This paper concerns linear regression with interval censored data. M-estimators for the regression coefficients are derived. Asymptotic consistency and normality of the M-estimators are obtained via an exponential ine...
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This paper concerns linear regression with interval censored data. M-estimators for the regression coefficients are derived. Asymptotic consistency and normality of the M-estimators are obtained via an exponential inequality for U-statistics. Asymptotically efficient estimators are provided under mild conditions.
SUMMARYConsider a collection of individual linear regression models, in which each individual parameter vector is independently drawn from a common multivariate normal distribution and is fixed over successive observa...
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SUMMARYConsider a collection of individual linear regression models, in which each individual parameter vector is independently drawn from a common multivariate normal distribution and is fixed over successive observations on that individual. Maximum likelihood estimators of the mean and dispersion of the parameters and of the disturbance variance are derived. These estimators yield empirical Bayes estimators of the individual parameter veotors. The properties of the estimators are exhibited in the case where the parameter dispersion is known.
The problem of estimating parameters of a linear regression with allowance for inequality constraints on the parameters is considered in the special case when its variables have a trend. A parameter estimation algorit...
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The problem of estimating parameters of a linear regression with allowance for inequality constraints on the parameters is considered in the special case when its variables have a trend. A parameter estimation algorithm is described. The consistency of parameter estimates is proved and their asymptotic distribution is found. Consistent estimates are proposed for the mean-square error matrix of estimates of regression parameters and noise dispersion under rather general assumptions on the law of noise distribution.
The oculomotor system produces eye-position signals during fixations and head movements by integrating velocity-coded saccadic and vestibular inputs. A previous analysis of nucleus prepositus hypoglossi (nph) lesions ...
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The oculomotor system produces eye-position signals during fixations and head movements by integrating velocity-coded saccadic and vestibular inputs. A previous analysis of nucleus prepositus hypoglossi (nph) lesions in monkeys found that the integration time constant for maintaining fixations decreased, while that for the vestibuloocular reflex (VOR) did not. On this basis, it was concluded that saccadic inputs are integrated by the nph, but that the vestibular inputs are integrated elsewhere. We re-analyze the data from which this conclusion was drawn by performing a linear regression of eye velocity on eye position and head velocity to derive the time constant and velocity bias of an imperfect oculomotor neural integrator. The velocity-position regression procedure reveals that the integration time constants for both VOR and saccades decrease in tandem with consecutive nph lesions, consistent with the hypothesis of a single common integrator. The previous evaluation of the integrator time constant relied upon fitting methods that are prone to error in the presence of velocity bias and saccades. The algorithm used to evaluate imperfect fixations in the dark did not account for the nonzero null position of the eyes associated with velocity bias. The phase-shift analysis used in evaluating the response to sinusoidal vestibular input neglects the effect of saccadic resets of eye position on intersaccadic eye velocity, resulting in gross underestimates of the imperfections in integration during VOR. The linear regression method presented here is valid for both fixation and low head velocity VOR data and is easy to implement.
Interval-valued data refers to collection of observations in the form of intervals, rather than single numbers. It originally arose from situations of imprecision due to factors such as measurement or computation erro...
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Interval-valued data refers to collection of observations in the form of intervals, rather than single numbers. It originally arose from situations of imprecision due to factors such as measurement or computation errors, where intervals are used to represent the true data points that are inside the intervals but not exactly known. Other circumstances include grouping and censoring. Recently, with the trend of big data, there is an increasing popularity of interval-valued data resulting from data aggregation. In the past decades, a great deal of effort has been seen in the literature to investigate linear regression with interval-value data. Various models that provide predictive tools and statistical inferences have been proposed and studied. The framework thus established is also well suited for both theoretical and computational advancements in the future. (C) 2015 Wiley Periodicals, Inc.
This paper presents guidelines for obtaining the correct regression line by taking into account the errors in both axes when there are outliers in the data set. We have adapted the weighted residual plots to take into...
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This paper presents guidelines for obtaining the correct regression line by taking into account the errors in both axes when there are outliers in the data set. We have adapted the weighted residual plots to take into account the experimental errors in both axes, and have combined it with robust regression methods and methods for detecting outliers. The protocol has been checked with real data sets from the literature to show how it can be used to find the best regression line when there are outliers in the data set. In all cases the errors in both axes are taken into account.
Energy properties (total electronic energies, kinetic energies, atomization energies, zero point energies, thermal energies, and thermal enthalpies) of several linear homologous of poly heterocyclic compounds have bee...
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Energy properties (total electronic energies, kinetic energies, atomization energies, zero point energies, thermal energies, and thermal enthalpies) of several linear homologous of poly heterocyclic compounds have been calculated using HF and B3LYP in conjunction with 6-31G(d) basis set. Calculated energy properties of each family of homologous series have been employed to generate a fit function versus the total number of electrons as well as the number of repeating units. The observed perfect linearity of regression lines of every homologous compound can be used to predict estimated energy properties of homologous from the regression parameters determined for a set of known energy properties of smaller compounds which belong to the same homologous series. From these values, extrapolated energy properties of even large molecules are accessible within chemical accuracy. Also, it has been found that, except for absolute values, the trends of various energy properties remain the same, at two levels of calculation. The success of the linear fittings with respect to either the number of electrons or the number of repeating units is insensitive to the inclusion of electron correlation. (C) 2009 Elsevier B.V. All rights reserved.
linear regression on network-linked observations has been an essential tool in modelling the relationship between response and covariates with additional network structures. Previous methods either lack inference tool...
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linear regression on network-linked observations has been an essential tool in modelling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive assumptions on social effects and usually assume that networks are observed without errors. This paper proposes a regression model with non-parametric network effects. The model does not assume that the relational data or network structure is exactly observed and can be provably robust to network perturbations. Asymptotic inference framework is established under a general requirement of the network observational errors, and the robustness of this method is studied in the specific setting when the errors come from random network models. We discover a phase-transition phenomenon of the inference validity concerning the network density when no prior knowledge of the network model is available while also showing a significant improvement achieved by knowing the network model. Simulation studies are conducted to verify these theoretical results and demonstrate the advantage of the proposed method over existing work in terms of accuracy and computational efficiency under different data-generating models. The method is then applied to middle school students' network data to study the effectiveness of educational workshops in reducing school conflicts.
Quantitative correlations between the contents of the flavonolignans silychristin A and silybins A/B provide biosynthetic clues that support a pathway in which one mesomeric form of a taxifolin radical is undergoing a...
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Quantitative correlations between the contents of the flavonolignans silychristin A and silybins A/B provide biosynthetic clues that support a pathway in which one mesomeric form of a taxifolin radical is undergoing an oxidative coupling with a coniferyl alcohol radical. The flavonolignan content and patterns reported in the literature for 53 samples, representing populations of the Silybum marianum plant growing in different parts of the world, were subject to a meta-analysis. linear regression analyses were carried out on these data sets, and a mathematical model was derived that predicts the content of silychristin A relative to the metabolomic pattern of its congeners. The validity of the model was verified by applying it to test samples. This approach could potentially become a tool to enhance the understanding of both the relative composition of the silymarin complex and the biosynthetic pathways that underlie its formation.
In a clinical trial with binary outcome, analyses are required for treatment or study group comparisons adjusted for covariate effects. A special problem arises with "mixed binary and Gaussian covariates", i...
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In a clinical trial with binary outcome, analyses are required for treatment or study group comparisons adjusted for covariate effects. A special problem arises with "mixed binary and Gaussian covariates", i.e., when some covariates are binary and some are continuous and may be assumed to be Gaussian. The correct model for such a data structure is of the logistic form. In the past, analyses of such data have been carried out by linear regression as well as by logistic regression methods. In this article, computer simulation was used to study the type I error level of linear regression analysis tests for treatment comparisons, when applied to a binary outcome variate obeying a logistic model with mixed binary and Gaussian covariates. It was found that the true type I error level depends on the distribution of covariates among treatment groups and on the magnitudes of the actual covariate effects, and can differ importantly from that assumed under Gaussian theory. Some recommendations are made for developing computer package programs for this problem.
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