Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L. P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85, 809--822.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....ed, and that the most ecient estimator is obtained by correctly specifying the within cluster correlation. To allow for more exible dependence of an outcome variable on covariates, there has been substantial recent interest in modeling covariate e ects nonparametrically (Wild and Yee, 1996; Hoover, et al. 1998; Lin and Carroll, 2000) In contrast to parametric GEEs, Lin and Carroll (2000) showed that when standard kernel methods are used, typically the most ecient estimator of the nonparametric function is obtained by completely ignoring the within cluster correlation: correct speci cation of the ....

Hoover, D. R., Rice, J. A., Wu, C. O. & Yang, Y. (1998), \Nonparametric Smoothing Estimates of Time{Varying Coecient Models with Longitudinal Data," Biometrika, 85, 809-822.

....some replication of covariate values. The alternative is to use contextual information as much as possible but, often, in practice, the parametric form must be guessed and experimented with which is less than satisfactory. Other semiparametric approaches to related problems can be found in Hoover, Rice, Wu, and Yang (1996), Brumbach and Rice (1996) and Zhang, Lin, Raz, and Sowers (1996) The method we propose here is exploratory and graphical in nature. Parametric assumptions are avoided because the method is intended to suggest a suitable parameterization. The spirit of the method is similar to the ACE method of ....

Hoover, D., J. Rice, C. Wu, and L. Yang (1996). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Technical Report 459, Dept. of Statistics, Univ. California, Berkeley.

....been successfully applied to analyze the continuous longitudinal data with repeated measurements by assuming that the link function is identity and the coecients change over time. For details, we refer to the articles by Brumback and Rice (1998) Hoover, Rice, Wu and Yang (1998) Wu, Chiang and Hoover (1998), and Fan and Zhang (2000) However, to the best of our knowledge, the use of such nonparametric methods to analyze discrete time series data has not been previously advocated, nor has it been shown theoretically to give the consistent estimates of coecient functions and covariance. In this ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying-coecient models with longitudinal data. Biometrika 85, 809-822.

....to us and much in line with those of Ruckstuhl, et al. Specifically, we show that the asymptotically most e#cient estimator of the nonparametric function is obtained by entirely ignoring the correlation within each cluster. This result has by the way been conjectured in the Gaussian case by Hoover, et al. 1998) and Wu, Chiang and Hoover (1998) and used as the basis for their methods. Two methods emerge from our analysis. The first simply pools the data and runs a standard nonparametric regression analysis, possibly with weighting for variability. The second method applies to the panel data problem, in ....

....of Ruckstuhl, et al. Specifically, we show that the asymptotically most e#cient estimator of the nonparametric function is obtained by entirely ignoring the correlation within each cluster. This result has by the way been conjectured in the Gaussian case by Hoover, et al. 1998) and Wu, Chiang and Hoover (1998) and used as the basis for their methods. Two methods emerge from our analysis. The first simply pools the data and runs a standard nonparametric regression analysis, possibly with weighting for variability. The second method applies to the panel data problem, in which case it makes sense to ....

Hoover, D. R., Rice, J. A., Wu, C. O. & Yang, Y. (1998). "Nonparametric Smoothing Estimates of Time--Varying Coe#cient Models with Longitudinal Data," Biometrika, 85, 809--822.

....Some asymptotic results for the local polynomial estimators are established. Two longitudinal data sets, one of which involves time dependent covariates, are used to demonstrate the proposed approach. Simulation studies show that our two step approach improves the kernel method proposed in Hoover, et al. (1998) in several aspects such as accuracy, computation time and visual appealingness of the estimators. Key Words And Phrases: Functional linear models, functional ANOVA, local polynomial smoothing, longitudinal data analysis. Short title : Functional linear models 1 1 Introduction Longitudinal ....

....in Hastie and Tibshirani (1993) Fan and Zhang (1997) propose a two step procedure to overcome inflexibilityof the traditional spline and kernel methods. Some of these methods can also be adopted in the context of functional linear models. Examples are provided by Ramsay and Silverman(1997) Hoover, et al. (1998) and Brumback and Rice (1998) In the Hoover, et al. (1998) the smoothing spline and kernel methods are studied while in Brumback and Rice (1998) the smoothing spline method is considered for functional ANOVA models which are special cases of functional linear models. While the spline method has ....

[Article contains additional citation context not shown here]

Hoover, D. R., Rice, J. A., Wu, C. O. and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, to appear.

....varying coecient models are a simple and useful extension of classical linear models. This extension admits simple interpretability. The models are particularly appealing in longitudinal studies where they allow one to explore the extent to which covariates a ect responses changing over time. See Hoover et al. 1998), Brumback and Rice (1998) and Fan and Zhang (1998) for details on novel applications of the varying coecient models to longitudinal data. For nonlinear time series applications, see Chen and Tsay (1993) and Cai, Fan and Yao (1998) for statistical inferences based on functional coecient ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1998), \Nonparametric smoothing estimates of time-varying coecient models with longitudinal data," Biometrika, ##, 809-822.

....Some asymptotic results for the local polynomial estimators are established. Two longitudinal data sets, one of which involves time dependent covariates, are used to demonstrate the proposed approach. Simulation studies show that our two step approach improves the kernel method proposed in Hoover, et al. (1998) in several aspects such as accuracy, computation time and visual appealingness of the estimators. Key Words And Phrases: Functional linear models, functional ANOVA, local polynomial smoothing, longitudinal data analysis. Short title : Functional linear models 1 1 Introduction Longitudinal ....

....in Hastie and Tibshirani (1993) Fan and Zhang (1997) propose a two step procedure to overcome in exibility of the traditional spline and kernel methods. Some of these methods can also be adopted in the context of functional linear models. Examples are provided by Ramsay and Silverman(1997) Hoover, et al. (1998) and Brumback and Rice (1998) In Hoover, et al. (1998) the smoothing spline and kernel methods are studied while in Brumback and Rice (1998) the smoothing spline method is considered for functional ANOVA models which are special cases of functional linear models. While the spline method has ....

[Article contains additional citation context not shown here]

Hoover, D. R., Rice, J. A., Wu, C. O. and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying coecient models with longitudinal data. Biometrika, to appear.

....models are a simple and useful extension of classical generalized linear models. This extension admits simple interpretation. The models are particularly appealing in longitudinal studies where they allow one to explore the extent to which covariates a ect responses changing over time. See Hoover et al. 1998), Brumback and Rice (1998) and Fan and Zhang (2000) for details on novel applications of the varying coecient models to longitudinal data. For nonlinear time series applications, see Chen and Tsay (1993) and Cai, Fan and Yao (1998) for statistical inferences based on the functional coecient ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1998), \Nonparametric smoothing estimates of time-varying coecient models with longitudinal data," Biometrika, 85, 809-822.

....diagnostic techniques need further developments. Simple and powerful diagnostic tools for checking survival time models are useful. Longitudinal data arise often from biostatistical studies. To monitor disease progression and to examine time e ect, various parametric and nonparametric models (Hoover, et al., 1998) have been developed. Semiparametric modeling of covariance matrices and ecient estimation of timevarying coecient functions are needed. We still lack inference tools to answer clinically important questions such as detecting if coecients are really time varying or if certain covariate e ects ....

Hoover, D. R., Rice, J. A., Wu, C. O. and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying coecient models with longitudinal data. Biometrika, 85, 809-822.

....sacrifice of estimability (see Theorem 2 in x6 below) The specified form of (1.2) also facilitates the interpret ability of the fitted model when k is small. This is particularly relevant in modeling longitudinal data where it is reasonable to assume that the coefficients change over time t. See Hoover et al. 1997) for a novel application of functionalcoefficient models to longitudinal data. Model (1.2) is also important for modeling the population dynamics where it is reasonable to expect that animals behave differently based on its population size. Thus, using model (1.2) with u being the population size ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1997). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, to appear.

....of thresholding models in Tong (1990) and Chen and Tsay (1993) in the time series setup. It also appears natural in the longitudinal data analysis where one wishes to explore the extent to which covariates a ect response changing over time. See for example Hoover et al. 1997) Wu, Chiang and Hoover (1998), and Fan and Zhang 2 (2000) for novel applications of the model to longitudinal data. The varying coecient models are also useful for analyzing functional types of data. See Ramsay and Silverman (1997) and Brumback and Rice (1998) for details. Assuming the coecient functions a j (U) possess ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1998). Nonparametric smoothing estimates of time-varying coecient models with longitudinal data. Biometrika, to appear.

....In recent years, a great progress has been made towards increasing the flexibility of generalized linear models. Of importance is the varying coefficient (VC) model in literature. Recently, the VC model has gained a considerable attention due to its various applications in many areas. See Hoover, Rice, Wu and Yang (1998), Brumback and Rice (1998) and Fan and Zhang (1998) for details on novel applications of the VC model to longitudinal data. For nonlinear time series applications, see Chen and Tsay (1993) Cai, Fan and Yao (1998) and Cai and Tiwari (1999) for statistical inferences on the functional coefficient ....

....As mentioned above, the choice of the initial bandwidth is not very sensitive to the two step estimation as long as it is small enough so that the bias in the first step is not too large. This gives us a rule of thumb: Use the cross validation or generalized cross validation criterion (see, e.g. Hoover, Rice, Wu and Yang, 1998) to select the bandwidth b h 1 for the one step fitting. Then, use h 0 = b h 1 =2 (say, or smaller) or choose a small h 0 as the initial bandwidth. One of the advantages for the two step procedure is that in the second step, the choice of bandwidth becomes really a univariate problem. ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85, 809--822.

....models are a simple and useful extension of classical generalized linear models. This extension admits simple interpretation. The models are particularly appealing in longitudinal studies where they allow one to explore the extent to which covariates affect responses changing over time. See Hoover et al. 1998), Brumback and Rice (1998) and Fan and Zhang (2000) for details on novel applications of the varying coefficient models to longitudinal data. For nonlinear time series applications, see Chen and Tsay (1993) and Cai, Fan and Yao (1998) for 1 statistical inferences based on the ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1998), "Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data," Biometrika, 85, 809--822.

....of estimability (see Theorem 2 in x6 below) The specified form of (1.2) also facilitates the interpret ability of the fitted model when k is small. This is particularly relevant in modeling longitudinal data where it is reasonable to assume that the regression coefficients change over time t. See Hoover et al. 1998) for a novel application of functional coefficient models to longitudinal data. Model (1.2) is also important for modeling the population dynamics where it is reasonable to expect that animals behave differently based on its population size. Thus, using model (1.2) with u being the population size ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1998), "Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data," Biometrika, 85, 809-822.

....is its interpretability. It arises naturally when one is interested in exploring how regression coefficients change over different groups such as age. It is particularly appealing in longitudinal studies where it allows one to examine the extent to which covariates affect responses over time. See Hoover et al. (1997) and Fan and Zhang (1998) for details on novel applications of varying coefficient models to longitudinal data. For nonlinear time series applications, see Chen and Tsay (1993) where functional coefficient AR models are proposed and studied. 1.2 Estimation Methods Suppose that we have a random ....

....choices of initial bandwidth are not very sensitive to the twostep estimator as long as it is small enough so that the bias in the first step smoothing is negligible. 5 This suggests the following simple automatic rule. Use the cross validation or generalized crossvalidation (see e.g. Hoover et al. 1997) to select the bandwidth h for the one step fit. Then, use h 0 = 0:5 h (say) as the initial bandwidth. An advantage of the two step procedure is that in the second step, the problem is really a univariate smoothing problem. Therefore, one can apply univariate bandwidth selection procedures ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1997). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, 85, 809-822.

....depend on U , the modeling bias can significantly be reduced and curse of dimensionality can be avoided. Another advantage of this model is its interpretability. This is particularly the case in the longitudinal study where it is reasonable to assume that the coefficients change over time t. See Hoover et al. (1997) for details on novel applications of varying coefficient models to longitudinal data. For nonlinear time series applications, see Chen and Tsay (1993) where functional coefficient AR models are proposed and studied. 1.2 Estimation Methods Suppose that we have a random sample f(U i ; X i1 ; ....

....introduction, the choice of initial bandwidth is not very sensitive to the two step estimation as long as it is small enough so that the bias in the first step is not too large. This suggests the following simple automatic rule. Use the cross validation or Generalized cross validation (see e.g. Hoover et al. 1997) to select the bandwidth h for the one step fit. Then, use h 0 = 0:5 h (say) as the initial bandwidth. An advantage of the two step procedure is that in the second step, the problem is really a univariate smoothing problem. Therefore, one can apply the univariate bandwidth selection procedures ....

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L.P. (1997). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika, to appear.

....represented by equation (3) in the examples later. The TVC model is a special case of the varying coe#cient model proposed by Hastie and Tibshirani in [7] where t and # are the e#ect modifiers and T # (t, #) is the independent variable. Hoover et al. used the same model for longitudinal data in [9]. Our approach also bears close relationship to the locally weighted regression (loess)methodproposedin[2] Both of the methods use local linear fitting where the notion of localness is imposed via the weight functions. loess uses a weight function related to the distance in the independent ....

Donald R. Hoover, John A. Rice, Colin O. Wu, and Li-Ping Yang. Nonparametric smoothing estimates of time-varying coe#cient models with longituninal data. Biometrika, 85(4):809--822, 1998.

....individual curves in a quite different way. In particular, we do not fit each curve separately indeed the data from an individual subject may be too sparse to support such a fit. In Rice and Silverman (1991) the data are assumed to be collected on a regular grid. Fan and Zhang (1998) and Hoover, Rice, Wu and Yang (1998) treat nonparametric estimation of the mean function, but not the covariance function. Diggle and Verbyla (1998) constructs an estimate of the covariance function of repeated measures data by locally smoothing empirical variograms, but not a direct estimate of random effects. In contrast, our ....

.... effect curve (8) resulting from modeling the dependence on age linearly as in (9) and (10) The assumption of linearity was informally checked by plotting age versus BLUP estimates of spline coefficients. Also shown are error bars (conditional on four breakpoints) found by the bootstrap as in Hoover et al. 1998) (subjects were sampled with replacement 100 times; the error bars are the pointwise standard deviations of the 100 resulting estimates) The covariate effect is small even its sign cannot be reliably determined. Smoking, on the other hand, is associated with an increased, but possibly ....

Hoover, D., Rice, J., Wu, C. and Yang, L. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data, Biometrika 85: 809--822.

....64. Figure 11 shows the covariate effect curve (8) resulting from modeling the dependence on age linearly as in (9) and (10) The assumption of linearity was informally checked by plotting age versus BLUP estimates of spline coefficients. Also shown are error bars found by the bootstrap as in Hoover, Rice, Wu and Yang (1998) (subjects were sampled with replacement 100 times; the error bars are the pointwise standard deviations of the 2000 1500 1000 500 0 500 1000 600 400 200 0 200 400 600 800 second eigenscore Figure 9: Scores on second and third eigenvectors 0 20 40 60 80 100 500 1000 1500 2000 2500 3000 ....

Hoover, D., Rice, J., Wu, C. and Yang, L. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data, Biometrika . (to appear).

No context found.

Hoover, D. R., Rice, J. A., Wu, C. O., and Yang, L. P. (1998). Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85, 809--822.

No context found.

Hoover, D.R., Rice, J.A., Wu, C.O. and Yang, L (1998). Nonparametric smoothing estimates of time-varying coe#cient models with longitudinal data. Biometrika, 85, 4, 809--822.

No context found.

D. R. Hoover, J. A. Rice, C. O. Wu, and Y. Yang. Nonparametric smoothing estimates of time{varying coecient models with longitudinal data. Biometrika, 85:809-822, 1998.

No context found.

Hoover, D. R., Rice, J. A., Wu, C. O. and Yang, L.-P. (1998). Nonparametric smoothing estimates of time-varying coecient models with longitudinal data. Biometrika, 85, 809-822.

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