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Statistical inference on linear and partly linear regression with spatial dependence: parametric and nonparametric approaches

Thawornkaiwong, Supachoke (2012) Statistical inference on linear and partly linear regression with spatial dependence: parametric and nonparametric approaches. PhD thesis, The London School of Economics and Political Science (LSE).

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Abstract

The typical assumption made in regression analysis with cross-sectional data is that of independent observations. However, this assumption can be questionable in some economic applications where spatial dependence of observations may arise, for example, from local shocks in an economy, interaction among economic agents and spillovers. The main focus of this thesis is on regression models under three di§erent models of spatial dependence. First, a multivariate linear regression model with the disturbances following the Spatial Autoregressive process is considered. It is shown that the Gaussian pseudo-maximum likelihood estimate of the regression and the spatial autoregressive parameters can be root-n-consistent under strong spatial dependence or explosive variances, given that they are not too strong, without making restrictive assumptions on the parameter space. To achieve e¢ ciency improvement, adaptive estimation, in the sense of Stein (1956), is also discussed where the unknown score function is nonparametrically estimated by power series estimation. A large section is devoted to an extension of power series estimation for random variables with unbounded supports. Second, linear and semiparametric partly linear regression models with the disturbances following a generalized linear process for triangular arrays proposed by Robinson (2011) are considered. It is shown that instrumental variables estimates of the unknown slope parameters can be root-n-consistent even under some strong spatial dependence. A simple nonparametric estimate of the asymptotic variance matrix of the slope parameters is proposed. An empirical illustration of the estimation technique is also conducted. Finally, linear regression where the random variables follow a marked point process is considered. The focus is on a family of random signed measures, constructed from the marked point process, that are second-order stationary and their spectral properties are discussed. Asymptotic normality of the least squares estimate of the regression parameters are derived from the associated random signed measures under mixing assumptions. Nonparametric estimation of the asymptotic variance matrix of the slope parameters is discussed where an algorithm to obtain a positive deÖnite estimate, with faster rates of convergence than the traditional ones, is proposed.

Item Type: Thesis (PhD)
Additional Information: © 2012 Supachoke Thawornkaiwong
Library of Congress subject classification: H Social Sciences > HA Statistics
Sets: Departments > Economics
Supervisor: Robinson, Peter
URI: http://etheses.lse.ac.uk/id/eprint/620

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