We have Exchange 2013 on-premise with In-Place Archives hosted in Office365.  I want to run get-mailboxstatistics against my hosted archive to check out statistics on the user of the archives.  

I've connected to O365 with a new-pssession and imported the msonline module in PowerShell.

However, I get this error:

[PS] C:\Windows\system32>Get-Mailboxstatistics blahblahblah -archive

"The user 'blah blah blah' has a cloud-based archive. Currently, you can't run Get-MailboxStatistics -Archive on a
cloud-based archive."

Any ideas?

What exact steps are you using to connect to ExO?

Should be something like:

$Cred = Get-Credential

$s = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell -Credential $cred -Authentication Basic AllowRedirection

Import-PSSession $s

Hi,

Please refer to Andy's suggestion to connect to Exchange Online using remote Windows PowerShell or follow the arctile below:

https://technet.microsoft.com/en-us/library/JJ984289%28v=EXCHG.150%29.aspx?f=255&MSPPError=-2147217396

If it still not work, please run the following command in Exchange 2013 on-premises server EMS to have a try:

Get-Mailbox -Identity blahblahblah -archive

Get-Mailboxstatistics blahblahblah -archive

Regards,