Motivated by interval/region prediction in nonlinear time series, we propose a minimum volume predictor (MV-predictor) for a strictly stationary process. The MV-predictor varies with respect to the current position in the state space and has the minimum Lebesgue measure among all regions with...

We consider a conditional empirical distribution of the form Fn(C ∣ x)=∑nt=1 ωn(Xt−x) I{Yt∈C} indexed by C∈ ℓ, where {(Xt, Yt), t=1, …, n} are observations from a strictly stationary and strong mixing stochastic process, {ωn(Xt−x)} are kernel weights, and ℓ is a class of...

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed...

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed...

We consider a conditional empirical distribution of the form Fn(C | x)=[summation operator]nt=1 [omega]n(Xt-x) I{Yt[set membership, variant]C} indexed by C[set membership, variant], where {(Xt, Yt), t=1, ..., n} are observations from a strictly stationary and strong...

This paper discusses a universal approach to the construction of confidence regions for level sets {h(x)≥0}⊂Rq of a function h of interest. The proposed construction is based on a plug-in estimate of the level sets using an appropriate estimate ĥn of h. The approach provides finite sample...

Bahadur-Kiefer approximations for generalized quantile processes as defined in Einmahl and Mason (1992) are given which generalize results for the classical one-dimensional quantile processes. An as application we consider the special case of the volume process of minimum volume sets in classes...

This paper analyzes a data mining/bump hunting technique known as PRIM [1]. PRIM finds regions in high-dimensional input space with large values of a real output variable. This paper provides the first thorough study of statistical properties of PRIM. Amongst others, we characterize the output...

Multivariate mode hunting is of increasing practical importance. Only a few such methods exist, however, and there usually is a trade-off between practical feasibility and theoretical justification. In this paper we attempt to do both. We propose a method for locating isolated modes (or better,...