Unbiased Risk Research Articles

Stunting Prevalence Modeling Using Nonparametric Regression of Quadratic Splines

The nonparametric regression approach is used when the shape of the regression curve between the response variable and the predictor variable is assumed to be of unknown shape. The advantages of nonparametric regression have high flexibility. A nonparametric regression approach that is often used is truncated spline which has an excellent ability to handle data whose behavior changes at certain sub-sub intervals. The purpose of this study is to obtain the best model of multivariable nonparametric regression with linear and quadratic truncated spline approaches using the Generalized Cross Validation (GCV) and Unbiased Risk (UBR) methods and to find out the factors that influence the prevalence of stunting in Indonesia in 2021. The data used were the prevalence of stunting as a response variable and the predictor variable used was the percentage of infants receiving exclusive breastfeeding for 6 months, the percentage of households that have proper sanitation, the percentage of toddlers who get Early Initiation of Breastfeeding (IMD), the percentage of poor people, and the percentage of pregnant women at risk of SEZ. The results showed that the best quadratic truncated spline nonparametric regression model in modeling stunting prevalence was quadraic truncated spline using the GCV method with three knot points. This model has a minimum GCV value of 7.29 with an MSE value of 1.82 and a R2 value of 94.07%.

Nonparametric Spline Truncated Regression with Knot Point Selection Method Generalized Cross Validation and Unbiased Risk

Nonparametric Spline Truncated Regression with Knot Point Selection Method Generalized Cross Validation and Unbiased Risk

The Efficiency of the Proposed Smoothing Method over the Classical Cubic Smoothing Spline Regression Model with Autocorrelated Residual

Spline smoothing is a technique used to filter out noise in time series observations when predicting nonparametric regression models. Its performance depends on the choice of the smoothing parameter. Most of the existing smoothing methods applied to time series data tend to over fit in the presence of autocorrelated errors. This study aims to determine the optimum performance value, goodness of fit and model overfitting properties of the proposed Smoothing Method (PSM), Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) smoothing parameter selection methods. A Monte Carlo experiment of 1,000 trials was carried out at three different sample sizes (20, 60, and 100) and three levels of autocorrelation (0.2, 05, and 0.8). The four smoothing methods' performances were estimated and compared using the Predictive Mean Squared Error (PMSE) criterion. The findings of the study revealed that: for a time series observation with autocorrelated errors, provides the best-fit smoothing method for the model, the PSM does not over-fit data at all the autocorrelation levels considered ( the optimum value of the PSM was at the weighted value of 0.04 when there is autocorrelation in the error term, PSM performed better than the GCV, GML, and UBR smoothing methods were considered at all-time series sizes (T = 20, 60 and 100). For the real-life data employed in the study, PSM proved to be the most efficient among the GCV, GML, PSM, and UBR smoothing methods compared. The study concluded that the PSM method provides the best fit as a smoothing method, works well at autocorrelation levels (ρ=0.2, 0.5, and 0.8), and does not over fit time-series observations. The study recommended that the proposed smoothing is appropriate for time series observations with autocorrelation in the error term and econometrics real-life data. This study can be applied to; non – parametric regression, non – parametric forecasting, spatial, survival, and econometrics observations.

On some techniques of selecting spline smoothing parameters for a correlated dataset with autocorrelation structure in the residual

Residuals are minimized in a correlated dataset by selecting a smoothing parameter with optimum performance in the smoothing spline. The selection methods utilized in this study include Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), Unbiased Risk (UBR), and the Proposed Smoothing Method (PSM). The aim of this study is to compare the smoothing parameter selection ability of the four parameter selection methods for a correlated dataset with autocorrelation structure in the error term. To achieve this purpose, a Monte-Carlo simulation was conducted by utilizing program written in R-4.2.2. The performance of the parameter selection methods were evaluated using predictive Mean Squared Error (PMSE). Findings from the study indicated that GCV and GML were mostly affected by the presence of auto correlation in the residual and therefore had an asymptotically similar behavioural pattern. The estimators conformed to the asymptotic properties of the smoothing parameter selection methods considered; this is noticed in all the sample sizes and at all the smoothing parameters. The result also showed that; the most consistent and efficient among the four spline smoothing parameter selection methods considered in this study based on sample size and performance in the presence of autocorrelated residual error is the proposed smoothing method (PSM) because it does not undersmooth relative to the other smoothing method especially for small sample and medium sample size of 50 and 100.

The Efficiency of the Proposed Smoothing Method over the Classical Cubic Smoothing Spline Regression Model with Autocorrelated Residual

Spline smoothing is a technique used to filter out noise in time series observations when predicting nonparametric regression models. Its performance depends on the choice of the smoothing parameter. Most of the existing smoothing methods applied to time series data tend to overfit in the presence of autocorrelated errors. This study aims to determine the optimum performance value, goodness of fit and model overfitting properties of the proposed Smoothing Method (PSM), Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) smoothing parameter selection methods. A Monte Carlo experiment of 1,000 trials was carried out at three different sample sizes (20, 60, and 100) and three levels of autocorrelation (0.2, 05, and 0.8). The four smoothing methods' performances were estimated and compared using the Predictive Mean Squared Error (PMSE) criterion. The findings of the study revealed that: for a time series observation with autocorrelated errors, provides the best-fit smoothing method for the model, the PSM does not over-fit data at all the autocorrelation levels considered ( the optimum value of the PSM was at the weighted value of 0.04 when there is autocorrelation in the error term, PSM performed better than the GCV, GML, and UBR smoothing methods were considered at all-time series sizes (T = 20, 60 and 100). For the real-life data employed in the study, PSM proved to be the most efficient among the GCV, GML, PSM, and UBR smoothing methods compared. The study concluded that the PSM method provides the best fit as a smoothing method, works well at autocorrelation levels (ρ=0.2, 0.5, and 0.8), and does not over fit time-series observations. The study recommended that the proposed smoothing is appropriate for time series observations with autocorrelation in the error term and econometrics real-life data. This study can be applied to; non – parametric regression, non – parametric forecasting, spatial, survival, and econometrics observations.

Low-CP-Rank Tensor Completion via Practical Regularization

Dimension reduction is analytical methods for reconstructing high-order tensors that the intrinsic rank of these tensor data is relatively much smaller than the dimension of the ambient measurement space. Typically, this is the case for most real world datasets in signals, images and machine learning. The CANDECOMP/PARAFAC (CP, aka Canonical Polyadic) tensor completion is a widely used approach to find a low-rank approximation for a given tensor. In the tensor model (Sanogo and Navasca in 2018 52nd Asilomar conference on signals, systems, and computers, pp 845–849, https://doi.org/10.1109/ACSSC.2018.8645405, 2018), a sparse regularization minimization problem via ell _1 norm was formulated with an appropriate choice of the regularization parameter. The choice of the regularization parameter is important in the approximation accuracy. Due to the emergence of the massive data, one is faced with an onerous computational burden for computing the regularization parameter via classical approaches (Gazzola and Sabaté Landman in GAMM-Mitteilungen 43:e202000017, 2020) such as the weighted generalized cross validation (WGCV) (Chung et al. in Electr Trans Numer Anal 28:2008, 2008), the unbiased predictive risk estimator (Stein in Ann Stat 9:1135–1151, 1981; Vogel in Computational methods for inverse problems, 2002), and the discrepancy principle (Morozov in Doklady Akademii Nauk, Russian Academy of Sciences, pp 510–512, 1966). In order to improve the efficiency of choosing the regularization parameter and leverage the accuracy of the CP tensor, we propose a new algorithm for tensor completion by embedding the flexible hybrid method (Gazzola in Flexible krylov methods for lp regularization) into the framework of the CP tensor. The main benefits of this method include incorporating the regularization automatically and efficiently as well as improving accuracy in the reconstruction and algorithmic robustness. Numerical examples from image reconstruction and model order reduction demonstrate the efficacy of the proposed algorithm.

Nonparametric Regression Mixed Estimators of Truncated Spline and Gaussian Kernel based on Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) Methods

<p class='IJASEITAbtract'>Nowadays, most nonparametric regression research involves more than one predictor variable and generally uses the same type of estimator for all predictors. In the real case, each predictor variable likely has a different form of regression curve so that if it is forced, it can produce an estimation form that does not match the data pattern. Thus, it is necessary to develop a regression curve estimation model under the data pattern, namely the mixed estimator. The focus of this study is an additive nonparametric regression model, a mix of the Truncated Spline and Gaussian Kernel. There is a knot point in the Truncated Spline, while in the Gaussian Kernel, there is bandwidth. To choose the optimal knot point and bandwidth in a mixed estimator model, various methods can be used, including Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). This research proposes the optimal knot point and bandwidth estimation on the mixed estimator Truncated Spline and Gaussian Kernel model. Furthermore, the comparison between CV, GCV, and UBR is used to validate the proposed method. The simulation study was carried out by generating the Truncated Spline function and the Gaussian Kernel on a combination of sample size variations and variances. The simulation results show that the GCV method provides a higher coefficient of determination (R²) value and better accuracy for each combination of sample sizes and variance variations.

An efficient variance estimator for cross-validation under partition sampling

This paper concerns the problem of variance estimation of cross-validation. We consider the unbiased cross-validation risk estimate in the form of a general U-statistic and focus on estimating the variance of the U-statistic risk score. We propose an efficient variance estimator under a half-sampling design where the bias of the estimator can be expressed explicitly. Furthermore, we discuss a practical approach to estimate its bias by a two-layer Monte Carlo method so as to obtain a bias-corrected variance estimator. In the simulation study and real data examples, we evaluate the performance of the proposed variance estimator, in comparison to the commonly used bootstrap and jackknife methods, in the context of model selection under the one-standard-error rule. The numerical results suggest that the proposal yields identical or similar conclusion for model selection compared to its counterparts. Moreover, the developed variance estimator is much more efficient to calculate than its competitors. In the end, we discuss the generalization of the methodology to other partition-sampling scenarios.

Optimal Knots Point and Bandwidth Selection in Modeling Mixed Estimator Nonparametric Regression

The nonparametric regression model that is currently developing is limited to only one estimator form that is used. This happens, due to the assumption from the researcher that each of these predictors has the same data pattern. However, when we model the predictor variable with the response variable, what happens is that each predictor may have a different pattern, so it is necessary to develop a mixed estimator. The mixed estimator used in this study is the truncated spline and the Gaussian Kernel. Furthermore, it becomes a separate problem, when combining the truncated spline with the Gaussian Kernel, so it must determine the optimal knot point and bandwidth. Determine the optimal knot point and bandwidth is very important. The methods used are Cross-Validation (CV), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR). In this study, the nonparametric regression model was applied to the data on the percentage of poor people in Districts/Cities on Borneo Island in 2019. Based on analysis, the modeling of the nonparametric regression approach with a mixed estimator of the truncated spline and the Gaussian Kernel uses the GCV method which gives the best results. This is supported by the coefficient of determination obtained by 90.52% and the MSE value of 1.10. This means that the nonparametric regression model built can explain the effect of the predictor variable on the response variable, namely the percentage of poor people by 90.52%.

Optimal knot selection in spline regression using unbiased risk and generalized cross validation methods

Spline regression is a nonparametric regression method that estimates data patterns that do not form certain patterns with the help of knots. The best model is obtained from the optimal knot. There are several methods that can be used to select optimal knots, including Generalized Cross-Validation (GCV) and Unbiassed Risk (UBR). The best model selection criteria used are based on the Mean Squared Error (MSE) and R-Square values. This study discusses the comparison of spline regression models using the UBR and GCV methods as a method for selecting optimal knots in data generation simulations. This research resulted in the best nonparametric spline regression model from the UBR method obtained by using three knots which produced an MSE value of 738.67 and R -Square of 85.65%. Whereas, the best nonparametric spline regression model of the GCV method was obtained using three knots which produced an MSE value of 121.43 and R-Square of 97.64%. It can be concluded that the more appropriate method used for the selection of optimal knot is the GCV method because it produces a smaller MSE value and a larger R-Square compared to the UBR method.

A New Smoothing Method for Time Series Data in the Presence of Autocorrelated Error

Spline Smoothing is used to filter out noise or disturbance in an observation, its performance depends on the choice of smoothing parameters. There are many methods of estimating smoothing parameters; most popular among them are; Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR), this methods tend to overfit smoothing parameters in the presence of autocorrelation error. A new Spline Smoothing estimation method is proposed and compare with three existing methods in order to eliminate the problem of over fitting associated with the presence of Autocorrelation in the error term. It is demonstrated through a simulation study performed by using a program written in R based on the predictive Mean Score Error criteria. The result indicated that the predictive mean square error (PMSE) of the four smoothing methods decreases as the smoothing parameters increases and decreases as the sample sizes increases. This study discovered that the proposed smoothing method is the best for time series observations with Autocorrelated error because it doesn’t over fit and works well for large sample sizes. This study will help researchers overcome the problem of over fitting associated with applying Smoothing spline method time series observation.

Bias in cohort-based comparisons of immigrants\u2019 health outcomes between countries: a simulation study

BackgroundCohort-type data are increasingly used to compare health outcomes of immigrants between countries, e.g. to assess the effects of different national integration policies. In such international comparisons, small differences in cardiovascular diseases risk or mortality rates have been interpreted as showing effects of different policies. We conjecture that cohort-type data sets available for such comparisons might not provide unbiased relative risk estimates between countries because of differentials in migration patterns occurring before the cohorts are being observed.MethodTwo simulation studies were performed to assess whether comparisons are biased if there are differences in 1. the way migrants arrived in the host countries, i.e. in a wave or continuously; 2. the effects on health of exposure to the host country; or 3., patterns of return-migration before a cohort is recruited. In the first simulation cardiovascular disease was the outcome and immortality in the second. Bias was evaluated using a Cox regression model adjusted for age and other dependant variables.ResultsComparing populations from wave vs. continuous migration may lead to bias only if the duration of stay has a dose-response effect (increase in simulated cardiovascular disease risk by 5% every 5 years vs. no risk: hazard-ratio 1.20(0.15); by 10% every 5 years: 1.47(0.14)). Differentials in return-migration patterns lead to bias in mortality rate ratios (MRR). The direction (under- or overestimation) and size of the bias depends on the model (MRR from 0.92(0.01) to 1.09(0.01)).ConclusionThe order of magnitude of the effects interpreted as due to integration policies in the literature is the same as the bias in our simulations. Future studies need to take into account duration and relevance of exposure and return-migration to make valid inferences about the effects of integration policies on the health of immigrants.

Comparison of generalized cross validation and unbiased risk method for selecting optimal knot in spline truncated

Gini ratio is an indicator to measure income inequality. Gini ratio of Indonesia in 2017 is 0.391, still far from Gini ratio target by Bappenas in 2019, that is 0.36. The Gini ratio modeling in this study uses a nonparametric regression approach because the form of the regression curve between the Gini ratio and its predictive variables is unknown. One of the estimators in nonparametric regression is spline truncated. Spline truncated has a knot that adjusts to the local characteristics of a function or data more effectively. The number of knots and their location affect the form of regression curve estimation, so it’s important to obtain optimal knot. There are methods for selecting optimal knots, such as Generalized Cross Validation (GCV) and Unbiased Risk (UBR). This study compares GCV and UBR in selecting optimal knots on Gini Ratio data in Indonesia 2017. The criteria of the best model are based on Mean Squared Error (MSE) and R2 values. From the result, the optimal knot from GCV was a combination of 3-2-2-3 knot with MSE of 0.00085 and R2 of 79.18%. Meanwhile, by using UBR, the optimal knot is three knots with MSE of 0.00095 and R2 of 66.42%. In conclusion, GCV generated better model than UBR.

The Smallest Reported Distal 11q25 Deletion in Jacobsen Syndrome (JBS): Two Patients with Variable Phenotype

all non-coding RNA (ncRNA) genes and regulatory elements. NGS-based proximity mapping has revealed a nuclear organization of the genome, with about 2,000 to 3,000 topologically associating domains (TAD), which can be further organized into loops. To facilitate the functional characterization of TADs, TAD-boundaries and loops, we have initiated a systematic mapping of constitutional “balanced” chromosomal rearrangements (BCR) that must affect this nuclear organization. Our first unbiased re-examination of prenatally diagnosed de novo BCRs (pBCRdn) showed breakpoints affect genomic compartments according to their size, e.g., protein coding/noncoding genes; regulatory domains associated with long-range position effects (LRPE); unannotated gaps; and TAD and TADboundaries. We also showed that the unbiased morbidity risk of pBCRdn are 2to 3-fold higher than previously estimated (approximately 20%), due to later onset neurodevelopmental disorders. This morbidity can in some cases be linked to truncation of known disease genes and LRPE-regions, but we also highlight the existing gap in genotype-phenotype knowledge. To address this gap, we have established IBMC, presently involving >150 partners from >50 countries and 6 continents, with the aim to mate-pair map w10,000 chromosomal breakpoints. This will target an estimated w2,700 protein coding genes, w1,500 ncRNA genes, most of the LRPEregions that specify the vertebrate body plan, link phenotypes with disruption/rearrangement of nuclear domains, and identify human models for their functional characterization. The project will include participants from undeveloped, developing and developed countries, and hence facilitate global mobility and technology transfer.

Colored Noise and Regularization Parameter Selection for Waveform Metrology

We study six algorithms to select a regularization parameter for deconvolution problems appearing in high-speed communication measurement applications. We investigate these algorithms in the presence of unspecified noise correlation analyzing their performance as components of a multivariate random variable and study their joint distribution by Monte Carlo. We find that several parameter selection algorithms, despite their widespread use, are not robust to unspecified noise correlations. Specifically, the discrepancy principle fails to return adequate regularizations for rough noise, while the generalized cross validation (GCV), unbiased predictive risk, and information complexity selectors can fail for smooth noise. For some experimental configurations, GCV failed completely, returning zero successful inversions out of 500 noise instantiations. These parameter selection algorithms share in the characteristic that they do not contain mechanisms to monitor quantities derived from the parameter-dependent solution vector. By contrast, the L-curve and quasi-optimality criteria do contain such mechanisms, and furthermore exhibited significantly fewer failures and correlated highly with the optimal inversion across all noise levels and correlations.

Percentile estimators in location-scale parameter families under absolute loss

Estimators of percentiles of location-scale parameter families are optimized based on median unbiasedness and absolute risk. Median unbiased estimators and minimum absolute risk estimators are shown to exist within a class of equivariant estimators and depend upon medians of two completely specified distributions. This work extends earlier findings to a larger class of equivariant estimators. These estimators are illustrated in the normal and exponential distributions.

Smoothing Spline Estimation of Variance Functions

This article considers spline smoothing of variance functions. We focus on selection of the smoothing parameters and develop three direct data-driven methods: unbiased risk (UBR), generalized approximate cross-validation (GACV), and generalized maximum likelihood (GML). In addition to guaranteed convergence, simulations show that these direct methods perform better than existing indirect UBR, generalized cross-validation (GCV), and GML methods. The direct UBR and GML methods perform better than the GACV method. An application to array-based comparative genomic hybridization data illustrates the usefulness of the proposed methods.

Estimating haplotype relative risks in complex disease from unphased SNPs data in families using a likelihood adjusted for ascertainment

The understanding of complex diseases and insights to improve their medical management may be achieved through the deduction of how specific haplotypes may play a joint effect to change relative risk information. In this paper we describe an ascertainment adjusted likelihood-based method to estimate haplotype relative risks using pooled family data coming from association and/or linkage studies that were used to identify specific haplotypes. Haplotype-based analysis tends to require a large amount of parameters to capture all the information that leads to efficiency problems. An adaptation of the Stochastic Expectation Maximization algorithm is used for haplotypes inference from genotypic data and to reduce the number of nuisance parameters for risk estimation. Using different simulations, we show that this method provides unbiased relative risk estimates even in case of departure from Hardy-Weinberg equilibrium.

Bias introduced in rainfall risk assessment by a rain gauges network

When large periods of observation are considered, the densest information are often a collection of the daily rain gauges network. As this information is scattered in space, the stochastic results and specially the rainfall risk assessment, are biased because of the rainfall events that are not ‘observed’ by the network. Rainfall risk can be assessed using a punctual approach with the estimation of regional return period of a punctual rainfall depth exceeding a given value, or using a spatial approach with the frequency analysis of the areas of isohyets defined at a given rain threshold τ. This last approach consists, for a given τ, in estimating the return period of isohyet areas. Using simulation, a method of unbiased rainfall risk assessment is proposed for the Languedoc-Roussillon region (France). It has been shown that the bias influence is negligible for the regional return periods of isohyet areas, for 24-hour and 48-hour duration, when compared to their confident limits. On the contrary the return periods of punctual rainfall depths above a given value are more sensitive: for values above 170 mm/24h and 270 mm/48h, the biased return periods could be up to 3 times overestimated.

Smoothing Spline Models with Correlated Random Errors

Spline-smoothing techniques are commonly used to estimate the mean function in a nonparametric regression model. Their performances depend greatly on the choice of smoothing parameters. Many methods of selecting smoothing parameters such as generalized maximum likelihood (GML), generalized cross-validation (GCV), and unbiased risk (UBR), have been developed under the assumption of independent observations. They tend to underestimate smoothing parameters when data are correlated. In this article, I assume that observations are correlated and that the correlation matrix depends on a parsimonious set of parameters. I extend the GML, GCV, and UBR methods to estimate the smoothing parameters and the correlation parameters simultaneously. I also relate a smoothing spline model to three mixed-effects models. These relationships show that the smoothing spline estimates evaluated at design points are best linear unbiased prediction (BLUP) estimates and that the GML estimates of the smoothing parameters and the correlation parameters are restricted maximum likelihood (REML) estimates. They also provide a way to fit a spline model with correlated errors using the SAS procedure proc mixed. Simulations are conducted to evaluate and compare the performance of the GML, GCV, UBR methods and the method proposed by Diggle and Hutchinson. The GML method is recommended, because it is stable and works well in all simulations. It performs better than other methods, especially when the sample size is not large. I illustrate my methods with applications to time series data and to spatial data.