In the common nonparametric regression model the problem of testing for a specific parametric form of the variance function is considered. Recently Dette and Hetzler (2008) proposed a test statistic, which is based on an empirical process of pseudo residuals. The process converges weakly to a...

Mortgage terminations arise because borrowers exercise options. This paper investigates the apparently irrational behavior of those borrowers who do not terminate their mortgages even when the exercise value of the option is deeply in the money. We develop an option-based empirical model to...

Let f, g be two Hilbert-space-valued martingales such that g is differentially subordinate to f. The paper contains the proof of the estimate ‖g‖p,∞≤2p(p+1)p−1‖f‖p,∞,1p∞. The constant is shown to be of optimal order for p→∞ and for p→1. Related results for transforms of...

Suppose that f is a martingale taking values in a Banach space B and g is its transform by a deterministic sequence of numbers in {−1,1}, such that supn‖gn‖≥1 almost surely. We show that a certain family of Φ-estimates for f holds true if and only B is a Hilbert space.

Let X be a nonnegative martingale, let H be a predictable process taking values in [−1,1] and let Y be an Itô integral of H with respect to X. We establish the bound ‖supt≥0|Yt|‖1≤3‖supt≥0Xt‖1 and show that the constant 3 is the best possible.

Bounds on the order of magnitude of sums of negative powers of integrated processes are derived.

Mortgage terminations arise because borrowers exercise options. This paper investigates the apparently irrational behavior of those borrowers who do not terminate their mortgages even when the exercise value of the option is deeply in the money. We develop an option-based empirical model to...

We outline a general paradigm for constructing asymptotically distribution-free (ADF) goodness-of-fit tests, which can be regarded as a generalization of Khmaladze (1993). This is achieved by a nonorthogonal projection of a class of functions onto the ortho-complement of the extended tangent...

We describe how to test the null hypothesis that errors from two parametrically specified regression models have the same distribution versus a general alternative. First we obtain the asymptotic properties of test-statistics derived from the difference between the two residual-based empirical...