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...

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...

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...

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,...