Despite substantial criticism, variants of the capital asset pricing model (CAPM) remain to this day the primary statistical tools for portfolio managers to assess the performance of financial assets. In the CAPM, the risk of an asset is expressed through its correlation with the market, widely...

Functional principal components (FPC’s) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC’s to be used in a specific procedure has attracted a fair amount of attention, and a number...

In this work, we extend our study in Chochola et al. [7] and propose some robust sequential procedure for the detection of structural breaks in a Functional Capital Asset Pricing Model (FCAPM). The procedure is again based on M-estimates and partial weighted sums of M-residuals and...

Some robust sequential procedures for the detection of structural breaks in the Capital Asset Pricing Model (CAPM) are proposed and studied. Most of the existing procedures for this model are based on ordinary least squares (OLS) estimates. Here we propose a class of cumulative sum (CUSUM)-type...

Motivated by our earlier work on change-point analysis we prove a number of limit theorems for increments of renewal counting processes, or the corresponding first passage times. The starting point of the increments is deterministic as well as random, a typical example being the first stopping...

We obtain a lower bound for the rate of approximation of bootstrapped empirical processes with Brownian bridges. Our result corresponds to the optimality of the Komlós et al. (1975, 1976, Z. Wahrsch. Verw. Gebiete 32, 111-131; 34, 33-58) approximation of empirical processes.

Let {(Xi,Yi)}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1=y)=0 for all y. Put Mn=Mn(Ln)=max0[less-than-or-equals, slant]k[less-than-or-equals, slant]n-Ln(Xk+1+...+Xk+Ln)Ik,Ln, where Ik,l=I{Yk+1[less-than-or-equals, slant]...[less-than-or-equals, slant]Yk+l} denotes the...

For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results...