Nichtparametrische Analyse und Prognose von Zeitreihen

Michels, Paul

doi:10.1007/978-3-642-99765-5

Cited by 6 publications

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“…2 Bias of kernel regression estimates Collomb (1976Collomb ( , 1977Collomb ( , 1983obtains expressions for bias, variance and mean square error of kernel regression estimates for symmetric kernels and independent data (X;, 1';). Michels (1991Michels ( , 1992 extends these results without using these assumptions. He derives the expectation and the variance of the leading terms in the Taylor expansion for asymmetric kernel functions in the case of *-mixing data (X;, 1';), i = 1,... , n. Including terms up to second order he obtains the following approximation of the expectation of the kernel regression estimate:…”

Section: Introductionmentioning

confidence: 69%

“…For the asymptotic variance of J1.nK several authors (e.g. Robinson, 1983;Boente & Fraiman, 1990;Michels, 1991Michels, , 1992 obtain the approximation…”

Section: Ip(anb)-p(a)p(b)i~l/jtp(a)p(b)mentioning

confidence: 99%

“…The amount of calculation is reduced considerably when ..1.1 is determined by using equation (15) instead of(14). For an explicit determination of ..1.1 by means of(14) or (15) see Michels (1992). In the remainder of this section a more formal way of developing conditions on the free parameter ..1.1 is considered.…”

Section: Bias Reduction By Asymmetric Kernelsmentioning

confidence: 99%

“…46,Germany. regression function. The form (2) of kernel weights has been proposed by Nadaraya (1964) and Watson (1964).During the last two decades various asymptotic properties have been shown for the Nadaraya-Watson kernel estimate To minimize the number of references we refer to the monographs of Hardie (1990) and Michels (1992)and the references therein. Observe that the estimate J.L/(x)can be written as a fraction with numerator where fnK is the kernel density estimate proposed by Rosenblatt (1956).…”

Section: Introductionmentioning

confidence: 99%

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Asymmetric Kernel Functions in Non-Parametric Regression Analysis and Prediction

Michels¹

1992

The Statistician

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Non-parametric kernel and nearest neighbour estimates represent flexible alternatives to parametric modelling. For non-constant densities of the explanatory variables, kernel estimates are usually biased for finite samples, even in the case oflinear regression functions. This can be seen by looking at the asymptotic expression of the bias of kernel regression estimates derived under certain mixing conditions. In this paper bias reduction techniques using asymmetric kernel functions are suggested. In contrast to well-designed experiments, in environmental data analysis the positions of the design points are not under control, and therefore the measurements of the explanatory variables are arbitrarily scattered over the factor space in an unbalanced way. In this case the asymmetric kernel techniques outperform the usual symmetric kernel methods as demonstrated by an application of both methods to the relationship between the oxygen concentration and the temperature of river water. Furthermore the new methods lead to better predictions in an autoregressive time series model for air pollution measurements such as nitrogen dioxide and sulphur dioxide concentrations.

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Section: Introductionmentioning

confidence: 69%

“…For the asymptotic variance of J1.nK several authors (e.g. Robinson, 1983;Boente & Fraiman, 1990;Michels, 1991Michels, , 1992 obtain the approximation…”

Section: Ip(anb)-p(a)p(b)i~l/jtp(a)p(b)mentioning

confidence: 99%

Section: Bias Reduction By Asymmetric Kernelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations