Dipartimento di Scienze Economiche e Statistichehttp://hdl.handle.net/10556/15412018-07-24T19:15:47Z2018-07-24T19:15:47ZBias-corrected inference for multivariate nonparametric regression: model selection and oracle propertyGiordano, FrancescoParrella, Maria Luciahttp://hdl.handle.net/10556/21282016-07-15T00:08:16Z2014-01-01T00:00:00ZBias-corrected inference for multivariate nonparametric regression: model selection and oracle property
Giordano, Francesco; Parrella, Maria Lucia
The local polynomial estimator is particularly affected by the curse of di-
mensionality. So, the potentialities of such a tool become ineffective for large dimensional
applications. Motivated by this, we propose a new estimation procedure based on the local
linear estimator and a nonlinearity sparseness condition, which focuses on the number
of covariates for which the gradient is not constant. Our procedure, called BID for
Bias-Inflation-Deflation, is automatic and easily applicable to models with many covariates
without any additive assumption to the model. It simultaneously gives a consistent
estimation of a) the optimal bandwidth matrix, b) the multivariate regression function and
c) the multivariate, bias-corrected, confidence bands. Moreover, it automatically identify
the relevant covariates and it separates the nonlinear from the linear effects. We do not
need pilot bandwidths. Some theoretical properties of the method are discussed in the
paper. In particular, we show the nonparametric oracle property. For linear models, the
BID automatically reaches the optimal rate Op(nā1/2), equivalent to the parametric case.
A simulation study shows a good performance of the BID procedure, compared with its
direct competitor.
2014-01-01T00:00:00ZGRID for model structure discovering in high dimensional regressionGiordano, FrancescoLahiri, Soumendra NathParrella, Maria Luciahttp://hdl.handle.net/10556/21272016-07-15T00:08:13Z2014-01-01T00:00:00ZGRID for model structure discovering in high dimensional regression
Giordano, Francesco; Lahiri, Soumendra Nath; Parrella, Maria Lucia
Given a nonparametric regression model, we assume that the number of
covariates d ā ā but only some of these covariates are relevant for the model. Our goal
is to identify the relevant covariates and to obtain some information about the structure of
the model. We propose a new nonparametric procedure, called GRID, having the following
features: (a) it automatically identifies the relevant covariates of the regression model, also
distinguishing the nonlinear from the linear ones (a covariate is defined linear/nonlinear
depending on the marginal relation between the response variable and such a covariate);
(b) the interactions between the covariates (mixed effect terms) are automatically identified,
without the necessity of considering some kind of stepwise selection method. In
particular, our procedure can identify the mixed terms of any order (two way, three way,
...) without increasing the computational complexity of the algorithm; (c) it is completely
data-driven, so being easily implementable for the analysis of real datasets. In particular,
it does not depend on the selection of crucial regularization parameters, nor it requires the
estimation of the nuisance parameter 2 (self scaling). The acronym GRID has a twofold
meaning: first, it derives from Gradient Relevant Identification Derivatives, meaning that
the procedure is based on testing the significance of a partial derivative estimator; second,
it refers to a graphical tool which can help in representing the identified structure of the
regression model. The properties of the GRID procedure are investigated theoretically.
2014-01-01T00:00:00ZA general coalition structure: some equivalence resultsBimonte, Giovannahttp://hdl.handle.net/10556/21192016-07-15T00:08:14Z2013-01-01T00:00:00ZA general coalition structure: some equivalence results
Bimonte, Giovanna
The formation of coalition may imply some theoretical difficulties,
such as costs arising from forming a coalition or sharing information
among agents. In this paper we will assume that only a subset S of
the set of all possible coalitions in an economy is the set of admissible
coalitions. We define the S-core concept, as in Hervs-Moreno. We will
extend to a model with both uncertainty and asymmetric informations
the results showed in Okuda and Shitovitz.
2013-01-01T00:00:00ZNew insights on the relationships between geographic and institutional distance in research collaborations: a long period analysisD'Amore, RosamariaIorio, Robertohttp://hdl.handle.net/10556/21182016-07-15T00:08:11Z2014-01-01T00:00:00ZNew insights on the relationships between geographic and institutional distance in research collaborations: a long period analysis
D'Amore, Rosamaria; Iorio, Roberto
This paper analyses the relationship between institutional and geographic distance in
scientific collaborations, evaluating the possible changes when a long period (sixteen
years) is taken into consideration and discussing the use of some alternative measures of
institutional distance. The main result, obtained by analysing the publications of the Italian
biotech firms, is that international publications present an higher institutional distance than
national papers, particularly in the early years, while there is no significant difference in
institutional distance between regional and extra-regional papers, suggesting that opposite
incentives are in action at different geographic scales and in different periods.
2014-01-01T00:00:00Z