You can't use REST API to filter list view (for exemple your SPView: /TestList/AllItems.aspx)
To filter list view you should use CAML query (in the list settings, you could edit your views, and ADD filter to fields of your list). (ou can group, and do operation like count/sum/avarage ....). The user will not view this filter (so give to it a good title).
This is the best way to filter a view, and it's simple. You can do this simply by using the SharePoint UI (List Settings => Views => Clic on your view To edit it => see Filter section)
Or you can do this programmatically (by using the property Query) and Build your own SPQuery. (to build SPQuery there is a lot of doc/tuto on internet)
If this solution is not appropriate, you could use REST API yes. But you must create your own application page, Build a custom logic to render fields Data. And use REST API to get your data. Using REST API you can Filter data. But when you query the list you have to use GET protocol with specific parameter in URL. THis will help you to understand the logic to build filter with REST API : query operations in SharePoint REST
But with this solution, you have to manage everything by hand (paginate query to avoid threshold list, the Quick edit, .....).
It depend on your need and if you have times.