Cleveland, W. S., Grosse, E., and Shyu, W. M. (1992). Local regression models. In Chambers, J.M.andHastie,T.J.,editors,Statistical Models in S, pages 309--376. Wadsworth and Brooks, Pacific Grove, California.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... direction (drift) The drift term (r,t) was first modeled as a function of location r(t) and the time of day at time t, henceforth denoted by t (0 t 24) The estimation was done using the difference equations described in (3) and nonparametric locally weighted regression function (loess, [17]) within a generalized additive model [18] The response variables were the speeds (Km hr) in the x and y directions, namely, x(t i ) x(t i 1 ) t i t i 1 ) and [y(t i ) y(t i 1 ) t i t i 1 ) and the variance was proportional to (t i t i 1 ) 1 . Figure 3 is a plot of the resulting ....

Cleveland, W. S., Grosse, E., Shyu, W. M.: Local regression models. In Chambers, J. M., Hastie, T. J. (eds.) Statistical Models in S, Pacific Grove: Wadsworth (1992) 309-376

....(Y (t) g(x) see Hardle [13] This reference also provides a substantial review of nonparametric regression in the case that the noise values are independent. Alternately to estimate the function g one might employ a local linear estimate such as produced by the Splus function loess( [11]. References concerned with nonparametric regression in the presence of time series errors include: 1] 15] 23] 14] 22] and [18] The case of concern in this paper involves the data values ( X(# j ) # k ) j=1, J T ; k =1, K T where T the observation interval is [0,T) and ....

W. S. Cleveland, E. Grosse, and W. M. Shyu. Local regression models. In J. M. Chambers and T. J. Hastie, editors, Statistical Models in S, pages 309--376, Pacific Grove, California, 1992. Wadsworth.

....the nature of destruction. It and the corresponding cloglog link mean that the function glm( may be used for the computations, see McCullagh and Nelder [20] Chapter 5. In [5] f x,y is estimated using the generalized additive models fitter gam( of Hastie and the smoother loess( of Cleveland [9], on data from the Loma Prieta event employed. Figure 5 provides the estimate of f . One see a general dying o# of the function values as one moves away from the epicenter, except for a rise near San Francisco. This increase is associated with reclaimed land. b) Attenuation. Next a relationship ....

CLEVELAND, W. S., GROSSE, E. and SHYU, W. M. (1992). Local regression models. Pp. 309-376 in Statistical Models in S. (Eds. Chambers, J.M. and Hastie, T.J.). Wadsworth, Pacific Grove.

....components of r one can write DeltaX (t) Deltat = 1 (X; Y ) noise DeltaY (t) Deltat = 2 (X; Y ) noise further assuming time invariance. If the drift functions, 1 ; 2 , are smooth, one has a nonparametric regression problem. The functions 1 ; 2 may be estimated via loess( [7], or by a kernel method, 14] Acting as if H exists, from estimates of 1 ; 2 one has an estimate of H s gradient ( H x ; H y ) Gamma ( 1 ; 2 ) The function H itself may then be estimated following (2.2) specifically one could employ X i H x (x i ; y i )4x i X i H y (x i ; y ....

Cleveland, W. S., Grosse, E. and Shyu, W. M. (1992). Local regression models. Pp. 309-376 in Statistical Models in S (Eds. J. M. Chambers and T. J. Hastie). Pacific Grove, Wadsworth.

....obtaining centroids based on populations appears preferable for this type of data. Step 4 is to model the point data. Common modeling approaches for point data include kriging, splines, and polynomial regression. The choice here was to model the mortality rates using local regression (loess) Cleveland, Grosse and Shyu (1990) discuss the modeling options available. The particular options used for Figure 1 include local quadratic modeling, the Euclidean distance option for the independent variables, inverse variance weights and direct modeling of data. The independent variables were the Albers coordinates representing ....

Cleveland, W. S., E. Grosse, and W. Shyu. (1990), "Local Regression Models," in Statistical Models in S, Eds. J. Chambers and T. Hastie. Wadsworth & Brook/Cole. Pacific Grove CA. pp 309--376.

....the universal threshold makes a useful starting value for the optimiser as its value is independent of (V; p) 3 Example: the ethanol data Before we describe a simulation study we present an applied example in detail. The wellstudied ethanol data from Brinkman (1981) has been analysis by Cleveland et al. 1993) and Hastie (1993) but more importantly for our purposes by Kovac and Silverman (2000) The data consist of n = 88 measurements from an experiment where ethanol was burned in a single cylinder engine. The concentration of the total amount of nitric oxide and nitrogen dioxide in engine exhaust, ....

Cleveland, W.S., Grosse, E., & Shyu, W.M. 1993. Local Regression Models. Pages 309-- 376 of: Chambers, J.M., & Hastie, T.J. (eds), Statistical Models in S. Pacific Grove, California: Chapman and Hall.

....splines is kept small. Finally, neural networks all but sacri ce interpretability in the pursuit of accuracy [e.g. Cheng and Titterington (1994) A popular alternative, that is both interpretable and exible, is provided by the use of local linear and piecewise linear models. See for example, Cleveland, Grosse and Shyu (1992), Fan and Gijbels (1996) Friedman and Silverman (1989) and the articles in Murray Smith and Johansen (1997) Worthy of special mention is the paper of Breiman (1993) who considered a piecewise linear model that is closest to the one we discuss here, which Breiman called hinging hyperplanes . ....

Cleveland, W. S., Grosse, E. and Shyu, W. M. (1992). Local regression models, in J. M. Chambers and T. J. Hastie (eds), Statistical models in S, Chapman and Hall: London, chapter 8.

....for bandwidth selection. Model (1.2) is a specific model of a class of functional linear models introduced by Ramsayand Silverman (1997) in a somewhat different context. It is closely related to the varying coefficient models (for cross sectional data other than functional data) proposed in Cleveland, et al. (1991). For the varying coefficient models, smoothing spline and kernel methods are proposed 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 ....

Cleveland, W. S., Grosse, E. and Shyu, W. M. (1991). Local regression models. In Statistical Models in S (Chambers, J. M. and Hastie, T. J., eds), 309--376. Wadsworth & Brooks, Pacific Grove.

....that can be written in the form (4) for some matrix S that does not depend on Y are called linear smoothers. Most estimators used in practice, including kernel regression, local polynomial regression and the estimators discussed later in this article, are linear smoothers. Cleveland et al. [8] describe loess, the local polynomial regression routines implemented in S Plus and widely used in practice. Loess uses the tricube kernel function(2) and can fit local linear or local quadratic models. The bandwidth parameter h is defined not as a positive constant, as done above, but is chosen ....

.... including multivariate regression (see also Section 4 below) estimation of model standard deviation, correlation coefficient, the ability to use optional observation weights, and a robust local polynomial version as originally proposed in Cleveland [6] The reader is referred to Cleveland et al. [8] for details. Kernel regression and local polynomial regression have generated large amounts of theoretical and methodological research among statisticians since their introduction. Both kernel regression and local polynomial regression estimators are biased but consistent estimators of the ....

W.S. Cleveland, E. Grosse, and W.M. Shyu. Local regression models. In J.M. Chambers and T.J. Hastie, editors, Statistical Models in S, pages 309--376. Chapman & Hall, London, 1993. 18

....If we assume further that the function # # (#) is also a constant, the model reduces to a familiar parametric generalized linear model (see McCullagh and Nelder 1989) ###(## #)# = # # ### # # # # # (1.3) 1 In the least squares setting, model (1. 1) with the identity link was introduced by Cleveland, Grosse and Shyu (1992) and extended by Hastie and Tibshirani (1993) to various aspects. Furthermore, a two step estimation procedure was proposed by Fan and Zhang (1997) to deal with the situations where coecient functions admit di erent degrees of smoothness. An advantage of the model (1.1) is that via allowing ....

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1992), \Local regression models," in Statistical Models in S (Chambers, J.M. and Hastie, T.J., eds), 309-376. Pacic Grove, California: Wadsworth & Brooks.

....practice because quite often the universal threshold is usually a fairly reasonable threshold irrespective of (V; p) 3 Example: the ethanol data Before we describe a simulation study we present an applied example in detail. The wellstudied ethanol data from Brinkman (1981) has been analysis by Cleveland et al. 1993) and Hastie (1993) but more importantly for our purposes by Kovac and Silverman (2000) The data consist of n = 88 measurements from an experiment where ethanol was burned in a single cylinder engine. The concentration of the total amount of nitric oxide and nitrogen dioxide in engine exhaust, ....

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1993) Local regression models. In Chambers and Hastie (eds), Statistical Models in S. Pacific Grove, California: Chapman and Hall, 309--376.

....exploring possible nonlinear relationship. This raises many important inference questions such as if a parametric family adequately ts a given data set. Take for instance additive models (Hastie and Tibshrani 1990) Y = m 1 (X 1 ) m p (X p ) 1. 1) or varying coecient models (Cleveland, Grosse and Shyu 1992) Y = a 1 (U)X 1 a p (U)X p ; 1.2) where U and X 1 ; X p are covariates. After tting these models, one often asks if certain parametric forms such as linear models t the data adequately. This amounts to testing if each additive component is linear in the additive model ....

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1992). Local regression models. In Statistical Models in S (Chambers, J.M. and Hastie, T.J., eds), 309-376. Wadsworth & Brooks, Pacic Grove.

....thresholds are used in each case; for the bottom figures these are noise proportional. 1.2. An example. Before reviewing our regression methodology, we present a particular example. Figure 1 shows a data set of Brinkmann (1981) that has been analyzed extensively, for example by Hastie (1992) and Cleveland et al. 1992). The data consist of 88 measurements from an experiment in which ethanol was burned in a single cylinder automobile test engine. The concentration of the sum of nitric oxide (NO) and nitrogen dioxide (NO 2 )inengine exhaust, normalized by the work done by the engine, is related to the ....

Cleveland, W. S., Grosse, E., and Shyu, W. M. (1992). Local regression models. In Chambers, J.M.andHastie,T.J.,editors,Statistical Models in S, pages 309--376. Wadsworth and Brooks, Pacific Grove, California.

....for bandwidth selection. Model (1.2) is a speci c model of a class of functional linear models introduced by Ramsay and Silverman (1997) in a somewhat di erent context. It is closely related to the varying coecient models (for cross sectional data rather than functional data) proposed in Cleveland, et al. (1991). For the varying coecient models, smoothing spline and kernel methods are proposed 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 ....

Cleveland, W. S., Grosse, E. and Shyu, W. M. (1991). Local regression models. In Statistical Models in S (Chambers, J. M. and Hastie, T. J., eds), 309-376. Wadsworth & Brooks, Pacic Grove.

....context, one is interested in studying how the variables such as burn area and gender a ect survival probabilities for di erent age of burn victims. Detailed analyses of these two data sets will be reported in x3. In the least squares setting, model (1. 1) with the identity link was introduced by Cleveland, Grosse and Shyu (1992) and extended by Hastie and Tibshirani (1993) to various aspects. Recently, some new developement has been made to the model (1.1) Kauermann and Tutz (1999) proposed a graphical procedure to diagnose the discrepancy between the parametric model and the smoothing alternative by using the local ....

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1992), \Local regression models," in Statistical Models in S (Chambers, J.M. and Hastie, T.J., eds), 309-376, Pacic Grove, California: Wadsworth & Brooks.

....and hence attenuate the problems of the curse of dimensionality . Di erent models incorporate di erent knowledge into data analyses and explore di erent aspects of data. Examples include additive models (Breiman and Friedman, 1985; Hastie and Tibshirani 1990; Stone, 1994) varying coecient models (Cleveland, et al., 1991, Hastie and Tibshirani, 1993) low dimensional interaction models (Friedman 1991; Gu and Wahba, 1993; Stone, et al. 1997) multiple index models (H ardle and Stoker 1989, Li 1991) and partially linear models (Speckman 1988; Green and Silverman 1994) and their hybrids (Carroll, et al. 1997; Fan ....

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1991). Local regression models. In Statistical Models in S (Chambers, J.M. and Hastie, T.J., eds), 309-376. Wadsworth & Brooks, Pacic Grove.

....Nicholls and Quinn (1982) In fact, many useful time series models may be regarded as special cases of model (1. 2) often with specified parametric forms for a j ( Delta) s; see x2 below) However, the potential of this modeling technique had not been fully explored until the seminal work of Cleveland et al. 1992) and Hastie and Tibshirani (1993) and Chen and Tsay (1993) 1 in which nonparametric techniques were developed for estimation of the functions a j ( Delta) s. In the context of independent samples, Fan and Zhang (1997) provided an innovative two step method and insightful asymptotic results for ....

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1992). Local regression models. In Statistical Models in S (Chambers, J.M. and Hastie, T.J., eds), 309--376. Wadsworth & Brooks, Pacific Grove.

....of the VC models is that by allowing the coefficients fa j ( Delta)g to depend on certain covariate U , the modeling bias can be significantly reduced and the curse of dimensionality can be avoided. For the identity link function and the Gaussian errors, the model (1. 1) was thoroughly studied by Cleveland, Grosse and Shyu (1992), Hastie and Tibshirani (1993) Fan and Zhang (2000) among others. For the known link function and the exponential family, an extensive study on the model (1.1) was carried out by Cai, Fan and Li (1999) who proposed using a local polynomial technique to estimate the coefficient functions and ....

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1992). Local regression models. In Statistical Models in S (Chambers, J.M. and Hastie, T.J., eds), 309--376. Pacific Grove: Wadsworth & Brooks.

....packet rates for the standard blocks. spectra of and , respectively. 4.3 Dependence: Spectrum Estimation For each block we form an estimate a APN of a APN and an estimate APN of APN . The estimation is carried out by fitting local regression models [5, 6], but we alter the standard procedures to provide for long range dependence, which results in a rapidly rising log spectrum as P tends to 0. The details are given in Section 4.8. Based on the estimates, we have observed three types of spectra for the 946 blocks the standard spectrum, and two ....

W. S. Cleveland, E. Grosse, and M. J. Shyu. Local Regression Models. In J. M. Chambers and T. Hastie, editors, Statistical Models in S, pages 309--376. Chapman and Hall, New York, 1992.

....against the log packet rates for the standard blocks. spectra of h j and q j , respectively. 4. 3 Dependence: Spectrum Estimation For each block b we form an estimate b Q b (f) of Q b (f) and an estimate b H b (f) of H b (f) The estimation is carried out by fitting local regression models [5, 6], but we alter the standard procedures to provide for long range dependence, which results in a rapidly rising log spectrum as f tends to 0. The details are given in Section 4.8. Based on the estimates, we have observed three types of spectra for the 946 blocks the standard spectrum, and two ....

W. S. Cleveland, E. Grosse, and M. J. Shyu. Local Regression Models. In J. M. Chambers and T. Hastie, editors, Statistical Models in S, pages 309--376. Chapman and Hall, New York, 1992.

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Cleveland, W. S., Grosse, E., and Shyu, W. M. (1992). Local regression models. In Chambers, J.M.andHastie,T.J.,editors,Statistical Models in S, pages 309--376. Wadsworth and Brooks, Pacific Grove, California.

No context found.

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1991). Local regression models. In Statistical Models in S (Chambers, J.M. and Hastie, T.J., eds), 309-376. Wadsworth & Brooks, Paci c Grove.

No context found.

Cleveland, W.S., Grosse, E. and Shyu, W.M. (1991). Local regression model. In Statistical Models in S (Chambers, J.M. and Hastie, T.J. eds.) Wadsworth & Brooks, Pacific Grove. 309--376.

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-308. Cleveland, W.S., Grosse, E. and Shyu, W.M. #1991#. Local regression models. In Statistical Models in S #Chambers, J.M. and Hastie, T.J., eds#, 309#376. Wadsworth & Brooks, Paci#c Grove. Friedman, J.H. #1991#. Multivariate adaptive regression splines #with discussion#. Ann. Statist.,

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Cleveland, W.S.; Grosse E.; Shyu W.M. 1992. "Local regression models" In Statistical Models in S, J.M. Chambers and T.J. Hastie, eds. Wadsworth, Pacific Grove, CA, 1992, 309-376.

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