The holiday shopping season is in the rearview mirror and retailers are just now beginning to look back on their performances.

In its typically cryptic press release, online seller (AMZN -0.17%) provided sparse details about the results of its just-completed holiday shopping season. The company revealed that the "Echo Dot and Fire TV Stick with Alexa Voice Remote were the #1 and #2 top-selling products across all categories on Amazon," and "in one week alone, more than four million people started Prime free trials or began paid memberships." Since the company doesn't report on the sales numbers of its devices or its Prime memberships, those numbers are essentially meaningless.

Amazon does, however, provide important information regarding the best sellers in a variety of categories and that can give investors insight into some of the companies that do business on the e-commerce behemoths website.

A Nerf N-Strike Elite Strongarm Blaster.

Hasbro made the list with the most purchased toy in the U.S. on Amazon's website. Image source: Hasbro.

Fire at will

Hasbro's Nerf N-Strike Elite Strongarm Blaster was the best-selling toy and game item in the U.S. on Amazon's online store.

This is good news for the global play-and-entertainment company, which was taken down last quarter by the same news that negatively affected the rest of the toy industry -- Toys R Us, the biggest toy store chain in the U.S., filed for bankruptcy. As a result, Hasbro lowered its guidance for the all-important holiday quarter, expecting revenue growth in a range of 4% to 7%. This was much lower than the consensus estimate of 11% growth, and the stock slumped 10%. 

Nerf was one of the franchise brands that was called out in the company's 2017 third-quarter results as helping drive an increase of 7% over the prior-year quarter. The news of strong online holiday sales via Amazon likely points to continued strength of the brand and bodes well for Hasbro's results.

The iRobot Roomba 650 self-piloting vacuum cleaner cleaning a wood floor.

The iRobot Roomba was a best-seller on Prime Day. Can it make a repeat performance for the holidays? Image source: iRobot.

Robotic vacuums

Earlier this year, robotic vacuum maker iRobot (IRBT 3.12%) revealed that it had sold more than twice as many self-piloting vacuums during Amazon's Prime Day 2017 as it had during the prior year's event -- which itself was twice as many as the year before. The Roomba 652 model was the best-selling robotic vacuum cleaner, as well as the top seller in floor care, and No. 2 among home and kitchen items. 

Being among the best sellers on the e-commerce site boosted iRobot's results. For its 2017 third quarter -- which included Prime Day -- iRobot reported revenue that increased 22% year over year and the company raised its forecast for the full year. 

While Amazon didn't single out iRobot in its holiday sales press release, it did say, "Robot vacuums were among the best-selling home items on over the holiday season." Judging by how well the company did during the Prime Day sale, this might just be a happy holiday for iRobot.

A television showing viewing choices on The Roku Channel.

Roku TV's were among the hottest sellers during Amazon's holiday sales. Image source: Roku.

Streaming sensation

Roku, Inc. (ROKU 1.00%) got its start by developing the first dedicated streaming player for Netflix, Inc. (NFLX 1.74%) in 2008. Since those humble beginnings, Roku has expanded to selling advertising on its platform and producing a number of different internet streaming devices.

During Amazon's holiday sales, two of the four top-selling TV's on Amazon were Roku models: the TCL 32-Inch 720p Roku Smart LED TV and the TCL 49-Inch 4K Ultra HD Roku Smart LED TV. This provides the company with future revenue possibilities as well. In its 2017 third quarter, Roku reported that its active accounts totaled 16.7 million, up 48% year over year. More importantly, more than half of the new accounts in the quarter came from licensed sources and the largest and fastest growing portion of those came from Roku TVs. "One in five smart TVs sold in the U.S. and Canada were licensed Roku TVs," reported Roku. 

Since Amazon doesn't reveal any specific numbers, we won't know how each of these companies fared during the holidays until each releases its own quarterly earnings report. However, making to the top of Amazon's best-sellers list is likely a positive sign for investors in Hasbro, iRobot, and Roku.