Indeed, you are correct.
In certain accents, history, hotel, etc. are pronounced with an h sound. In those accents, a should be used. In other accents, such as my own, it is pronounced without an h sound, and therefore starts with a vowel. In that accent, it would be correct for one to say an.
Queen Elizabeth II is one such person who could correctly say an historic event. President Obama is one such person who could correctly say a historic event.
In writing, it doesn't really matter which one is used.
You find both accusative pronouns (me/him/her/them) and nominative pronouns (I/he/she/they) in this syntactic position in standard English. The forms with the nominal genitive pronouns (mine/yours/hers etc.) are a red herring because they stand for something possessed rather than the person themself.
The traditional rule for comparison with a person is that you must use nominative. However, according to my research, accusative is more common.
I searched the Corpus of Contemporary American English for this syntactic structure, followed by a comma or a period to ensure we are not looking for cases like faster than he is, with a verb following the pronoun, in which case nominative is obligatory.
There were 1046 results for the accusative pronouns and 450 for nominative pronouns, more than 2 to 1 in favor of accusative pronouns—the “traditionally wrong” form. Both forms are standard, so my advice to a writer choosing between these forms is to consider that the “traditionally correct” form is unimpeachably correct but a bit formal. Choose the form that best matches tone and formality level of your writing.
For the curious, the queries looked like this:
[jjr*] than me|him|her|us|them .|,
[jjr*] than I|he|she|we|they .|,
where[jjr*] means any comparative adjective.
Update 2011-05-23
Using the new Google Book Corpus search, I was able to construct a Google ngrams-like graph comparing these usages over time, using these two queries: accusative, nominative:
As you can see, until the late 1980s, the formal usage was more common than the informal usage. Since then, however, accusative has very rapidly eclipsed nominative, even in this corpus, which represents professionally published works.
Best Answer
Frequency is a noun, and you want to modify the verb phrase makes purchases, so you want an adverbial phrase or clause. We can provide this with at which or with which:
We could also replace it the related adverb frequently
There are other variations, but these are the two that make the least change to the original.