<b>Sample Size Determination for Subsampling in the Analysis of Big Data, Multiplicative models for confidence intervals and Free-Knot changepoint models</b>

<p dir="ltr">We studied the relationship between subsample size and the accuracy of resulted estimation under big data setup.</p><p dir="ltr">We also proposed a novel approach to the construction of confidence intervals based on improved concentration inequalities.</p><p dir="ltr">Lastly, we studied irregular change-point models using free-knot splines.</p>