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Global and local statistical properties of fixed-length nonparametric smoothers

Author

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  • Estela Bee Dagum

    (University of Bologna)

  • Alessandra Luati

    (University of Bologna)

Abstract

The main purpose of this study is to analyze the global and local statistical properties of nonparametric smoothers subject to a priori fixed length restriction. In order to do so, we introduce a set of local statistical measures based on their weighting system shapes and weight values. In this way, the local statistical measures of bias, variance and mean square error are intrinsic to the smoothers and independent of the data to which they will be applied on. One major advantage of the statistical measures relative to the classical spectral ones is their easiness of calculation. However, in this paper we use both in a complementary manner. The smoothers studied are based on two broad classes of weighting generating functions, local polynomials and probability distributions. We consider within the first class, the locally weighted regression smoother (loess) of degree 1 and 2 (L1 and L2), the cubic smoothing spline (CSS), and the Henderson smoothing linear filter (H); and in the second class, the Gaussian kernel (GK). The weighting systems of these estimators depend on a smoothing parameter that traditionally, is estimated by means of data dependent optimization criteria. However, by imposing to all of them the condition of an equal number of weights, it will be shown that some of their optimal statistical properties are no longer valid. Without any loss of generality, the analysis is carried out for 13- and 9-term lengths because these are the most often selected for the Henderson filters in the context of monthly time series decomposition.

Suggested Citation

  • Estela Bee Dagum & Alessandra Luati, 2002. "Global and local statistical properties of fixed-length nonparametric smoothers," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(3), pages 313-333, October.
    • Handle: RePEc:spr:stmapp:v:11:y:2002:i:3:d:10.1007_bf02509830
    DOI: 10.1007/BF02509830
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    References listed on IDEAS

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    1. Frederick R. Macaulay, 1931. "The Smoothing of Time Series," NBER Books, National Bureau of Economic Research, Inc, number maca31-1.
    2. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    3. Hardle, W. & Mammen, E., 1990. "Bootstarp Methods in Nonparametric Regression," LIDAM Discussion Papers CORE 1990049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Hardle, W. & Tsybakov, A., 1990. "Robust locally adaptive nonparametric regression," LIDAM Discussion Papers CORE 1990028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. McElroy, Tucker S. & Wildi, Marc, 2020. "The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions," Econometrics and Statistics, Elsevier, vol. 14(C), pages 112-130.
    2. Estela Bee Dagum & Alessandra Luati, 2009. "A Cascade Linear Filter to Reduce Revisions and False Turning Points for Real Time Trend-Cycle Estimation," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 40-59.

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