This research will investigate limit theorems for trimmed sums and self normalizing sums. Limit theorems for sums of random variables have been of great interest in probability theory for both their mathematical beauty and their enormous potential for applications. Major such application has been the use of Central Limit Theorem for estimation of the mean. The average of the observed values viz. the sample mean is generally a good estimator of this. However, it needs to be "trimmed" occasionally if the data is contaminated by outliers. The limit theory of such trimmed sums becomes quite complex, especially if the trimming is not fixed. If the normalizing constants are determined by the sample as well then the sums are called self normalizing. Self normalizing has great application potential since it requires minimum assumptions on the distribution of the sample.
