Summary
Consider the standard linear modely i =z i β+e i ,i=1, 2,...,n, where zi denotes theith row of ann x p design matrix,β∈ℝp is an unknown parameter to be estimated ande i are independent random variables with a common distribution functionF. The least absolute deviation (LAD) estimate\(\tilde \beta \) of β is defined as any solution of the minimization problem
In this paper Bahadur type representations are obtained for\(\tilde \beta \) under very mild conditions onF near zero and onz i,i=1,...,n. These results are extended to the case, when {e i} is a mixing sequence. In particular the results are applicable when the residualse i form a simple autoregressive process.
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Babu, G.J. Strong representations for LAD estimators in linear models. Probab. Th. Rel. Fields 83, 547–558 (1989). https://doi.org/10.1007/BF01845702
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DOI: https://doi.org/10.1007/BF01845702
Keywords
- Linear Model
- Absolute Deviation
- Minimization Problem
- Unknown Parameter
- Mathematical Biology