Watson, G.S. (1964), "Smooth Regression Analysis," Sankhya, Series A, 26, pp. 359-372. Home/Search Document Not in Database Summary Related Articles Check |
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Nonparametric Identification of Nonlinear Oscillating Systems - Peifer, Timmer, Voss (2003) (Correct)
....method for estimating functions is the kernel method. Here, a predefined kernel function K h (x) determines the weighting of adjacent points. The bandwidth h of the kernel function defines the amount of smoothing by widening or narrowing the shape of K h . The so called Nadaraya Watson estimator [8, 9] f(x) x j )y j (4) is then an estimate for the unknown function f(x) This smoother is linear because S ij = K h (x i i=1 K h (x i is the corresponding hat matrix. In order to obtain a consistent estimator, in which the bias and the variance asymptotically vanish, the ....
Watson G. S. Smooth regression analysis. Sankhya, Series A, 26:359--372, 1964.
On Estimation of a Probability Density Function and Mode - Parzen (1962) (203 citations) (Correct)
....and C(y) too. Thus, set m(y) i=1 K h 2 (y Y i )Z i j=1 K h 2 (y Y j ) 5) W h 2 (y Y i )Z i ; y 2 R ; where the weights W h2 (y Y i ) K h2 (y Y i ) j=1 K h 2 (y Y j ) 6) sum to 1. The formula (5) can be recognized as a multivariate NadarayaWatson regression estimator [11, 12] of the conditional mean function m. Similarly, the conditional covariance can be estimated as C(y) W h3 (y Y i ) Z i m(y) Z i m(y) y 2 R : 7) A parametric estimator for the conditional density f ZjY =y is now given by f ZjY =y (z) 2 ) det i 1=2 e ; z ....
G. Watson, Smooth regression analysis, Sankhya, Ser. A 26 (1964) 359-372.
Adaptive Power Increase Estimation in WCDMA - Hämäläinen, Valkealahti (Correct)
....is available. The theoretically optimal regression function of Y on X is given by = dy y x f dy y x f y x X Y E x g ) 7) If the joint density f(x,y) is estimated using kernel density estimation [8] one gets the Nadaraya Watson type regression function estimator [9,10] which is = i h N i h i x x K x x K y x g 1 ) 8) where N is the training sample size, i i y x is the pair of a training sample and h x K x K h ) 9) where K is a density function (kernel) In this paper K is a Gaussian density function. The parameter h is a ....
G. S. Watson, "Smooth regression analysis", Sankhya Ser. A, 26:359-372, 1964.
Semi-parametric Pricing of Derivative Warrants - Duan, Yan (1999) (Correct)
....the pricing of warrants. Keywords: Warrants, Black Scholes Model, Local Linear Kernel Regression. Jin Chuan Duan: Department of Finance, School of Business and Management, Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong. Tel: 852) 2358 7661; Fax: 852) 2358 1749; E marl: jcduanust.hk. tYuhong Yah: Department of Finance, School of Business and Management, Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong. Tel: 852) 2358 8943; Fax: 852) 2358 1749; E marl: acyyhongust.hk. 1 Introduction Since their origination in ....
....Clear Water Bay, Kowloon, Hong Kong. Tel: 852) 2358 7661; Fax: 852) 2358 1749; E marl: jcduanust.hk. tYuhong Yah: Department of Finance, School of Business and Management, Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong. Tel: 852) 2358 8943; Fax: 852) 2358 1749; E marl: acyyhongust.hk. 1 Introduction Since their origination in 1980 s, derivative warrants have become a very popular way of repackaging securities into units more accessible to small investors. Derivative warrants are long term options issued by a company, typically an investment bank, ....
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Watson,G.S.,1964, "Smooth regression analysis", Sankhya. Series A 26, 359-372.
Clustered Partial Linear Regression - Torgo, Costa (2000) (Correct)
....using other regression techniques. Partial linear models belong to the class of semiparametric approaches that integrate parametric with non parametric techniques. In the case of partial linear models, a standard least squares linear polynomial (e.g. 8] is integrated with a kernel smoother [14, 18]. The main motivation behind these models is to retain as much as possible the comprehensibility of linear polynomials, while trying to improve their accuracy by adding a smoothing component that compensates, on a query base, for the local inadequacies of the linearity assumption of first order ....
....As the inverse matrix does not always exists this process suffers from numerical instability. A better alternative [15] is to use a set of techniques known as Singular Value Decomposition (SVD) that can be used to find solutions of systems of equations with the form X[3 = Y. A kernel smoother [14, 18] can be seen as a form of lazy learner [1] that delays learning till prediction time. Given a query point Xq, a prediction is obtained using the following expression, d( is the distance function between two instances; K( is a kernel function; h is a bandwidth value; xl, yi is a training ....
Watson, G.S. : Smooth regression analysis. Sankhya: The Indian Journal of Statsitics, Series A, 26, 359-372, 1964.
Model on Demand: Algorithms, Analysis and Applications - Stenman (1999) (Correct)
....imposed by a parametric model. Local nonparametric regression models have been discussed and analyzed in the statistical literature for a long time. In the context of so called kernel regression methods, traditional approaches have involved the Nadaraya Watson estimator (Nadaraya, 1964; Watson, 1964) and some alternative kernel estimators, for example the Priestly Chao estimator (Priestly and Chao, 1972) and the Gasser Mller estimator (Gasser and Mller, 1979) In this chapter we give a brief introduction to a special class of such models, local polynomial estimators (Stone, 1977; Cleveland, ....
....special cases p = 0andp=1, simple explicit formulas exist. With p = 0, i.e. when fitting a local constant to data, the estimator becomes m(x, h) P N i=1 K h (X i x) Y i P N i=1 K h (X i x) 3. 14) which is widely known as the Nadaraya Watsonkernel estimator (Nadaraya, 1964; Watson, 1964). With p = 1, the estimator is termed local linear estimator (Fan, 1992) and can be explicitly expressed as m(x , h) 1 N N X i=1 s 2 (x , h) s 1 (x , h) X i x) K h (X i x) Y i s 2 (x, h)s 0 (x, h) s 2 1 (x, h) 3.15) where s j (x, h) # = 1 N N X i=1 ....
Watson, G. (1964). Smooth regression analysis. Sankhya A(26), 359--372.
Hierarchical Local Regression - Sadegh, Öjelund (Correct)
....variance at x, and nally 2 (x) is a global variance function that re ects the quality of the parametric model f( at x. Small values of 2 (x) 2 (x) P i w(x i x) 1 in the equation (2. 1) lead to the kernel estimator P i w(x i x)y i = P i w(x i x) Nadaraya, 1964; Watson, 1964; Gasser M uller, 1979) Large values of this ratio, on the other hand, simply render f(x; as the predicted response. The prediction formula (2.1) implies that f(x; is an attraction surface for (x) where 2 (x) 2 (x) P i w(x i x) 1 determines the magnitude of attraction ....
....we denote the parameters of 2 (x) by . We return to the problem of estimating the parameters of the measurement noise model later when estimation of global parameters is discussed. Using (2. 2) to obtain a maximum likelihood estimate for the mean leads to a kernel estimator (Nadaraya, 1964; Watson, 1964; Gasser M uller, 1979) It is easy to see that this estimate does not change if the weights are scaled. Such scaling will however change the estimated values of the global parameters and predicted values of the response for HLR. It is therefore important to scale the weights properly. The ....
Watson, G. S. (1964). Smooth regression analysis. Sankya A, 26, 359-372.
An Overview of Radial Basis Function Networks - Ghosh, Nag (2000) (3 citations) (Correct)
....by forming the regression, or conditional average of the target data, conditioned on the input variables. The conditional average can be expressed in terms of the conditional density which 20 in turn can be derived from Eq. 52. The regression function is known as the Nadaraya Watson estimator [Nad64, Wat64] and is given by : y(x) P n t n e jjx x n jj 2 2h 2 P n e jjx x n jj 2 2h 2 (53) It has been rediscovered in the context of neural networks[Spe90, SH92] The above expression can be looked upon as an expansion in normalized radial basis functions with the expansion ....
G. S. Watson. Smooth regression analysis. Sankhya: The Indian Journal of Statistics, Series A 26:359-372, 1964.
Nonparametric and Semiparametric Estimation and Testing - Pinkse (1994) (Correct)
....x is the point at which we wish to estimate m, then it makes sense to presume that m is large at x, also, provided of course that m is continuous. One may thus consider a weighted average of the Y i s, giving greater weight to 16 the ones that have X i that are close to x. Nadaraya (1964) and Watson (1964) proposed to define m(x) as the ratio of r(x) upon f(x) with r(x) 1 Nh # i k h (x X i )Y i , and f(x) defined as before. The denominator term is needed, because r(x) estimates r(x) m(x)f(x) rather than m(x) itself. r(x) is generally a consistent estimate of r(x) such that ....
Watson, G.S. (1964), Smooth Regression Analysis, Sankhya Series A 26, 359--372.
Feasible Multivariate Nonparametric Regression Estimation Using.. - Pinkse (1999) (Correct)
....giving an estimate of m. Since d x 1, the dimension of X i , g (Z i ) is less than d x d z , the resulting estimator of m also generally converges at a faster rate than does a. All nonparametric regression estimators used are nonparametric (Nadaraya Watson, see Nadaraya, 1964, and Watson, 1964) kernel regression estimators. The unconstrained Nadaraya Watson estimator of a is a(x, z) 1 nh d b g # n i=1 k hg (x X i )k hg (z Z i )Y i 1 nh d b g # n i=1 k hg (x X i )k hg (z Z i ) 2) with d b = d x d z , h g the practitioner chosen bandwidth, k hg (u) ....
Watson, G.S. (1964), "Smooth regression analysis," Sankhya A26, 359--372.
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Watson, G.S. (1964), "Smooth Regression Analysis," Sankhya, Series A, 26, pp. 359-372.
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Watson, G.S. (1964) "Smooth regression analysis", Sankhya, Series A, 26, 359-72.
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Watson, G.S. (1964), "Smooth Regression Analysis," Sankhya, Series A, 26, pp. 359-372.
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G.S. Watson. Smooth regression analysis. Sankhya Series A, 26:359-- 372, 1964.
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Watson, G.S. (1964). Smooth regression analysis. Sankhya 26:15, 175-184.
Kernel-Based Reinforcement Learning in Average-Cost Problems - Ormoneit, Glynn (2000) (2 citations) (Correct)
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G. S. Watson, "Smooth regression analysis," Sankhy~a Series A, vol. 26, pp. 359--372, 1964.
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G.S. Watson. Smooth regression analysis. Sankhya: The Indian Journal of Statsitics Series A, 26:359--372, 1964.
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Watson, G.S. (1964), Smooth Regression Analysis, Sankhya, Series A, 26, 359-372.
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WATSON, G. S. Smooth regression analysis. Sankhy a 26 (1964), 101--116.
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Watson, G.S. (1964). Smooth regression analysis. Sankhya Ser. A, 26, 359-372. 28 Figure captions.
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WATSON, G.S. (1964), Smooth regression analysis. Sankhy A, 26, 359-372. 31
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Watson, G.S., 1964, Smooth regression analysis, Sankhya, series A, 26, 359-372.
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G.S. Watson (1964). Smooth regression analysis. Sankhya, Ser. A, 26, 359-372.
Local Likelihood Density Estimation and Value at Risk - Gourieroux, Jasiak (2000) (Correct)
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Watson, G. (1964) : "Smooth Regression Analysis", Sankhia, Series A, 26, 359 - 372.
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G. S. Watson, "Smooth regression analysis," Sankhya Series A, vol. 26, pp. 359--372, 1964.
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