−1.

Resolvable mating-environmental designs for partial triallel cross experiments

Triallel crosses can be readily exploited as breeding tool for developing commercial hybrids with traits of genetical and commercial importance by acquiring information on specific combining ability effects along with general combining ability effects if the experimentation size is reduced to an economical extent. In this paper, methods of constructing designs involving partial triallel crosses in smaller blocks using different types of lattice designs have been introduced. The designs have low degree of fractionation, which suggests their utility when there is a resource crunch. Canonical efficiency factor of these designs relative to an orthogonal design with same number of lines, assuming constant error variance for both situations, is high indicating that adoption of these designs for the trials could bring about improvement as the recommendations from the experiment will be associated with a high precision.

Patterning of individual variability in neurocognitive health among South African women exposed to childhood maltreatment

There are individual differences in health outcomes following exposure to childhood maltreatment, yet constant individual variance is often assumed in analyses. Among 286 Black, South African women, the association between childhood maltreatment and neurocognitive health, defined here as neurocognitive performance (NP), was first estimated assuming constant variance. Then, without assuming constant variance, we applied Goldstein’s method (Encyclopedia of statistics in behavioral science, Wiley, 2005) to model “complex level-1 variation” in NP as a function of childhood maltreatment. Mean performance in some tests of information processing speed (Digit-symbol, Stroop Word, and Stroop Color) lowered with increasing severity of childhood maltreatment, without evidence of significant individual variation. Conversely, we found significant individual variation by severity of childhood maltreatment in tests of information processing speed (Trail Making Test) and executive function (Color Trails 2 and Stroop Color-Word), in the absence of mean differences. Exploratory results suggest that the presence of individual-level heterogeneity in neurocognitive performance among women exposed to childhood maltreatment warrants further exploration. The methods presented here may be used in a person-centered framework to better understand vulnerability to the toxic neurocognitive effects of childhood maltreatment at the individual level, ultimately informing personalized prevention and treatment.