Non-parametric regression with correlated errors using wavelets / Regressão não-paramétrica com erros correlacionados via ondaletas.

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

In this thesis, rates of convergence to zero are obtained for the estimation risk, for non-parametric regression using wavelets, when the errors are correlated. Four non-parametric regression methods using wavelets, with un-equally spaced design are studied in the presence of correlated errors, that come from stochastic processes. Conditions on the errors and adaptations to the procedures are presented, so that the estimators achieve quasi-minimax rates of convergence. Whenever is possible, rates of convergence are obtained for the estimators in the domain of the function, under mild conditions on the function to be estimated, on the design and on the error correlation. Through simulation studies, the behavior of some of the proposed methods is evaluated, when used on finite samples. Generally, it is suggested to use one of the studied methods, however applying thresholds by level. Since the estimation of the detail coecients can be dicult in some cases, it is also proposed a general semi-parametric iterative procedure, for wavelet methods in the presence of time-series errors.

ASSUNTO(S)

erros em séries temporais wavelets time-series errors lifting autocorrelation semi-parametric estimation regressão não-paramétrica estimação semi-paramética ondaletas adaptativas warped wavelets lifting ondaletas ondaletas deformadas autocorrelação non-parametric regression design-adapted wavelets

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