Local rank tests in a multivariate nonparametric relationship

Abstract

International audienc

Local and Global Rank Tests for Multivariate Varying-Coefficient Models

“…Note that, except h = 0.15, the test points to the local rank 2 at z = 1.2. Local rank smaller than 3 for larger values of z was also found in the same data set but using nonparametric model by Fortuna (2008). To complement Table 1, Table 4 presents the p-values for the local rank test at z = 1.…”

“…We shall apply this estimation procedure to estimate local and global ranks in the demand system constructed from the CEX and the ACCRA data sets. Related estimation of local ranks in a demand system given by a nonparametric model can be found in Fortuna (2008).…”

“…The global rank of the original (full) demand system is esti- can also be found in other work on ranks in demand systems: Lewbel (1991), Donald (1997) where variation in prices is ignored, and Fortuna (2008) where local ranks are considered. Note that Table 1 above is based on the interval [z min , z max ] = [0.911, 1.251] spanning the whole range of the values of Z i .…”

On Rank Estimation in Symmetric Matrices: The Case of Indefinite Matrix Estimators

“…The resulting EIG rank test is easy to formulate under stronger Assumptions (A), and becomes more involved when Assumptions (A * ) are used. Under Assumptions (A), the EIG rank test was already used, albeit implicitly, in Donald (1997) and Fortuna (2004). We state it here in general and also prove it under more general assumptions.…”

“…The aforementioned papers also discuss many situations where the rank estimation is of interest, for example, in the context of factor and state-space models, cointegration and the theory of demand systems. See also Anderson (1951), Camba-Mendez, Kapetanios, Smith and Weale (2003), Camba-Mendez and Kapetanios (2001), Donkers and Schafgans (2003), Lewbel (1991), Donald (1997), Fortuna (2004), Cook (2001, 2003) and others. The limiting covariance matrix C of M can have either a Kronecker product structure C = A ⊗ B or a general, non-Kronecker product structure.…”