Japanese dependency structure is usually represented by relationships between phrasal units called bunsetsus. One of the biggest problems with dependency structure analysis in spontaneous speech is that clause boundaries are ambiguous. This paper describes a method for detecting the boundaries of quotations and inserted clauses and that for improving the dependency accuracy by applying the detected boundaries to dependency structure analysis. The quotations and inserted clauses are determined by using an SVM-based text chunking method that considers information on morphemes, pauses, fillers, etc. The information on automatically analyzed dependency structure is also used to detect the beginning of the clauses. Our evaluation experiment using Corpus of Spontaneous Japanese (CSJ) showed that the automatically estimated boundaries of quotations and inserted clauses helped to improve the accuracy of dependency structure analysis.