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Abstract. The relevance-weighted likelihood function weights individual contributions to the likelihood according to their relevance for the inferential problem of interest. Consistency and asymptotic normality of the weighted maximum likelihood estimator were previously proved for independent sequences of random variables. We extend these results to apply to dependent sequences, and, in so doing,...
M-estimators and M-kernel estimators with a redescending ψ-function are not in general consistent. This is often handled by means of coupling the estimator to a consistent one. Coupling the estimator to the (inconsistent) starting point improves the jump preserving properties. However, the consistency depends heavily on the shape of the density of the residuals. This paper shows inconsistency under...
In this paper, we suggest a blockwise bootstrap wavelet to estimate the regression function in the nonparametric regression models with weakly dependent processes for both designs of fixed and random. We obtain the asymptotic orders of the biases and variances of the estimators and establish the asymptotic normality for a modified version of the estimators. We also introduce a principle to select...
In this article, we consider nonparametric regression analysis between two variables when data are sampled through a complex survey. While nonparametric regression analysis has been widely used with data that may be assumed to be generated from independently and identically distributed (iid) random variables, the methods and asymptotic analyses established for iid data need to be extended in the framework...
A sample selected from a single sampling frame may not represent adequatly the entire population. Multiple frame surveys are becoming increasingly used and popular among statistical agencies and private organizations, in particular in situations where several sampling frames may provide better coverage or can reduce sampling costs for estimating population quantities of interest. Auxiliary information...
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