Preheat oven to 350 degrees F (175 degrees C). Lightly grease and flour a 10-inch fluted tube pan.
Beat butter and sugar with an electric mixer in a large bowl until smooth. Beat first egg into butter until completely blended, then beat in vanilla extract with last egg; fold in bananas. Combine flour, baking powder, baking soda, and salt in a bowl. Stir flour mixture into creamed mixture alternately with yogurt, stirring until just combined. Fold in pecans and pour batter into prepared tube pan.
Bake in preheated oven until a toothpick inserted into cake comes out clean, about 50 minutes. Cool 10 minutes in pan before removing to a wire rack to cool completely. Dust with confectioner's sugar before serving.