In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard n...
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In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.
The paper investigates the sequential observations’ variance change in linear regression model. The procedure is based on a detection function constructed by residual squares of CUSUM and a boundary function which is...
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The paper investigates the sequential observations’ variance change in linear regression model. The procedure is based on a detection function constructed by residual squares of CUSUM and a boundary function which is designed so that the test has a small probability of false alarm and asymptotic power one. Simulation results show our monitoring procedure performs well when variance change occurs shortly after the monitoring time. The method is still feasible for regression coefficients change or both variance and regression coefficients change problem.
At present, there remain few studies on locus and co-articulation of the formant transition cue of stop endings in Chinese dialects. In order to fill the gap, the linear regression model is applied to build up locus e...
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COVID-19,one of the most deadly infectious diseases in a century,crossed the globe at the start of *** epidemic has flipped the world economy's prediction of modest growth at the start of 2020,and its effect on th...
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COVID-19,one of the most deadly infectious diseases in a century,crossed the globe at the start of *** epidemic has flipped the world economy's prediction of modest growth at the start of 2020,and its effect on the global economy has surpassed that of the 2008 international financial *** January 14 to May 7,2021,this paper focuses on the relationship between Pfizer stock returns and evidence on Coronavirus injection in the United *** find the linear relationship between the Pfizer's stock returns and the related data of vaccines,I used a multiple linearregression *** there exists evidence to conclude that the number of smoothed newly vaccinations is negatively correlated to stock price of Pfizer,and number of new case and number of people fully vaccinated per hundred are positively correlated to stock price of Pfizer.
This paper considers the on-line detection problem for the parameter change in linear regression model. A procedure based on the efficient score vector is proposed in this paper. Under the null hypothesis, it is prove...
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This paper considers the on-line detection problem for the parameter change in linear regression model. A procedure based on the efficient score vector is proposed in this paper. Under the null hypothesis, it is proved that the detector sequence converges to a Brownian motion. Under the alternative hypothesis, taking the coefficient as an example, this paper proves that the detector sequence converges to a Wiener process with a drift term. The simulation results demonstrate performances of the empirical level, the empirical power and stopping time, and further indicate the efficiency of our approach. (C) 2019 Elsevier B.V. All rights reserved.
Studying the relationship between river water and shallow groundwater (SGW) during flood events is a research topic receiving increasing attention for many reasons. This phenomenon was studied with respect to Mohacs I...
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Studying the relationship between river water and shallow groundwater (SGW) during flood events is a research topic receiving increasing attention for many reasons. This phenomenon was studied with respect to Mohacs Island of the Danube (Hungary) in an area protected by a levee. Floods only infiltrate into the island through the aquifer, where production wells for drinking water supply are located. Our objective was to reveal how the Danube and water abstraction from production wells control groundwater levels in the observation wells, and we also studied the effect of the precipitation events and the lag times of the influencing variables compared to the peak of groundwater waves in observation wells. The effects of these factors were summarized by a linear regression model (LM) with lag times. We developed an application because we had time-series for thirty groundwater wells and five major flood events of the Danube. Kriging was used to generate impact maps of the Danube and production wells. A propagation map of the Danube flood wave into the groundwater aquifer was also generated. We used geological information to explain the findings that the river flood waves propagate with the same wavelength and decreasing amplitude in the covered aquifer and with an elongated wavelength in uncovered conditions.
It is indispensable to scientifically predict the consumption of aero-material spare parts and to make scientific decisions on aviation equipment maintenance resources and make full use of existing resources to improv...
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It is indispensable to scientifically predict the consumption of aero-material spare parts and to make scientific decisions on aviation equipment maintenance resources and make full use of existing resources to improve maintenance capability. In this paper, the mathematic model and calculation method of linear regression model are introduced. And the parameter estimation and model test method of linear regression model is discussed. A linearization method is proposed for nonlinear problems. The application of linear regression model in forecasting the consumption of aero-material spare parts is analyzed by examples. Finally, the regression equation is analyzed for significance analysis, variance analysis and residual analysis. According to the analysis results, the regression equation is modified as necessary to further improve the prediction accuracy. The results show that the linear regression model is feasible and effective for the prediction of aero-material spare parts consumption.
Federated learning (FL) is a collaborative learning paradigm where multiple clients are used to build the model without sharing data and preserving privacy. An FL-based linear regression model is designed to predict t...
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Federated learning (FL) is a collaborative learning paradigm where multiple clients are used to build the model without sharing data and preserving privacy. An FL-based linear regression model is designed to predict the length of stay for patients at hospitals using the low-power Arduino Nano 33 BLE Sense microcontroller unit (MCU). FL uses a distributed learning technique that allows model building from decentralized data sources. The Arduino Nano 33 BLE Sense is a compact and energy-efficient MCU providing an ideal platform for implementing FL in resource-constrained environments. FL algorithms aggregate model parameters from multiple Arduino clients and collectively train and build a predictive model to estimate the length of stay at the hospital by patients. Experiments were conducted to understand the performance of FL on clients with data of equal and varying sizes and heterogeneous data from multiple sources. The performance of the algorithm is evaluated based on Mean Absolute Error (MAE), Percentage Decrease in Training error (PDTE), and Percentage Difference with Optimal Testing (PDOT) value. Experimental results show that the number of local epochs and FL rounds affects the convergence of clients to the optimal value. The experimental results demonstrate the applicability of FL on low-power MCUs, preserving privacy which is a core requirement for healthcare solutions.
Background: The accuracy of any bioanalytical method depends on the selection of an appropriate calibration model. The most commonly used calibration model is the unweighted linearregression, where the response (y-ax...
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Background: The accuracy of any bioanalytical method depends on the selection of an appropriate calibration model. The most commonly used calibration model is the unweighted linearregression, where the response (y-axis) is plotted against the corresponding concentration (x-axis). The degree of association between these two variables is expressed in terms of correlation coefficient (r(2)). However, the satisfactory r(2) alone is not adequate to accept the calibration model. The wide calibration curve range used in the bioanalytical methods is susceptible to the heteroscedasticity of the calibration curve data. The use of weighted linearregression with an appropriate weighting factor reduces the heteroscedasticity and improves the accuracy over the selected concentration range. Methods: The present work describes a rapid and simple RP-HPLC method for the estimation of chlorthalidone in spiked human plasma. The calibration curve standards were studied in the concentration range of 100-3200ng/mL. The chromatography was performed on a C18 column (250x4.6mm, 5m) in an isocratic mode at a flow rate of 1mL/min using methanol:water (60:40%, v/v) as a mobile phase. The detection was carried out at 276nm. Both the unweighted regressionmodel and weighted regressionmodels with different weighting factors (1/x, 1/x, and 1/x(2)) were evaluated for heteroscedasticity. The statistical approach for the selection of a suitable regressionmodel with appropriate weighting factors was discussed and the developed bioanalytical method was further validated, as per US-FDA guidelines. Results: In calibration curve experiments, although the acceptable r(2) of 0.998 was obtained, the % residual plot showed that the data were susceptible to heteroscedasticity. When the weighted linearregression was applied to the same calibration curve data set, no significant difference between % relative residual (% RR) was observed. Furthermore, when % relative error (% RE) was calculated for different
In this paper, we investigate the limit of the eigenvector empirical spectral distribution (VESD) of large dimensional information plus noise matrices Cn = 1 n T1/2 n (Xn + Rn)(Xn + Rn)' T1/2 n , where Xn are p x ...
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In this paper, we investigate the limit of the eigenvector empirical spectral distribution (VESD) of large dimensional information plus noise matrices Cn = 1 n T1/2 n (Xn + Rn)(Xn + Rn)' T1/2 n , where Xn are p x n random matrices with independent and identically distributed entries, Tn and Rn are non-random matrices. It is shown that as p/n -> c E (0, oo), the VESD of Cn has a deterministic limit under some mild conditions. The theoretical result is applied to the model selection problems in high dimensional linear regression model. (c) 2023 Elsevier B.V. All rights reserved.
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