On Time-Reversal Imaging by Statistical Testing

This letter is focused on the design and analysis of computational wideband time-reversal imaging algorithms, designed to be adaptive with respect to the noise levels pertaining to the frequencies being employed for scene probing. These algorithms are based on the concept of cell-by-cell processing and are obtained as theoretically-founded decision statistics for testing the hypothesis of single-scatterer presence (absence) at a specific location. These statistics are also validated in comparison with the maximal invariant statistic for the proposed problem.Comment: Reduced form accepted in IEEE Signal Processing Letter

Testing for threshold effects in regression models

In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function. The article provides an alternative, novel method that can be used to establish the asymptotic null distribution, even when the usual quadratic approximation is intractable. We illustrate the usefulness of our approach in the examples of the maximum score estimation, maximum likelihood estimation, quantile regression, and maximum rank correlation estimation. We establish consistency and local power properties of the test. We provide some simulation results and also an empirical application to tipping in racial segregation. This article has supplementary materials online.

Measuring Intratemporal and Intertemporal Substitutions When Both Income and Substitution Effects Are Present: The Role of Consumer Durables

Hall (1988) estimates the intertemporal substitutability for nondurable goods economically and statistically insignificant. Ogaki and Reinhart (1998) introduce the service flow from durable goods using within-period-nonseparable homothetic preference specification. They estimate the intertemporal substitutability significant - around 0.4, and the intratemporal substitutability greater than one. I show that homotheticity induces a surprisingly dramatic statistical bias in the estimates of the intratemporal and intertemporal substitutions. Using aggregate consumption data, I discover that the estimate of the intertemporal substitutability is economically quite negligible - on the order of 0.04, a magnitude close to Hall’s original estimate. In addition, I estimate the intratemporal substitutability between nondurable goods and service flow from the stock of consumer durable goods economically small as well - around 0.18. In addition, I find potent support in favor of nonhomotheticity, with nondurable goods being necessities and durable goods luxuries. Despite that, due to the secular decline of the rental cost, the budget share of consumer durable goods appears trendless.

Statistical signal processing of nonstationary tensor-valued data

Real-world signals, such as the evolution of three-dimensional vector fields over time, can exhibit highly structured probabilistic interactions across their multiple constitutive dimensions. This calls for analysis tools capable of directly capturing the inherent multi-way couplings present in such data. Yet, current analyses typically employ multivariate matrix models and their associated linear algebras which are agnostic to the global data structure and can only describe local linear pairwise relationships between data entries. To address this issue, this thesis uses the property of linear separability -- a notion intrinsic to multi-dimensional data structures called tensors -- as a linchpin to consider the probabilistic, statistical and spectral separability under one umbrella. This helps to both enhance physical meaning in the analysis and reduce the dimensionality of tensor-valued problems. We first introduce a new identifiable probability distribution which appropriately models the interactions between random tensors, whereby linear relationships are considered between tensor fibres as opposed to between individual entries as in standard matrix analysis. Unlike existing models, the proposed tensor probability distribution formulation is shown to yield a unique maximum likelihood estimator which is demonstrated to be statistically efficient. Both matrices and vectors are lower-order tensors, and this gives us a unique opportunity to consider some matrix signal processing models under the more powerful framework of multilinear tensor algebra. By introducing a model for the joint distribution of multiple random tensors, it is also possible to treat random tensor regression analyses and subspace methods within a unified separability framework. Practical utility of the proposed analysis is demonstrated through case studies over synthetic and real-world tensor-valued data, including the evolution over time of global atmospheric temperatures and international interest rates. Another overarching theme in this thesis is the nonstationarity inherent to real-world signals, which typically consist of both deterministic and stochastic components. This thesis aims to help bridge the gap between formal probabilistic theory of stochastic processes and empirical signal processing methods for deterministic signals by providing a spectral model for a class of nonstationary signals, whereby the deterministic and stochastic time-domain signal properties are designated respectively by the first- and second-order moments of the signal in the frequency domain. By virtue of the assumed probabilistic model, novel tests for nonstationarity detection are devised and demonstrated to be effective in low-SNR environments. The proposed spectral analysis framework, which is intrinsically complex-valued, is facilitated by augmented complex algebra in order to fully capture the joint distribution of the real and imaginary parts of complex random variables, using a compact formulation. Finally, motivated by the need for signal processing algorithms which naturally cater for the nonstationarity inherent to real-world tensors, the above contributions are employed simultaneously to derive a general statistical signal processing framework for nonstationary tensors. This is achieved by introducing a new augmented complex multilinear algebra which allows for a concise description of the multilinear interactions between the real and imaginary parts of complex tensors. These contributions are further supported by new physically meaningful empirical results on the statistical analysis of nonstationary global atmospheric temperatures.Open Acces

The EU demand for imports of virgin olive oil

This paper has analysed the import demand for virgin olive oil in the EU and more precisely in the Italian market, as it concentrates more than 80% of EU imports, aiming to determine the relative position of Mediterranean EU and non-EU countries exports and their degree of substitutability or complementarity. The methodology used is based on the specification of a Threshold Almost Ideal Demand System in which special attention has been paid to the stochastic properties of the series involved. In an empirical context, the paper has aimed to provide a set of import demand elasticities that can be useful in trade models. Results point to Spain as the leader in the Italian virgin olive oil market. It is expected that this position will be maintained in the future. Greece has improved its relative position after its accession into the EU. However, imports coming from Greece are highly dependent on the situation in Spain. Tunisia has good potential for future exports development as a consequence of new perspectives of trade liberalisation taking into account its relative position in the Italian market, in spite that its exports are currently constrained due to existing quotas.Olive oil, Italy, elasticities, imports, TAIDS, Demand and Price Analysis, International Relations/Trade,