sparsistency

English

Etymology

Blend of sparse +‎ consistency

Noun

sparsistency (uncountable)

1. (statistics) Let $\mathbf {b}$ be a vector and define the support $\operatorname {supp} (\mathbf {b} )=\{i:\mathbf {b} _{i}\neq 0\}$ where $\mathbf {b} _{i}$ is the $i$th element of $\mathbf {b}$. Let ${\hat {\mathbf {b} }}$ be an estimator for $\mathbf {b}$. Then sparsistency is the property that the support of the estimator converges to the true support as the number of samples grows to infinity.
   • 2015, Edouard Ollier, Vivian Viallon, “Regression modeling on stratified data: automatic and covariate-specific selection of the reference stratum with simple $L_{1}$-norm penalties”, in arXiv‎^[1]:

     Its implementation can be done with available packages under a variety of models and, in the linear regression model, we show it is sparsistent under conditions similar to those ensuring sparsistency for an oracular version of the reference stratum strategy.

Related terms

• sparsistent