M. Wand and M. Jones. Kernel Smoothing, volume 60. Chapman and Hall, London, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of similar accuracy (for example multidimensional histograms) but computing the estimator typically requires a lot more processing time. 4. 1 Using Multi dimensional Kernels for Density Estimation Kernel density estimation is based on statistics and in particular on kernel theory [Sco92] Cre93] WJ95] Kernel estimation is a generalized form of sampling. Each sample point has weight one, but it distributes its weight in the space around it. A kernel function describes the form of the weight distribution. For a dataset D, let S be a set of tuples drawn from D uniformly at random (with jSj = ....

M.P. Wand and M.C. Jones. Kernel Smoothing. Monographs on Statistics and Applied Probability, Chapman and Hall, 1995.

....method for estimating the regression function and its derivatives. Some of the advantages of this nonparametric estimation method over kernel based methods are better boundary behavior, adaptation to estimate regression derivatives, easy computation, and good minimax properties. See Wand and Jones [16] for a discussion of the properties of local polynomial regression when the errors are assumed to be independent. The local polynomial estimator is obtained by locally tting a pth degree polynomial to the data by weighted least squares, and as with any nonparametric regression procedure, one has ....

M. P. Wand and M. C. Jones, Kernel Smoothing, Chapman and Hall, London, 1995. 38

....equations (8) and (9) for the finite dimensional parameters. We turn now to the question of density estimation based on the above inference output. 3. New semiparametric density estimators The topic of kernel density estimation is the subject of several texts like [25] 24] and more recently [30]. Important contributions on the topic of semiparametric kernel density estimation include the work by [13] who discuss an estimator based on the concept of local likelihood, and the suggestion of [12] for a semiparametric technique related to kernel density estimation. In addition, 15] 31] ....

M. P. Wand and M. C. Jones, Kernel smoothing, Chapman and Hall, London, 1995.

....summing the n kernel functions in Y space, weighted by w j (x) in X space. Figure 3 about here Our approach in bandwidth selection will be to minimize the weighted integrated mean Bandwidth selection for conditional density estimation 5 square error function (IMSE) defined as (see, e.g. Wand and Jones, 1995) IMSE(a, b; f , f) # # E # f(y x) f(y x) # 2 h(x) dx dy. 1.4) Weighting the IMSE by the marginal density h(x) places more emphasis on the regions that have more data and it also eases the computational difficulty. We also define the integrated square error function (ISE) ....

....b; f , f) # # E # f(y x) f(y x) # 2 h(x) dx dy. 1.4) Weighting the IMSE by the marginal density h(x) places more emphasis on the regions that have more data and it also eases the computational difficulty. We also define the integrated square error function (ISE) as (Wand and Jones, 1995) ISE(a, b; f , f) # # # f(y x) f(y x) # 2 h(x) dx dy. 1.5) Note that this is the expected value of # # f(y X) f(y x) # 2 dy with respect to X . For numerical examples, we will estimate the ISE using I(a, b; X,Y , y # , f) # n N # j=1 n # i=1 # f(y # ....

Wand, M.P. and Jones, M.C. Kernel smoothing. (Chapman and Hall, London, 1995).

....model may be valid in a subset of the data but not in the whole data set. This can be overcome by a nonparametric approach. As this paper focuses on the DOAS evaluation algorithm we will only study the univariate regular fixed design case here. For a further discussion on the general case, see [8]. For the fixed design case the response variables are assumed to satisfy Y i = m(x i ) 1=2 (x i )i i i = 1; 2; n; 21) where i 1 ; i 2 ; i n are independent random variables with E (i i ) 0 and Var (i i ) 1 . We call m( Delta) the regression function, since E (Y i ) ....

M. Wand and M. Jones. Kernel Smoothing. Chapman and Hall, 1995.

....section briefly discusses robust local polynomial regression and presents the proposed estimator. 3.1 Nonparametric kernel regression As this paper treats the DOAS evaluation algorithm we focus on the univariate regular fixed design case. For a further discussion on the general case, see Wand [7]. For the fixed design case the response variables are assumed to satisfy Y i = m(x i ) i i i = 1; 2; n; 3.2) where i 1 ; i 2 ; i n are independent random variables with E (i i ) 0 and Var (i i ) The subject is now to estimate the regression function m( Delta) One ....

M. Wand and M. Jones. Kernel Smoothing. Chapman and Hall, 1995.

....on the choice of an appropriate distance measure. In order to check the usefulness of the chosen similarity concept as well as the goodness of the approximation of this similarity function by the neural net, a weighted nearest neighbor classfication, the variable kernel similarity metric (see [38]) and David G. Lowe s extension described in [29] has been implemented. This algorithm takes into account the distribution of the distances d(x; y) 1 Gamma sim(x; y) in the set of given instances. The influence of any of the k neighbors on the classification is weighted by a number proportional ....

M. P. Wand and M. C. Jones. Kernel Smoothing. Chapman and Hall, London, 1995.

....h ) where the kernel function K is (usually taken as) a symmetric probability density function and the bandwidth h is a non negative smoothing parameter that controls the amount of smoothing. It is well known that the choice of h is much more 6 crucial than the choice of K (e.g. see [16] or [23]) Also, in most other kernel smoothing problems the limits of the two summations in (2) are 0 and n Gamma 1. However, since in the present setting boundary effects can be handled by periodic smoothing, the limits are changed from 0 and n Gamma 1 to Gamman and 2n Gamma 1 respectively. The ....

M. P. Wand and M. C. Jones. Kernel Smoothing. Chapman and Hall, London, 1995. 17

....of the covariate and have smaller boundary bias than kernel regression. Ruppert and Wand [45] provide a useful framework for studying the properties of local polynomial estimators. For an excellent and accessible overview of the research on kernel type regression estimators, see Wand and Jones [53]. 2.3 Spline methods In the previous section, the unknown mean function was assumed to be locally well approximated by a polynomial, which lead to local polynomial regression. An alternative approach is to represent the fit as a piecewise polynomial, with the pieces separated by points of ....

M. P. Wand and M. C. Jones. Kernel Smoothing. Chapman and Hall, London, 1995.

....unknown distribution and is called f in the literature. f Y (x) 1 nb n X i=1 k x X i b Of course there remains the question of the choice of the bandwidth b and the kernel function k(x) Here we can use the results of the theory of density estimation as presented e.g. in [6] or [7]. To minimise the mean integrated squared error we use a very simple and robust variant of estimating the optimal bandwidth b as given in [6] b = k) 1:364 min(s; R=1:34) n 1=5 ; where the constant (k) is 0.776 for the Gaussian and 1.351 for the rectangular kernel respectively. s denotes the ....

M. Wand and M. Jones. Kernel Smoothing. Chapman and Hall, London, 1995. 7

.... density estimators using orthogonal series expansion reached a high level of development (see [17] 14] 22] 27] and [8] 11] 15] 5] for a selection of more recent contributions) We also refer the reader to [28] 9] 12] 3] for extensive bibliographies and to [4] 21] 19] [26] for monographs of the field. Our model of grouping observations is directed to possible applications in massive computer calculations and can be called the regular grouping. It consists in rounding observations to the points of the equidistant grid. Typical cases when the regular grouping may ....

Wand M.P. and Jones M.C. Kernel Smoothing. London, Chapman and Hall, 1995.

....any given time an MR touches more than one file by smoothing data in which each point corresponds to an MR. A point s x coordinate is time represented its the opening date, and its y coordinate is one when more than one file is touched, and zero otherwise. Three local linear smooths (See, e.g. [21] and [22] for introduction and discussion. are shown in the top plot. These smooths are essentially weighted local averages, where the weights have a Gaussian shape, and the widths of the windows (i.e. standard deviation of the weight function) are h = 0:3 (purple curve) h = 1:5 (multicolored ....

M. P. Wand and M. C. Jones, Kernel Smoothing, Chapman and Hall, London, 1995.

....regression models. The local linear regression estimator is an alternative kernel smoother and it has some favorable properties such as automatic boundary correction and adaptation to random designs; see recent monographs by Bowman and Azzalini (1997) Fan and Gijbels (1996) Simonoff (1996) and Wand and Jones (1995). In addition, local linear regression has an interesting connection with the ordinary linear regression. When the bandwidth h = 1, local linear regression is theoretically equivalent to global linear regression since all data points receive the same weight. This property links the model ....

Wand, M. P. and Jones, M. C., Kernel Smoothing (Chapman and Hall, London, 1995).

No context found.

M. Wand and M. Jones. Kernel Smoothing, volume 60. Chapman and Hall, London, 1995.

No context found.

M.P. Wand and M.C. Jones. Kernel Smoothing. Chapman and Hall, 1995.

No context found.

M.P. Wand and M. Jones. Kernel Smoothing. Chapman and Hall, 1995.

No context found.

M.P. Wand and M.C. Jones. Kernel Smoothing. Chapman and Hall, London, 1995.

No context found.

M.P. Wand and M.C. Jones, Kernel smoothing, Chapman and Hall, London, 1995.

No context found.

M.P. Wand and M.C. Jones. Kernel Smoothing. Chapman and Hall, 1995.

No context found.

M.P. Wand and M.C. Jones. Kernel Smoothing. Chapman and Hall, London, 1995. 12

No context found.

M.P. Wand and M.C. Jones, Kernel Smoothing, Chapman and Hall, London, 1995.

No context found.

M.P.Wand and M.C. Jones, Kernel Smoothing, Chapman and Hall, London, 1995.

No context found.

M.P. Wand and M.C. Jones, Kernel Smoothing, Chapman and Hall, London, 1995.

No context found.

M. P. Wand and M. C. Jones. Kernel Smoothing. Chapman and Hall, London, 1995.

No context found.

M. P. Wand, and M. C. Jones, Kernel Smoothing, Chapman and Hall, London, 1995.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC