Estimating the confidence interval of the regression coefficient of the blood sugar model through a multivariable linear spline with known variance

Islamiyati, Anna; Raupong,; Kalondeng, Anisa; Sari, Ummi

doi:10.2478/stattrans-2022-0012

Cited by 3 publications

(4 citation statements)

References 13 publications

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“…Hence, based on Equation (32), we obtain the penalty component of PWLS optimization, which can be expressed in matrix notation for the rth response as follows:…”

Section: Determining Goodness Of Fit and Penalty Components Of Pwls O...mentioning

confidence: 99%

“…These splines have been used and developed widely in several cases by many researchers. For example, Liu et al [14] and Gao and Shi [15] used M-type splines for analyzing the variance in correlated data, and for estimating regression functions of nonparametric and semiparametric regression models, respectively; Chamidah et al [16] used truncated splines to estimate mean arterial pressure for prediction purposes, Chamidah et al [17] and Lestari et al [18] developed truncated spline and smoothing spline estimators, respectively, for estimating semiparametric regression models and determining the asymptotic properties of the estimator; Tirosh et al [19], Irizarry [20], Adams et al [21,22], Lee [23], and Maharani and Saputro [24] discussed smoothing spline for problems of analyzing fractal-like signals, minimizing risk estimate, modeling ARMA observations and estimating smoothing parameter, selection smoothing parameter using simulation data, and determining GCV criterion, respectively; Wang [13], Wang and Ke [25], Gu [26], and Sun et al [27] discussed smoothing splines in ANOVA models; Wang et al [28] applied a bivariate smoothing spline to data of cortisol and ACTH hormones; Lu et al [29] used a penalized spline for analyzing current status data; Berry and Helwig [30] compared tuning methods for penalized splines; Islamiyati et al [31,32] developed a least square spline for estimating two responses of non-parametric regression models and discussed linear spline in the modeling of blood sugar; and Kirkby et al [33] estimated nonparametric density using B-Spline. Additionally, Osmani et al [34] estimated the coefficient of a rates model using kernel and spline estimators.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator

Chamidah,

Lestari,

Budiantara

et al. 2024

Symmetry

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In data analysis using a nonparametric regression approach, we are often faced with the problem of analyzing a set of data that has mixed patterns, namely, some of the data have a certain pattern and the rest of the data have a different pattern. To handle this kind of datum, we propose the use of a mixed estimator. In this study, we theoretically discuss a developed estimation method for a nonparametric regression model with two or more response variables and predictor variables, and there is a correlation between the response variables using a mixed estimator. The model is called the multiresponse multipredictor nonparametric regression (MMNR) model. The mixed estimator used for estimating the MMNR model is a mixed estimator of smoothing spline and Fourier series that is suitable for analyzing data with patterns that partly change at certain subintervals, and some others that follow a recurring pattern in a certain trend. Since in the MMNR model there is a correlation between responses, a symmetric weight matrix is involved in the estimation process of the MMNR model. To estimate the MMNR model, we apply the reproducing kernel Hilbert space (RKHS) method to penalized weighted least square (PWLS) optimization for estimating the regression function of the MMNR model, which consists of a smoothing spline component and a Fourier series component. A simulation study to show the performance of proposed method is also given. The obtained results are estimations of the smoothing spline component, Fourier series component, MMNR model, weight matrix, and consistency of estimated regression function. In conclusion, the estimation of the MMNR model using the mixed estimator is a combination of smoothing spline component and Fourier series component estimators. It depends on smoothing and oscillation parameters, and it has linear in observation and consistent properties.

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“…Hence, based on Equation (32), we obtain the penalty component of PWLS optimization, which can be expressed in matrix notation for the rth response as follows:…”

Section: Determining Goodness Of Fit and Penalty Components Of Pwls O...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator

Chamidah,

Lestari,

Budiantara

et al. 2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…Terdapat beberapa estimator dalam regresi nonparametrik, diantaranya spline [6], kernel [7], polinomial lokal [8], dan deret fourier [9]. Untuk estimator spline, perkembanganya juga sudah sangat pesat karena memiliki fleksibilitas tinggi yaitu data yang akan mencari pola data yang sesuai [10]. Jenis estimator spline yang telah dikembangkan peneliti, diantaranya spline truncated [11], penalized spline [12], spline smoothing [13] dan spline poisson [14].…”

Section: Pendahuluanunclassified

Model Regresi Kuantil Spline Orde Dua Dalam Menganalisis Perubahan Trombosit Pasien Demam Berdarah

et al. 2023

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Quantile regression can be used to analyze data containing outliers including DHF data. The spline is able to identify several patterns of change in the regression model, so this study uses a second-order quantile spline regression model in analyzing DHF data that occurred in Makassar City. In this article, the authors analyze the pattern of changes that occur in platelets based on changes in the hematocrit content of DHF patients. The selected quantiles are quartiles 0.25; 0.50; and 0.75 with 3-knot points. Based on the results of the analysis, the minimum GCV value obtained at the use of knot points is 30.30; 44.80; 47.10 for the 0.25 quartile; 0.50; and 0.75. This shows that in each quartile, there are four patterns of quadratic changes that occur in the platelet count of DHF patients. The parabolic curve formed in each pattern segmentation shows that there are times when platelets are increasing and there are times when platelets are decreasing. However, the average platelets decreased drastically, especially when the hematocrit reached 47.10%.

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“…Besides the difference estimator, usually with the use of PWLS by some researchers, it is different in the weighting value used. Some use a weighting of the covariance variance matrix [18], number of parameters [19], and bootstrap weighting [20]. However, in simpler conditions, we can use weights based on the number of samples, and that can provide accurate estimation results.…”

Section: Introductionmentioning

confidence: 99%

The Use of Penalized Weighted Least Square to Overcome Correlations Between Two Responses

Islamiyati

Anisa

Z̲ākir

et al. 2022

BAREKENG: J. Math. & App.

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The non-parametric regression model can consider two correlated responses. However, for these conditions, we cannot use the usual estimation process because there are violations of assumptions. To solve this problem, we use a penalized weighted least square involving knots, smoothing parameters, and weighting in the estimation criteria simultaneously. The estimation process involves a weighted criteria matrix in the estimation criteria. Estimation results show that the estimated two-response non-parametric regression function with penalized spline is a linear estimation class in y response observation and depends on the knot point and smoothing parameter. Furthermore, the use of the model on toddler growth data shows some changes in the pattern of weight and height gain. The pattern segmentation that experienced a gradual increase was age 7-43 months for weight and age 6-54 months for height

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Estimating the confidence interval of the regression coefficient of the blood sugar model through a multivariable linear spline with known variance

Cited by 3 publications

References 13 publications

Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator

Estimation of Multiresponse Multipredictor Nonparametric Regression Model Using Mixed Estimator

Model Regresi Kuantil Spline Orde Dua Dalam Menganalisis Perubahan Trombosit Pasien Demam Berdarah

The Use of Penalized Weighted Least Square to Overcome Correlations Between Two Responses

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