Abstract We propose a new method, the confidence interval (CI) to select valid instruments from larger set of potential for instrumental variable (IV) estimation causal effect an exposure on outcome. Invalid are such that they fail exclusion conditions and enter model as explanatory variables. The CI method is based CIs per instrument effects estimates selects largest group with all overlapping...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...