2-level fractional factorial designs which are the union of non trivial regular designs
| dc.creator | Fontana, Roberto | |
| dc.creator | Pistone, Giovanni | |
| dc.date | 2007-10-31 | |
| dc.date.accessioned | 2026-07-07T08:39:42Z | |
| dc.date.available | 2026-07-07T08:39:42Z | |
| dc.description | Every fraction is a union of points, which are trivial regular fractions. To characterize non trivial decomposition, we derive a condition for the inclusion of a regular fraction as follows. Let $F = \sum_αb_αX^α$ be the indicator polynomial of a generic fraction, see Fontana et al, JSPI 2000, 149-172. Regular fractions are characterized by $R = \frac 1l \sum_{α\in \mathcal L} e_αX^α$, where $α\mapsto e_α$ is an group homeomorphism from $\mathcal L \subset \mathbb Z_2^d$ into $\{-1,+1\}$. The regular $R$ is a subset of the fraction $F$ if $FR = R$, which in turn is equivalent to $\sum_t F(t)R(t) = \sum_t R(t)$. If $\mathcal H = \{α_1 >... α_k\}$ is a generating set of $\mathcal L$, and $R = \frac1{2^k}(1 + e_1X^{α_1}) ... (1 + e_kX^{α_k})$, $e_j = \pm 1$, $j=1 ... k$, the inclusion condition in term of the $b_α$'s is % \begin{equation}b_0 + e_1 b_{α_1} + >... + e_1 ... e_k b_{α_1 + ... + α_k} = 1. \tag{*}\end{equation} % The last part of the paper will discuss some examples to investigate the practical applicability of the previous condition (*). This paper is an offspring of the Alcotra 158 EU research contract on the planning of sequential designs for sample surveys in tourism statistics. | |
| dc.description | Presented by R. Fontana at the DAE 2007 Conference, The University of Memphis, November 2, 2007 | |
| dc.identifier | https://arxiv.org/abs/0710.5838 | |
| dc.identifier | http://arxiv.org/abs/0710.5838 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141162 | |
| dc.subject | Methodology | |
| dc.title | 2-level fractional factorial designs which are the union of non trivial regular designs | |
| dc.type | text |