Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

We introduce a general class of conditional U-statistics and present sufficient conditions for their universal consistency in rth mean. It is shown that under mild assumptions on the smoothing ...

We propose a group sequential method based on the sequential conditional probability ratio test and show that it has the conservatism desired in practice. We also propose calculating the discordant ...