I found a couple of articles with some stats http://www.cmo.com/content/cmo-com/home/articles/2013/11/4/15_Stats_LinkedIn.html
BUT nothing specifically comparing landing page results with Linked In.
FWIW my view on all social media advertising and marketing is that its purpose is to present your brand to folks inside that walled garden. I judge success by how many viewers move off the social page and onto our clients' website [this could be a landing page].
We wrote an e book about how to do this from Facebook. This has been very successful in gaining subscribers to our client Rowperfect.co.uk email newsletter while continuing to extend reach and likers inside FB.
Let me know if I can help further.
I would be pleased to answer if you'd add some clarifications. What kind of marketing on LinkedIN? Content marketing? Paid Promotion? And, since I've heard 100s of them, what is your definition of a landing page? A conversion-specific "squeeze" page? Or a page holding a valuable piece of content meant to whet the visitors information appetite?
It's hard to fully answer that question without more detail. In general, if you are advertising on Linkedin, I recommend you send them to a landing page on your website directly from the Linkedin ad. In our testing, it's worked the best.