WASHINGTON -- U.S. presidential adviser Stephen Miller peddled discredited theories about voter fraud during a round of TV appearances Sunday that won praise from his boss but brought no new evidence to light.

Miller mischaracterized research about wrongly registered voters and spread a debunked claim that busloads of Democrats came into New Hampshire and voted improperly in the November election. His Sunday morning performance on news shows earned him a "Good job!" on Twitter from President Donald Trump, who alleged days earlier that he lost New Hampshire in November only because "thousands" of people came by bus to vote against him.

A look at a few of the senior policy adviser's statements on ABC's "This Week."

MILLER: "I can tell you that this issue of busing voters in to New Hampshire is widely known by anyone who's worked in New Hampshire politics. It's very real, it's very serious. This morning on this show is not the venue for me lay out all the evidence."

The accusation that people from more liberal Massachusetts crossed state lines in buses and voted was made shortly before the election by Republican Chris Sununu, who won election as governor. Sununu quickly backed down, saying his talk about busloads of illegal voters was "more a figure of speech" -- in other words, not reality. Actual cases of voter fraud detected in New Hampshire have been in the single digits over recent elections.

After Miller's remarks, Fergus Cullen, chairman of the New Hampshire Republican Party for the 2008 election, lashed out.

"Miller makes false .magicbus claim, offers no proof," he tweeted. "Delusional. There are no bused-in voters." He also tweeted: "I will pay $1000 to 1st person proving even 1 out-of-state person took bus from MA 2 any NH polling place last Election Day."

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MILLER: "You have millions of people who are registered in two states or who are dead who are registered to vote. And you have 14 per cent of noncitizens, according to academic research, at a minimum, are registered to vote, which is an astonishing statistic."

THE FACTS: His claim about people with multiple voting registrations and registrations from beyond the grave is based on a Pew study that did not allege or illustrate voting fraud, and it was not about the 2016 election. Rather, the study, released in 2012 and based in part on 2008 results, was about outdated or otherwise inaccurate voter registration records. It pointed to sloppy record-keeping but nothing that would favour one party over the other.

David Becker, an author of the study, said it never found fraud. Moreover, he said voting integrity in 2016 was "better in this election than ever before."

Miller's claim about an "astonishing" number of non-citizens who are registered to vote is based on a study that has been disputed in academia and misrepresented in the political arena.

The study by Old Dominion University researchers did estimate that 14 per cent or more of noncitizens had registered to vote, but the methodology was challenged and the authors were upfront about the imprecision in their findings. As for how many non-citizens actually voted, their "best guess" was 6.4 per cent of them in 2008 and 2.2 per cent in 2010.

"There are many on the left side of that debate who have relentlessly sought to discredit our results and want to push the level of estimated non-citizen participation to zero," Jesse Richman, an associate professor of political science and international affairs and one of the authors, wrote. "On the right there has been a tendency to misread our results as proof of massive voter fraud, which we don't think they are."

He wrote that the study suggests "almost all elections in the US are not determined by non-citizen participation, with occasional and very rare potential exceptions."