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The notion of statistical convergence was extended to    $\mathfrak{I}$  I -convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the notion of statistically    $\mathfrak{A}^{\mathfrak{I}}$  A I -Cauchy and statistically    $\mathfrak{A}^{\mathfrak{I}^{\ast }}$  A I ∗ -Cauchy summability via the notion of ideal. We obtain some relations between them and prove that under certain conditions statistical    $\mathfrak{A}^{\mathfrak{I}}$  A I -Cauchy and statistical    $\mathfrak{A}^{\mathfrak{I}^{\ast }}$  A I ∗ -Cauchy summability are equivalent. Moreover, we give some Tauberian theorems for statistical    $\mathfrak{A}^{\mathfrak{I}}$  A I -summability.

On statistical $\mathfrak{A}$-Cauchy and statistical $\mathfrak{A}$-summability via ideal