In Anderson's short stories, the beginning often presents a problem or a state of being. In 'The Little Match Girl', the cold and poor start implies a theme of poverty and suffering. The end, where she dies, can be seen as a comment on the harshness of the world. So, to analyze themes, you need to consider how the beginning sets the stage for the theme, and how the end either resolves or emphasizes the theme. Sometimes, like in this story, the end may be a tragic statement on the theme that was introduced at the start.
Begin by looking at the mood at the start of Anderson's short stories. If it's a somber start, it could lead to a theme of melancholy or loss. The end then either deepens that feeling or offers a glimmer of hope. Take 'The Steadfast Tin Soldier'. It begins with the tin soldier's rather solitary existence, which could suggest a theme of perseverance in the face of loneliness. The end, where he melts away but is still remembered, can be interpreted as a theme of the endurance of the spirit even in the face of destruction. By comparing the start and end, we can uncover the deeper themes in his short stories.