Constant Variance Research Articles

Forecasting weekly dengue incidence in Sri Lanka: Modified Autoregressive Integrated Moving Average modeling approach.

Dengue poses a significant and multifaceted public health challenge in Sri Lanka, encompassing both preventive and curative aspects. Accurate dengue incidence forecasting is pivotal for effective surveillance and disease control. To address this, we developed an Autoregressive Integrated Moving Average (ARIMA) model tailored for predicting weekly dengue cases in the Colombo district. The modeling process drew on comprehensive weekly dengue fever data from the Weekly Epidemiological Reports (WER), spanning January 2015 to August 2020. Following rigorous model selection, the ARIMA (2,1,0) model, augmented with an autoregressive component (AR) of order 16, emerged as the best-fitted model. It underwent initial calibration and fine-tuning using data from January 2015 to August 2020, and was validated against independent 2000 data. Selection criteria included parameter significance, the Akaike Information Criterion (AIC), and Schwarz Bayesian Information Criterion (SBIC). Importantly, the residuals of the ARIMA model conformed to the assumptions of randomness, constant variance, and normality affirming its suitability. The forecasts closely matched observed dengue incidence, offering a valuable tool for public health decision-makers. However, an increased percentage error was noted in late 2020, likely attributed to factors including potential underreporting due to COVID-19-related disruptions amid rising dengue cases. This research contributes to the critical task of managing dengue outbreaks and underscores the dynamic challenges posed by external influences on disease surveillance.

Word Frequency and Predictability Dissociate in Naturalistic Reading.

Many studies of human language processing have shown that readers slow down at less frequent or less predictable words, but there is debate about whether frequency and predictability effects reflect separable cognitive phenomena: are cognitive operations that retrieve words from the mental lexicon based on sensory cues distinct from those that predict upcoming words based on context? Previous evidence for a frequency-predictability dissociation is mostly based on small samples (both for estimating predictability and frequency and for testing their effects on human behavior), artificial materials (e.g., isolated constructed sentences), and implausible modeling assumptions (discrete-time dynamics, linearity, additivity, constant variance, and invariance over time), which raises the question: do frequency and predictability dissociate in ordinary language comprehension, such as story reading? This study leverages recent progress in open data and computational modeling to address this question at scale. A large collection of naturalistic reading data (six datasets, >2.2 M datapoints) is analyzed using nonlinear continuous-time regression, and frequency and predictability are estimated using statistical language models trained on more data than is currently typical in psycholinguistics. Despite the use of naturalistic data, strong predictability estimates, and flexible regression models, results converge with earlier experimental studies in supporting dissociable and additive frequency and predictability effects.

대용량 자료의 이항 분류에서의 충분 차원 축소를 위한 전향적 접근 방법

Sufficient dimension reduction, aimed at finding a lower-dimensional subspace in explanatory variables that contains response variable information, typically relies on inverse-based methodologies. These methods are easy to implement but often require linear or constant variance conditions. To address these limitations, techniques for forwardly estimating the central subspace have been developed. In particular, methods utilizing the Reproducing Kernel Hilbert Space have gained attention, but their use in analyzing large datasets is limited due to the characteristics of the kernel space. In this paper, we study a novel forward approach for sufficient dimension reduction in binomial classification of large-scale data. We propose a method that employs a divide-and-conquer technique to split data into subsets, then independently perform dimension reduction on each subset before synthesizing them into a final model. It was shown that when the number of partitions of data was appropriately selected, the loss in prediction accuracy was not significant compared to the existing method, while being efficient in terms of storage space and calculation cost. In addition, simulations in various models showed superior prediction accuracy than other inverse-based techniques. The utility of the proposed method was confirmed through the real data analysis.

Time Series Model to Forecast Fresh Coconut Exports from Sri Lanka

Coconut accounts for approximately 12% of all agricultural produce in Sri Lanka with the total land area under cultivation covering 409, 244 hectares ranking second to rice production. The primary regions for coconut cultivation are the Puttalam and Kurunegala districts in North-Western Province and Gampaha district in the Western Province, forming what is known as the Coconut Triangle. This region accounts for 232,270 hectares (50.94%) of the overall coconut cultivation area. The remaining coconut cultivation areas are found in the Southern Province, specifically in the districts of Galle (13,833 hectares), Matara (14,946 hectares), and Hambantota (25,837 hectares), and in non-traditional regions of the Eastern and Northern provinces. The annual coconut production varies between 2,800 to 3,000 million nuts. Having advanced knowledge of exporting coconuts offers numerous advantages to Sri Lanka, particularly in terms of establishing forward contracts with other countries. Based on secondary data of annual fresh coconut exports from 1981 to 2020 obtained from the Coconut Development Authority (CDA) of Sri Lanka, the paper developed ARIMA (2,1,0) model to forecast export. The model was selected out of three parsimonious models which were identified from the Sample Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) of the stationary series and a comparison of significant parameters and lowest values of Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (SBIC) and Hannan-Quinn Information Criterion (HQIC). The errors of the fitted model were found to be random and constant variance. The model was validated using 2021 and 2022 data. The percentage errors for 2021 and 2022 are 20.23% and -29.57% respectively. The predictions for 2023 and 2024 are 14696 and 15052 respectively. The model can be used effectively by the Coconut Development Authority for decision-making. However, it is suggested to develop the model further to reduce the percentage error. Keywords: ARIMA model, Forecast, Fresh Coconut Exports and Validate

Asymptotically constant risk estimator of the time-average variance constant

Summary Estimation of the time-average variance constant is important for statistical analyses involving dependent data. This problem is difficult as it relies on a bandwidth parameter. Specifically, the optimal choices of the bandwidths of all existing estimators depend on the estimand itself and another unknown parameter that is very difficult to estimate. Thus, optimal variance estimation is unachievable. In this paper, we introduce a concept of converging flat-top kernels for constructing variance estimators whose optimal bandwidths are free of unknown parameters asymptotically and hence can be computed easily. We prove that the new estimator has an asymptotically constant risk and is locally asymptotically minimax.

Active Learning-Based Kriging Model with Noise Responses and Its Application to Reliability Analysis of Structures

This study introduces a reliability analysis methodology employing Kriging modeling enriched by a hybrid active learning process. Emphasizing noise integration into structural response predictions, this research presents a framework that combines Kriging modeling with regression to handle noisy data. The framework accommodates either constant variance of noise for all observed responses or varying, uncorrelated noise variances. Hyperparameters and the variance of the Kriging model with noisy data are determined through maximum likelihood estimation to address inherent uncertainties in structural predictions. An adaptive hybrid learning function guides design of experiment (DoE) point identification through an iterative enrichment process. This function strategically targets points near the limit-state approximation, farthest from existing training points, and explores candidate points to maximize the probability of misclassification. The framework’s application is demonstrated through metamodel-based reliability analysis for continuum and discrete structures with relatively large degrees of freedom, employing subset simulations. Numerical examples validate the framework’s effectiveness, highlighting its potential for accurate and efficient reliability assessments in complex structural systems.

Analisis Data Time Series Menggunakan Model Kernel: Pemodelan Data Harga Saham MDKA

<p>Classic time series data analysis techniques, such as autoregressive, model stationary data in which the values of prior observations influence the current observations through a process known as linear regression. There are several requirements for error assumptions in autoregressive, including independence, normal distribution with a zero mean and constant variance. It is frequently discovered that these assumptions are challenging to verify when modelling real data. Kernel time series regression is an alternative model that does not require error assumptions. Non-stationary time series data can be effectively modelled using the kernel time series method. Time series data that isn't yet stationary is made stationary first, then the data is modified by forming the current stationary time series data as the response variable and the previous period data as the predictor variable. Next, regression kernel modelling is carried out while applying kernel weight function and determining the optimal bandwidth. For development of science, the optimal bandwidth can be achieved by minimizing the MSE, CV, GCV, or UBR values. It is possible to use R<sup>2</sup> or MAPE as the kernel time series regression model's goodness metric. A strong model is generated while modelling MDKA stock price data using kernel regression utilizing the Gaussian kernel function and optimal bandwidth selection using GCV since R<sup>2</sup> is 0.9828372 more than 0.67 and MAPE is 1.985681% under 10%.</p><p><strong>Keywords</strong><strong>: </strong>3 time series; kernel regression; GCV; MDKA stock price.</p>

Adjusting for bias due to measurement error in functional quantile regression models with error-prone functional and scalar covariates

Wearable devices enable the continuous monitoring of physical activity (PA) but generate complex functional data with poorly characterized errors. Most work on functional data views the data as smooth, latent curves obtained at discrete time intervals with some random noise with mean zero and constant variance. Viewing this noise as homoscedastic and independent ignores potential serial correlations. Our preliminary studies indicate that failing to account for these serial correlations can bias estimations. In dietary assessments, epidemiologists often use self-reported measures based on food frequency questionnaires that are prone to recall bias. With the increased availability of complex, high-dimensional functional, and scalar biomedical data potentially prone to measurement errors, it is necessary to adjust for biases induced by these errors to permit accurate analyzes in various regression settings. However, there has been limited work to address measurement errors in functional and scalar covariates in the context of quantile regression. Therefore, we developed new statistical methods based on simulation extrapolation (SIMEX) and mixed effects regression with repeated measures to correct for measurement error biases in this context. We conducted simulation studies to establish the finite sample properties of our new methods. The methods are illustrated through application to a real data set.

A new estimator of between study variance of standardized mean difference in meta-analysis.

Meta-analysis is a statistical technique that combines the results of different environmental experiments regarding the populations, location, time, and so on. These results will differ more than the within-study variance, and the true effects being evaluated differ between studies. Thus, heterogeneity is present and should be measured. There are different estimators that were introduced to estimate between-study variance, which has received a lot of criticism from previous researchers. All of the estimators encountered the same problem, which was the correlation. To minimize the potential biases caused by interventions between the three estimators (i.e., overall effect size, within-study variance, and between-study variance), we proposed a new measure of heterogeneity known as the Environmental Effect Ratio (EER), the treatment-by-lab variability relative to the experimental error, under individual participant data (IPD) using the linear mixed model approach. We assume different between-study variances instead of constant between-study variances. The simulation of this study focuses on the performance of meta-analyses with small sample sizes. We compared our proposed estimator under two different expressions ([Formula: see text], and [Formula: see text]) with the best estimator nominated from previous studies to determine which one is the best performance. Based on the findings, our estimator ([Formula: see text]) was better for estimating between-study variance.

Generalised Least-Squares Fitting with Procedures for Uncorrelated Data of Constant Variance

Generalised Least-Squares Fitting with Procedures for Uncorrelated Data of Constant Variance

Analytically tractable heteroscedastic uncertainty quantification in Bayesian neural networks for regression tasks

The tractable approximate Gaussian inference (TAGI) method allows for analytical parameter inference in Bayesian neural networks. In its current form, TAGI can only model homoscedastic aleatory uncertainty that is quantified by a constant error variance across the input covariate-domain. In this paper, we present the approximate Gaussian variance inference (AGVI) method that enables analytical inference of the error variance term as a Gaussian random variable. The combined framework regrouping TAGI and AGVI, referred to as TAGI-V, enables modeling heteroscedastic aleatory uncertainty in Bayesian neural networks. TAGI-V outperforms the homoscedastic version of TAGI in terms of predictive performance for the benchmark regression datasets. In comparison with other approximate inference methods, TAGI-V is an order of magnitude faster and exhibits a comparable or superior predictive performance.

Power synergistic control between of power‐to‐hydrogen and SCESS‐DFIG considering “source–load” turbulence

AbstractHydrogen production from wind power can reduce wind abandonment and improve the utilization rate of wind power. However, both “source” turbulence caused by unstable wind speed and “load” turbulence caused by sudden load changes will adversely affect the stable operation of power‐to‐hydrogen systems and the grid connection stability of wind farms. A synergistic control strategy between a supercapacitor and power‐to‐hydrogen system is proposed to solve this problem. The strategy is based on the ensemble empirical‐mode decomposition algorithm. By using the supercapacitor to stabilize the high‐frequency component in the “source–load” turbulence, the stability of the power‐to‐hydrogen system is improved. An optimal allocation method of supercapacitor capacity suitable for the control strategy is then proposed. Considering the different states of each fan and supercapacitor, the unit inertia time constant variance is reduced by reasonably distributing the output of each unit. This effectively improves the inertia time constant and grid connection stability of the wind farm. Finally, the effectiveness of the strategy is verified by Simulink simulations.

Investigating the applicability and assumptions of the regression relationship between flow discharge and nitrogen concentrations for load estimation

The regression relationship between water discharge rates and nutrient concentrations can provide a quick and straightforward way to estimate nutrient loads. However, recent studies indicated that the relationship might produce large biases in load estimates and, therefore, may not be applicable in certain types of cases. The goal of this study is to explore the theoretical reasons behind the selective applicability of the regression relationship between flow rates and nitrate + nitrite concentrations. For this study, we examined daily flow and nitrate + nitrite concentration observations made at the outlets of 22 watersheds monitored by the Heidelberg Tributary Loading Program (HTLP). The statistical relationship between the flow rates and concentrations was explored using regression equations offered by the LOAD ESTimator (LOADEST). Results demonstrated that the use of the regression equations provided nitrate + nitrite load estimates at acceptable accuracy levels (NSE≥0.35 and |PBIAS|≤30.0%) in 14 watersheds (64 % of 22 study watersheds). The regression relationships provided highly biased results at eight watersheds (36 %), implying their limited applicability. The heteroscedasticity of the residuals led to the high bias and resulting inaccurate regression, which was commonly found in watersheds where low flow had high nitrate + nitrite concentration variations. Conversely, the regression relationships provided acceptable accuracy for watersheds that had a relatively constant variance of the nitrate + nitrite concentrations. The results indicate that the homoscedasticity of residuals is the key assumption to be satisfied to estimate nitrate + nitrite loads from a statistical regression between flow discharge and nitrate + nitrite concentrations. The transport capacity (capacity-limited) concept implicitly assumed in the regression relationship between flow discharge and nitrate + nitrite concentrations is not always applicable, especially to agricultural areas in which nitrate + nitrite loads are highly variable depending on management practices (supply-limited). The findings suggest that the regression relationship should be carefully applied to areas in which intensive agricultural activities, including crop management and conservation practices, are implemented. Thus, the transport capacity concept is reasonably regarded to contribute to the homoscedasticity of residuals.

A comparative study between the two methods GM6.IDRGP(RMVN) and the GM6 method for analyzing the multiple linear regression model in the presence of outliers using the simulation method.

Multiple linear regression is one of the most widely used statistical analysis methods in many scientific fields. Its parameters are estimated based on the ordinary least squares method. Which gives the best unbiased linear estimate if its assumptions are met. The most important of these assumptions is that it has a normal distribution of error with a mean of zero and a constant variance. If the data does not meet certain assumptions, the sample estimates and results may be misleading. The linear regression model is sensitive to the appearance of outliers and leverage points. Therefore, statistical techniques have been developed capable of dealing with or detecting outliers. This led to the emergence of many alternative methods to the OLS method, such as M-Huber, s, LTS, and MM, which have high efficiency and breakdown points, but are affected by HLPs, which result in the problem of Masking and Swamping. The GM6 method is one of the methods that was developed in order to treat such problems through the use of a weight function, but the weight function depends on the individual diagnosis, which gives inaccurate results. In order to overcome this problem, comprehensive diagnostic methods have been proposed, such as the DRGP and IDRGP.RMVN methods. Therefore, in this study, we proposed to employ the IDRGP.RMVN method in the GM6 method algorithm. And comparing it with some hippocampal regression methods through a simulation study in determining the best methods.

How to Estimate the Sigma Level of the Process

Purpose: This paper proposes a procedure for estimating the sigma level of the process through a confidence interval. Methodology/Approach: The approach is based on a model in which the process has a normal distribution and constant variance, and its mean is shifted to the right or left by 1.5 standard deviations. Findings: The paper explains a method for creating a random sample along with determining the sample size to estimate the “defects per million opportunities” characteristic through a confidence interval. Based on it, the confidence interval for the “sigma level” of the process is determined. Research Limitation/implication: We assume a discrete process in which n pieces of the product are selected. The proposed procedure assumes that the process is in statistical control. Originality/Value of paper: Applying the proposed random sampling and estimation procedure can improve evaluations of process performance, aiding decision-making for Six Sigma projects.

Statistical inference with large-scale trait imputation.

Recently a nonparametric method called LS-imputation has been proposed for large-scale trait imputation based on a GWAS summary dataset and a large set of genotyped individuals. The imputed trait values, along with the genotypes, can be treated as an individual-level dataset for downstream genetic analyses, including those that cannot be done with GWAS summary data. However, since the covariance matrix of the imputed trait values is often too large to calculate, the current method imposes a working assumption that the imputed trait values are identically and independently distributed, which is incorrect in truth. Here we propose a "divide and conquer/combine" strategy to estimate and account for the covariance matrix of the imputed trait values via batches, thus relaxing the incorrect working assumption. Applications of the methods to the UK Biobank data for marginal association analysis showed some improvement by the new method in some cases, but overall the original method performed well, which was explained by nearly constant variances of and mostly weak correlations among imputed trait values.

The Legendre transform-dual-asymptotic solution for optimal investment strategy with random incomes

. This article studies an optimal control problem for the financial investment strategy with random incomes. The investment portfolio is simplified to be composed of a risk-free asset and a risky asset. The price of a risky asset is followed by a constant variance elasticity (CEV) model. We consider any correlation coefficient ρ ∈ [ − 1 , 1 ] between the income risk and the risk of risky asset. By applying the Legendre transformation, dual theory, and asymptotic expansion approach, we obtain an asymptotic strategy for the exponential utility function. Numerical examples are presented to illustrate the effects of parameters on the optimal strategy.

On the construction of asymmetric third-order rotatable designs

Response surface methodology (RSM) has broader applicability, where numerous input variables may impact a given performance metric or quality attribute of the final product or process. It involves designing experiments, collecting data, and developing models to optimize the response. Rotatable designs have the property to generate information about the response surface equally in all locations, even when no or little prior knowledge is available about the nature of the response surface. These designs are constructed by imposing certain restrictions on the moment matrix of the design to achieve constancy in the variance of predicted response at all points equidistant from the design center and is invariant to rotation of axis with respect to any angle. Most rotatable response surface designs are symmetric in nature, although factors with mixed-level have more practical utility as it can explore more regions in the design space. In this article, we have proposed a procedure for creating asymmetric third-order rotatable designs (ATORDs) as well as a strategy for creating them with fewer design points when time and resources are the main limitations. Two classes of orthogonal transformation-based ATORDs viz., ATORD-I and ATORD-II have been obtained. ATORD-II does not completely satisfy the moment matrix constraints, although both ATORD-I and ATORD-II have constant prediction variance. ATORD-II is more cost-efficient for experimentation when resource and financial constraints are the primary factors to be taken into account. A comparison of the designs developed is also made using efficiency criterion and dispersion graphs.

Tuning parameter selection for nonparametric derivative estimation in random design

Estimation of a function, or its derivatives via nonparametric regression requires selection of one or more tuning parameters. In the present work, we propose a tuning parameter selection criterion called DCp for nonparametric derivative estimation in random design. Our criterion is general in that it can be applied with any nonparametric estimation method which is linear in the observed outcomes. Charnigo et al. [A generalized C p criterion for derivative estimation. Technometrics. 2011;53(3):238–253] had proposed a GCp criterion for a similar purpose, assuming values of the covariate to be fixed and constant error variance. Here we consider the setting with random design and non-constant error variance since the covariate values will not generally be fixed and equally spaced in real data applications. We justify DCp in this setting both theoretically and by simulation. We also illustrate use of DCp with two economics data sets.

Unifying Estimation and Inference for Linear Regression with Stationary and Integrated or Near-Integrated Variables

Abstract There is a discrepancy in the limiting distributions of least-squares estimators for stationary and integrated variables. For statistical inference, it must be decided which distribution should be used in advance. This motivates us to develop a unifying inference procedure based on weighted estimation. The asymptotic distributions of the proposed estimators are developed and a random weighting bootstrap method is proposed for constructing confidence regions. The proposed method outperforms existing methods (with time constant or time-varying error variance) in simulations. We further study the predictability of asset returns in a setting where some of our state variables are endogenous.