The unnamed protagonist in Charlotte Perkins Gilman's short story "The Yellow Wallpaper" can certainly be described as an unreliable narrator. Therefore, one can use many different thesis statements to examine and define this for an essay.The following provides one example of a thesis statement where one can examine the narrator's unreliability.
Given that the speaker admits to her "ailment," one could justify that her mental deficiency makes her an unreliable narrator. The fact that her mental ability is diminished supports this. Her "temporary nervous depression--a slight hysterical tendency" proves that readers can justifiably question her motives and story.
A thesis statement which supports this is: The speaker in Gilman's short story "The Yellow Wallpaper" can be justified as an unreliable narrator based upon her sole admittance that she functions with "slight hysterical" tendencies.
Another example which supports the narrator's unreliability is the fact that she speaks with one-sided concern. Everything about the story revolves around her and her interpretations of what others are doing and thinking. Her story remains one-sided offering only her admittedly twisted thoughts on her situation.