Generalized Cross Validation Research Articles

P6141Associations between atmospheric parameters and haemostatic factors: a case control study

Abstract Background One of the biggest health challenges in the 21st century is global climate change. The health effect of climate change is partly mediated through atmospheric parameters. There is a growing concern that atmospheric parameters might increase cardiovascular (CV) morbidity. Increased levels of haemostatic factors are predictors of CV events. The associations between CV diseases and atmospheric parameters have been widely reported, however there are few studies of atmospheric parameters' effects on markers of haemostasis. Purpose We examined the possible association between atmospheric parameters and several haemostatic markers. Methods The study consisted of 3800 hospitalized patients with acute CV diseases (ACVDs) and 260 healthy blood donors. We examined the relationship of haemoglobin (Hgb), white blood cells (WBC), thrombocytes (THR) and local atmospheric parameter conditions (temperature, atmospheric pressure, humidity, wind speed, atmospheric front) on a day-to-day basis in a 5-year period (2009–2013) using a General Additive Model with cubic splines of covariates, regularized by a ridge penalty, and employing generalized cross validation. Atmospheric parameters were allowed to have a lagged effect by up to 21 days. Results Among blood donors, the average of daily temperature lagged by 8–14 days had a significant effect on Hgb, exhibiting a U-shaped relationship, where higher Hgb values were associated with extremities of the observed temperature interval. For ACVD patients, all examined blood test variables has a significant association with at least some of the atmospheric parameters. Hgb was shown to have a negative linear relationship with mean daily humidity, and the average of daily temperature lagged by 15–21 days, while the average of daily temperature variation lagged by 2–7 days had highly non-linear effect. The relative strength of the association with Hgb was largest for daily temperature variation. WBC values had a slightly non-linear positive relationship with atmospheric pressure lagged by 1 day, with WBC being significantly increased above 1030 hPa. THR values decreased linearly with an increase in mean daily temperature averaged for days lagged 15–21. Atmospheric pressure lagged by 1 day also had a significant effect on THR, with a positive linear effect under 1010 and over 1020 hPa but no effect between. The relative effect of atmospheric pressure on THR was twice as large compared to temperature. Conclusions Our study showed that exposure to certain atmospheric parameters is associated with significant changes in haemostatic marker levels. In the context of global climate change, the importance of focusing on atmospheric parameters as minor CV risk factor is substantially growing. A better understanding of the fluctuation of the examined markers, in light of atmospheric parameters, appears to be of particular importance for future studies and could help establish new CV prevention strategies.

Bandlimited force identification based on sinc-dictionaries and Tikhonov regularization

A bandlimited force identification approach is proposed in this paper. It consists of two main ingredients. On the one hand, the sinc-dictionaries are established for bandlimited force representation. This motivates from the sampling formula that a bandlimited signal can be well interpolated by sinc functions. It is also noteworthy that using the sinc-dictionaries, the amount of variables is dramatically reduced. On the other hand, the Tikhonov regularization is introduced to circumvent the possible ill-posedness of force identification. In proceeding so, the generalized cross validation criterion is adopted to determine a proper regularization parameter. Numerical examples are conducted to testify the accuracy and efficiency of the proposed approach for bandlimited force identification.

Development and preliminary application of a gridded surface air temperature homogenized dataset for China

When meteorological stations are quite unevenly distributed, a simple regional arithmetic mean of observation data may assign an excessive weight to one region with dense stations, which affects the representativeness of the regional mean. In this study, we used the homogenized monthly maximum (Tmax), mean (Tm), and minimum (Tmin) temperature dataset at more than 2400 national surface meteorological stations in China. Based on a thin plate spline (TPS) interpolation method, we selected a three-dimensional (longitude, latitude, and elevation above sea level) interpolation model that is suitable for the temperature curve surface fitting in China, and constructed a gridded temperature dataset with a horizontal resolution of 0.5° during 1961 to 2015. Cross-validation indicates that the annual average of generalized cross-validation (GCV) is relatively small, and the ratio of GCV to the observed temperature is relatively low. Both the root of GCV and the root-mean-square error of temperature are smaller than those of the previous temperature gridded products. A comparison between our dataset and the Climate Research Unit (CRU) TS4.02 dataset indicates that the CRU’s data overestimate the warming trend in China during 1961–1984, whereas underestimate the warming trend during 1985–2015.

Sentinel-2 Sharpening Using a Reduced-Rank Method

Recently, the Sentinel-2 (S2) satellite constellation was deployed for mapping and monitoring the Earth environment. Images acquired by the sensors mounted on the S2 platforms have three levels of spatial resolution: 10, 20, and 60 m. In many remote sensing applications, the availability of images at the highest spatial resolution (i.e., 10 m for S2) is often desirable. This can be achieved by generating a synthetic high-resolution image through data fusion. To this end, researchers have proposed techniques exploiting the spectral/spatial correlation inherent in multispectral data to sharpen the lower resolution S2 bands to 10 m. In this paper, we propose a novel method that formulates the sharpening process as a solution to an inverse problem. We develop a cyclic descent algorithm called S2Sharp and an associated tuning parameter selection algorithm based on generalized cross validation and Bayesian optimization. The tuning parameter selection method is evaluated on a simulated data set. The effectiveness of S2Sharp is assessed experimentally by comparisons to state-of-the-art methods using both simulated and real data sets.

Pemodelan IPM Di Kawasan Timur Indonesia Menggunakan Multivariate Adaptive Regression Spline (MARS)

Human Development Index (HDI) is an important issue in designing and strategizing of sustainable development. Multivariate Adaptive Regression Spline (MARS) is a regression approach that produces models with continous character on knots. MARS models are determined based on trial and error for a combination of basis function (BF), maximum interaction (MI), and minimum observation (MO). The determination of knots is based on the minimum Generalized Cross Validation (GCV) value. The results of this study are the combination value of BF = 52, MI = 3, and MO = 2 with a minimum GCV of 0,00049. The factors that influence HDI are average school length (X2) per capita expenditure (X4), life expactancy (X3), persentage of poor woman aged 15-49 who use the birth control tool (X5).

An improved TSVD-GCV inversion algorithm of pore size distribution in time-domain induced polarization using migration Hankel matrix

Reservoir porosity obtained from time-domain induced polarization (TDIP) well logging plays a vital role in estimating the hydraulic properties and obtain the reservoir parameters in a water-flood oil-field. Improving the inversion accuracy of the reservoir porosity can enhance the oil recovery in the water-flood oil-filed. Evaluating reservoir pore size distribution through induced polarization decay curve is confronted with the problems of poor applicability of data pre-processing, low accuracy and lacking of evaluation criteria for inversion results of pore size distribution. The basic principles of TDIP are introduced and the relationship between pore relaxation time and pore diameter is given. Combining the mathematical characteristics of polarization decay curve data, the performance and the limitations of existing pre-processing algorithms are analyzed and pointed out, respectively. An improved data pre-processing algorithm using the spatial characteristics of linear transformation based on migration Hankel matrix is proposed, and this method improves the inversion accuracy of pore size distribution greatly. In the engineering application, 2-logarithmic sampling method is proposed to sample the polarization decay data for more efficient petroleum exploration with less sample points. The different regularization methods, regularization matrix and regularization parameter determination methods are compared and analyzed for the inversion of the pore size distribution. The numerical simulation experimental results show that the stability and accuracy of Truncated Singular Value Decomposition - Generalized Cross Validation (TSVD-GCV), Truncated Singular Value Decomposition - L Curve (TSVD-L) and Tikhonov-I-L are appropriate for the inversion of pore size distribution. Because of the truth that the pore size distribution of rock is unknown, Backus-Gilbert (BG) theory is introduced to evaluate the inversion results of rock polarization decay curve data of a mining area in Jilin Province. The rock sample experiment shows that the TSVD-GCV inversion algorithm has the best performance.

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.

ANALISIS PENGARUH ANGKA KEMATIAN BAYI TERHADAP ANGKA HARAPAN HIDUP DI PROVINSI JAWA TIMUR BERDASARKAN ESTIMATOR LEAST SQUARE SPINE

Life expectancy can be used to evaluate the government's performance for improving the welfare of the population in the health sector. Life expectancy is closely related to infant mortality rate. Theoretically, decreasing of infant mortality rate will cause increasing of life expectancy. A statistical method that can be used to model life expectancy is nonparametric regression model based on least square spline estimator. This method provides high flexibility to accommodate pattern of data by using smoothing technique. The best estimated model is order one spline model with one knot based on minimum generalized cross validation (GCV) value of 0.607. Each increasing of one infant mortality rate unit will cause decreasing of life expectancy of 0.2314 for infant mortality rate less than 27, and of 0.0666 for infant mortality rate more than and equals to 27. In addition, based on mean square error (MSE) of 0.492 and R2value of 76.59% for nonparametric model approach compared with MSE of 0.634 and R2 value of 71.8% for parametric model approach, we conclude that the use of nonparametric model approach based on least square spline estimator is better than that of parametric model approach.

PEMODELAN REGRESI NONPARAMETRIK SPLINE TRUNCATED PADA FAKTOR-FAKTOR YANG MEMPENGARUHI PERTUMBUHAN EKONOMI DI PROVINSI MALUKU

Economic growth is a benchmark for the success of a region's development, especially in the economic field. The purpose of economic development in an area is basically to improve the welfare and prosperity of the community. Economic growth in Maluku Province experienced a positive increase. However, there is still a disparity between districts/cities in Maluku Province, which has an impact on increasing unemployment and an increasingly poor population. This is inseparable from the influencing factors so that it can be precisely done by modeling these factors using the truncated nonparametric spline regression method. the advantages of this method occur because in nonparametric spline truncated regression has knot points, which are joint fusion points that indicate changes in data behavior patterns. Besides, this method can be used to model data patterns that change at certain sub-intervals. The best model is very dependent on determining the optimal knot point by using the minimum Generalized Cross-Validation (GCV) value. The results obtained in this study were the highest percentage of economic growth in Maluku Province, Ambon City with a percentage of 6.17%, and the lowest economic growth was in the East Seram District (SBT) with a percentage of 5.03%. Furthermore, the best model is obtained with a model with three knots and a GCV value of 11.61, a value of 2 of 0.94 and an MSE value of 0.005. This means that statistically, the variables used in this study affect economic growth by 94%. While the rest is influenced by other variables outside the research.

Numerical investigation of an inverse problem based on regularization method

In this study, a numerical approach of the spectral collocation method coupled with a regularization technique is applied for solving an inverse parabolic problem of the heat equation in a quarter plane. The problem includes the estimation of an unknown boundary condition from an overspecified condition. The stable solution of the problem exists and is proved by Tikhonov regularization technique. The algorithm works without any mesh points or elements, and accurate results can be obtained efficiently. By employing the numerical algorithm on the problem, the resultant matrix equation is ill-condition. To regularize this matrix equation, we apply regularization technique, with the L-curve and general cross-validation criteria for choosing the regularization parameter. For demonstrating the performance and ability of the proposed algorithm, a test example is presented. The numerical results showed that the solution obtained with the algorithm designed in this paper is stable with the noisy data and the unknown boundary condition was recovered very well.

Penerapan Multivariate Adaptive Regression Spline (MARS) Pada Kasus Indeks Pembangunan Manusia di Kawasan Timur Indonesia

Human Development Index (HDI) is an important indicator to measure success in effort to build the quality of human life. Multivariate Adaptive Regression Spline (MARS) is a regression approach developed from the Recursive Partitioning Regression (RPR) method and combined with the spline method to produce a model that is continuous on knots. MARS modeling is determined based on trial and error for a combination of basis function (BF), maximum interaction (MI), and minimum observation (MO) to get the value of minimum smoothing parameter. Automatic determination of knots on MARS uses a forward stepwise and backward stepwise algorithm based on minimum Generalized Cross Validation (GCV) values. The results of this study, obtained a combination value of BF = 52, MI = 3, and MO = 2 with a minimum GCV of 0,00049 then the best MARS model is as follows.Y = –1,045 + 0,446*BF1 – 0,592*BF2 + 0,234*BF3 – 0,352*BF4 + 0,218*BF5 – 0,254*BF6 + 0,338*BF7 – 0,304*BF8 – 3,974*BF9 + 0,097*BF13 – 1,267*BF15 – 41,784*BF16 – 1,845*BF18 – 0,519*BF19 – 0,046*BF21 + 1,275*BF23 – 0,006*BF24 – 0,110*BF25 + 0,021*BF26 + 0,153*BF27 + 14,607*BF28 – 9,276*BF30 – 5,335*BF32 – 0,053*BF34 – 0,219*BF35 – 0,111*BF36 + 0,033*BF37 – 0,238*BF38 + 0,037*BF39 – 0,017*BF41 – 0,039*BF42 – 0,632*BF43 + 0,096*BF45 – 0,147*BF46 + 0,070*BF48 + 0,339*BF49 + 0,017*BF50. The factors that influence HDI based on the level of importance in the best MARS model are per capita expenditure (X9), life expectancy (X7), long school expectations (X8), average school length (X6), poverty severity index (X4), percentage of poor people (X5), percentage of per capita expenditure for food (X12), population density per km2 (X1), and percentage of poor people aged 15 years and over do not work (X11).

Model Regresi Semiparametrik Spline Hasil Produksi Padi di Kabupaten Lombok Timur

Beras merupakan suatu sumber bahan makanan pokok penting yang harus tetap terjaga ketersediannya sepanjang tahun. Namun untuk tahun-tahun terakhir ini Indonesia yang dikenal dengan kekayaan alamnya, menjadi salah satu negara pengimpor beras. Hal ini dikarenakan konsumsi beras di indonesia terus meningkat setiap tahunnya, sedangkan produksi beras yang dihasilkan kurang mencukupi konsumsi masyarakat Indonesia. Penelitian ini dilakukan dengan tujuan untuk menentukan model regresi semiparametrik spline pada analisis faktor-faktor yang mempengaruhi hasil produksi padi di Kabupaten Lombok Timur tahun 2014, serta mengetahui faktor-faktor apa saja yang mempengaruhi hasil produksi padi tersebut. Metode yang digunakan adalah regresi semiparametrik spline dengan pemilihan titik knot optimum menggunakan Generalized Cross Validation. Hasil yang diperoleh menunjukkan bahwa variabel yang secara signifikan mempengaruhi hasil produksi padi adalah ketinggian wilayah dari permukaan laut, dengan nilai koefisien determinasi sebesar 99,71% dan nilai Root Mean Square Error of Prediction sebesar 41,65.

Impact Force Identification on Carbon Fibre–Epoxy Honeycomb Composite Panel Based on Local Convex Curve Criterion

Identification of impact force is essential for various engineering applications, such as performance evaluation, design optimisation, noise suppression, and vibration control. There are two categories available for impact force identification, namely, direct measurement and indirect acquisition. For actual engineering structures, direct measurement is often not feasible. Therefore, indirect acquisition, or force identification, is the only means to achieve this goal. Owing to the existence of noise, ill-posedness occurs during the inversion process of force identification, which is the decisive factor for the instability and inaccuracy of this method. The most popular among the existing methods for impact force identification is the Tikhonov regularisation method. The accuracy of this method depends on the determination of the regularisation parameters. This study proposes a new criterion, which is the local convex curve, for the selection of the regularisation parameter. This criterion is compared with the generalised cross validation, L-curve criterion, and other criteria. A carbon fibre–epoxy honeycomb composite panel is selected as the experimental research object, and three indicators, namely, peak relative error, relative error, and correlation coefficient, are used as the evaluation standards. The experimental results indicate that this new criterion can obtain a superior regularisation parameter in comparison with the other seven criteria. This new criterion can realise the accurate reconstruction of the impact force time history and be effective in suppressing the tail disturbance of the reconstructed impact force time history.

How old are you now? A new ageing method for nonadults based on dental wear

AbstractThe main aim of this study is to present a novel method of nonadult (ca. 1–19 years) age‐at‐death estimation using the dental wear of deciduous, mixed deciduous‐permanent, and permanent dentitions, including the incisors, canines, premolars, and first and second molars. The stage‐based method is derived from degrees of dental wear in known‐age (n = 39) and estimated‐age (n = 11) nonadults containing 951 teeth from the predominately 19th century cemetery of Middenbeemster, The Netherlands. The need for such a method is warranted in cases where dental development and/or eruption cannot be assessed for age‐at‐death estimation. As well, by establishing a baseline for normal age‐related nonadult tooth wear, users may better document wear that could be due to extramasticatory behaviours. The regression analysis reveals a strong quadratic correlation—F(2, 47) = 555.1, p < .001, R2 = .95, standard error of the estimate = 1.14, residual sum of squares (RSS) = 68.89, predicted residual error sum of squares (PRESS) = 77.67—between age and wear and multivariate adaptive regression splines (R2 = .95, generalised cross validation = 1.67, RSS = 67.68, PRESS = 89.34), which are used to develop an R‐package that users may employ to estimate age‐at‐death from dental wear. The accuracy of this method (78–98%) is evaluated using leave‐one‐out cross‐validation. Analyses of males versus females, deciduous versus permanent, upper versus lower, and anterior versus posterior teeth revealed no apparent reason to warrant separate methods for these groups of separated dentitions. This method fills a disciplinary gap in the understudied area of deciduous and nonadult dental wear and hopes to stimulate much future research. With the R‐package, we also provide the foundation and framework for the development of additional reference populations across different spatiotemporal contexts, to make the method more widely applicable.

Unbiased predictive risk estimation of the Tikhonov regularization parameter: convergence with increasing rank approximations of the singular value decomposition

The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between the sizes of the fit to data function and the regularization term. The unbiased predictive risk estimator is one suggested method for finding the regularization parameter when the noise in the measurements is normally distributed with known variance. In this paper we provide an algorithm using the unbiased predictive risk estimator that automatically finds both the regularization parameter and the number of terms to use from the singular value decomposition. Underlying the algorithm is a new result that proves that the regularization parameter converges with the number of terms from the singular value decomposition. For the analysis it is sufficient to assume that the discrete Picard condition is satisfied for exact data and that noise completely contaminates the measured data coefficients for a sufficiently large number of terms, dependent on both the noise level and the degree of ill-posedness of the system. A lower bound for the regularization parameter is provided leading to a computationally efficient algorithm. Supporting results are compared with those obtained using the method of generalized cross validation. Simulations for two-dimensional examples verify the theoretical analysis and the effectiveness of the algorithm for increasing noise levels, and demonstrate that the relative reconstruction errors obtained using the truncated singular value decomposition are less than those obtained using the singular value decomposition. This is a pre-print of an article published in BIT Numerical Mathematics. The final authenticated version is available online at: https://doi.org/10.1007%2Fs10543-019-00762-7.

Switching arc inversion based on analysis of electromagnetic characteristics

Abstract It is difficult to describe the characteristics of an arc in low-voltage switching equipment in terms of its most essential features using conventional arc models. In this paper, arc inversion is introduced to explore a new research approach to examine the nature of low-voltage switching arcs. Based on electromagnetic analysis, the arc is equivalent to a group of threadlike current segments. Then, the arc parameters are obtained by inverting the magnetic data calculated at the sampling point array. The multi-population genetic algorithm (MPGA) is adopted to solve the Biot-Savart operator equations to search the arc position, with the current density inverted by the truncated generalized singular value decomposition (TGSVD), in which the regularization parameter is chosen by the generalized cross-validation (GCV) criterion. The result shows that, by combining the MPGA with TGSVD, both the position and current distribution of an arc can be reconstructed accurately, which can help realize arc control and guide the design of low-voltage switches with improved performance parameters.

A study on short-term power load probability density forecasting considering wind power effects

Short-term load forecasting (STLF) is the foundation of safe and stable operation for power systems. In recent years, large amount of intermittent wind power has integrated into the power system, which significantly increases the uncertainties of power load forecasting. Along with the gradual increase for the proportion of wind power in the power grid, the frequency stability problem attributed to wind power connection attracts increasing attention from various aspects. Fully considering the impact of the wind power factor, a method of probability density forecasting based on Least Absolute Shrinkage and Selection Operator-Quantile Regression (LASSO-QR) is proposed in this paper. Firstly, the significant explanatory variables are screened out from the historical power load and wind power factors based on LASSO algorithm via generalized cross validation (GCV), and the LASSO-QR model is established. Secondly, in combination with kernel density estimation (KDE) method, short-term power load probability density forecasting based on LASSO-QR is implemented utilizing Epanechnikov kernel function. Thirdly, the paper appraises the exactitude of the prediction interval (PI) in accordance with two criteria, prediction interval coverage probability (PICP) and prediction interval normalized average width (PINAW). Two real datasets from Ontario of Canada in summer and winter, are exploited to validate the LASSO-QR method. Fully considering the impact of wind power factor on the power load, experiment results demonstrate that the LASSO-QR method can construct more accurate PI and obtain more precise probability density forecasting results than quantile regression (QR). Contrastive analysis with the existing state-of-the-art methods further verifies superiority of the method proposed, which reduces the nondeterminacy of the prediction process to avoid large prediction errors and economic losses.

Estimation of Truncated Spline Function in Non-parametric Path Analysis Based on Weighted Least Square (WLS)

The purpose of this research is to identify a particular relationship pattern among predictors and response variables where the response variables are multi-response and correlated. Path analysis is one of the appropriate statistical parametric method to estimate the parameter when the curves are known, but in fact the curves is unknown. Nonparametric approach is a suitable method to estimate the unknown curve in Path Analysis. Truncated spline provides a powerful tool for estimating curve in non-parametric path model with the optimal knots will be estimated by using Generalized Cross Validation. Truncated spline estimator is obtained from Weighted Least Square (WLS) technique that depends on polynomial degree and knot.

Genetic Algorithm Based Tikhonov Regularization Method for Displacement Reconstruction

In this paper, a genetic algorithm based Tikhonov regularization method is proposed for determination of globally optimal regularization factor in displacement reconstruction. Optimization mathematic models are built by using the generalized cross-validation (GCV) criterion, L-curve criterion and Engl’s error minimization (EEM) criterion as the objective functions to prevent the regularization factor sinking into the locally optimal solution. The validity of the proposed algorithm is demonstrated through a numerical study of the frame structure model. Additionally, the influence of the noise level and the number of sampling points on the optimal regularization factor is analyzed. The results show that the proposed algorithm improves the robustness of the algorithm effectively, and reconstructs the displacement accurately.

The Effect of the Outliers and Leverage Points in the Construction of the Bayesian and Bootstrap Confidence Intervals

The aim of this research is to compare the bootstrap confidence intervals with the Bayesian confidence intervals for smoothing splines as well as the traditional confidence intervals to determine which of these limits are best in the presence of Outliers and Leverage points in data. The simulation experiments were conducted on two models: the first was linear in the presence of data that was contaminated with outliers and the other with the Leverage points: The second model was nonlinear in the presence of data contaminated with outlying observations Simulation experiments were carried out on different samples. The Penalized Least Squares method was used to fit the Nonparametric regression. The Generalized Cross Validation function (GCV) was used to select the amount of smoothing.