T.J. Hastie, D. Pregibon, Generalized linear models, in: J.M. Chambers, T.J. Hastie (Eds.), Statistical Models in S, Wadsworth, Paci"c Grove, 1992, pp. 195}247.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and other habitat features. This circumstance will be addressed in later research. There is also an apparent difference between day and night distributions, which is no surprise because the animals forage at dawn and dusk and rest in the daytime. 4. THE STATISTICAL METHODS USED Kernel methods, [14], may be employed to form an estimate of the longrun density of elk locations. Estimates take the form (r) X m;k K(r Gamma r(t mk ) X m;k 1 (4:1) for some kernel function K( Such an estimate will be employed later in the paper, together with the realtion (2.5) to obtain an ....

....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 i )4y i for some path of ....

Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Linear Models. Chapman and Hall, London.

....that kwk 2 should be minimized. It is important that the regularizer reflects a property of F , hence regularizers depend on a priori knowledge about the function to be modeled. Selecting a good family G = fGw ; w 2 q g of functions is a difficult task, sometimes known as model selection [16, 14]. If G contains a large family of functions, it is more likely that it will contain a good approximation of F (the function we are trying to approximate) but it is also more likely that the selected candidate (using the training set) will generalize poorly because many functions in G will agree ....

T. J. Hestie and R. J. Tibshirani. Generalized Linear Models. Chapman and Hall, London, 1990.

....through the examples. Right: The fitted curves not only go through each example but also its derivatives evaluated at the examples agree with the derivatives of the given function. Selecting a good family G = fGw#w 2 q g of functions is a difficult task, sometimes known as model selection [16, 14]. If G contains a large family of functions, it is more likely that it will contain a good approximation of F (the function we are trying to approximate) but it is also more likely that the selected candidate (using the training set) will generalize poorly because many functions in G will agree ....

T. J. Hestie and R. J. Tibshirani. Generalized Linear Models. Chapman and Hall, London, 1990.

.... for diagnostics in binary regression (Altman, 1992; Azzalini, Bowman and Hardle, 1989; Copas, 1983; Fowlkes, 1987) However, a selection criterion for the choice of bandwidth for this problem has not been previously studied, although one has been suggested (Azzalini, Bowman and Hardle, 1989; Hastie and Tibshirani, 1990, p.159) In this article we examine the use of cross validation (CV) Allen, 1974; Stone, 1974) and Mallows CL (Mallows, 1973) for selecting bandwidths for kernel binary regression. Consistency of the adaptive estimators and convergence of the selected bandwidth are shown under average squared ....

....given in Jenner Steinmetz and Gasser (1988) Gasser and Engel (1990) and Chu and Marron (1991) for the case of ordinary nonparametric regression. We also discuss weighted least squares where the weights depend on estimates of the variance function, and the cross validated likelihood method of Hastie and Tibshirani (1990, p. 159) and Azzalini, Bowman and Hardle (1989) 2 Asymptotic Optimality of CV and C L Performance of a nonparametric regression estimator is generally assessed by average squared error (ASE) or its expectation (MASE) nASE( k H( y Gamma k 2 and nMASE( nE[ASE( tr SigmaH( H( 0 k ....

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Hastie, T. J. and Tibshirani, R. J. (1990) Generalized Linear Models. Chapman and Hall: New York.

....to error variance (0, 5, 1, 1.7, 2.5, 5) 46 Appendix B: Software for GAMs A statistical computing environment with strong graphics capabilities is essential for using GAMs and scatterplot smoothers. S is such an environment, though most people use S via its enhanced commercial version, Splus. Hastie (1992) provide a lengthy exposition of estimating GAMs in S. Venables and Ripley (1994, ch10) is also an excellent guide. Estimating GAMs is extremely simple in S, and uses a simple syntax. Consider the Pennsylvania State Senate data introduced in Figure 2. The following S commands fit GAMs to these ....

....directly on the GLM framework. GAMs borrow two important concepts from GLMs: a link function, h###, that describes how the mean of y, E#y#=# depends on the additive predictors; and a variance function that captures how the variance of y depends upon the mean, i.e. var(y) #V###, with # constant (Hastie and Pregibon 1992, 196 7) For instance, logistic regression models for binary outcomes can be dealt with by making the link function the logit transformation h###=log##=#1 ,###, and specifying a binomial variance function, V###=##1 , ##=n. S makes extensive use of this GLM type syntax in its support for GAMs. ....

Hastie, Trevor J. and Daryl Pregibon. 1992. Generalized Linear Models. In Statistical Models in S, ed. John M. Chambers and Trevor J. Hastie. Pacific Grove, California: Wadsworth and Brooks/Cole Chapter 6.

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T.J. Hastie, D. Pregibon, Generalized linear models, in: J.M. Chambers, T.J. Hastie (Eds.), Statistical Models in S, Wadsworth, Paci"c Grove, 1992, pp. 195}247.

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