A kernel mode estimate under random left truncation and time series model: asymptotic normality

Let \(\left\{ Y_{N}, N\ge 1\right\} \) be a sequence of random variables of interest and \(\left\{ T_{N}, N\ge 1\right\} \) be a sequence of truncating variables. For a given \(n-\)sample \(\left( n\le N\right) \) of truncated replicates of \(Y\) fulfilling the \(\alpha -\)mixing condition, we establish asymptotic normality and construct confidence intervals for a proposed kernel mode estimator (say, \(\widehat{\theta }_n\)) of the true mode \(\theta \) of \(Y\).