On Portfolio Selection: Improved Covariance Matrix Estimation for Swedish Asset Returns

Christoffer Bengtsson

Handledare: Jan Holst

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

When treating cancer it can be considered important to estimate the growth rate of the tumour. Of basic interest in this context is to estimate the time for the DNA synthesis, i.e. the time it takes for the DNA in the nucleus of the cell to duplicate, Ts.
Using a bromodeoxyuridine (BrdUrd)-DNA flowcytometry (FCM)-method it is possible to measure the relative DNA content in the cell and separate the cells in the DNA synthesis phase at time zero from the rest of the population. The DNA distributions for these cells can then be followed through the cell cycle.
An established way to describe the movement through the DNA synthesis phase is the relative movement curve (RM). When all BrdUrd-labelled DNA is replicated the RM value should theoretically reach one and then remain there. Since this is not normally the case in practice, the interpretation of Ts is the time when the RM curve reaches its maximum and local polynomial kernel regression is used to estimate the derivative of the curve.
A simple Markov model approach to the estimation of Ts is also suggested. A state in the Markov model corresponds to an interval of DNA content. Divided BrdUrd-labelled cells are moved back to the last state and an absorbing state is created. The intensity matrix will contain the estimated rates of the DNA replication and when an initial DNA distribution is estimated the time to absorption and a distribution for that time are estimated. Ts will be the estimated mean time to absorption.