On Empirical Likelihood and Non-parametric Pearson's Chi-square Statistic
نویسنده
چکیده
Owen (1988) showed that the non-parametric empirical likelihood ratio under a linear constrain has an asymptotic chi-square distribution, same as in the paramet-ric case. This fact can be used to form (non-parametric, asymptotic) conndence intervals. We suggest here to use the non-parametric version of the Pearson's chi-square statistic instead of the likelihood ratio to form conndence intervals. We show that under weaker conditions than Owen (1988), the non-parametric Pear-son's chi-square statistic has the same asymptotic chi-square distribution. It is of interest to study which method will produce better conndence intervals for small samples. Also we suggest it is important to study the above limit theorems for some non-linear constrain. This arise naturally from the study of censored data, it can help to form conndence intervals which are otherwise diicult.
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