Long-Run Structural Modelling

The paper develops a general framework for identification, estimation, and hypothesis testing in cointegrated systems when the cointegrating coefficients are subject to (possibly) non-linear and cross-equation restrictions, obtained from economic theory or other relevant a priori information. It provides a proof of the consistency of the maximum likelihood (ML) estimators, establishes the relative rates of convergence of the ML estimators of the short-run and the long-run parameters, and derives their asymptotic distribution; thus generalizing the results already available in the literature for the linear case. The paper also develops tests of the over-identifying (possibly) non-linear restrictions on the cointegrating vectors. The estimation and hypothesis testing procedures are applied to an Almost Ideal Demand System estimated on U.K. quarterly observations. Unlike many other studies of consumer demand this application does not treat relative prices and real per capita expenditures as exogenously given.Cointegration, identification, testing non-linear restrictions, consistency, asymptotic distribution, Almost Ideal Demand Systems

Robust nonparametric detection of objects in noisy images

We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathematical formalism of our method and explore important connections to the mathematical theory of percolation and statistical physics. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behavior of the method, but also a finite sample performance of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049. Link to the abstract at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd

On the estimation and testing of functional-coefficient linear models

In this paper we investigate the estimation and testing of the functional coefficient linear models under dependence, which includes the functional coefficient autoregressive model of Chen and Tsay (1993). We use local linear smoothing to estimate the coefficient functions of a functional-coefficient linear model, prove their uniform consistency, and derive their asymptotic distributions in terms of Gaussian processes. From these distributions we can obtain some tests about coefficient functions and the model. Some simulations and a study of real data are reported.published_or_final_versio

A latent factor model for ordinal data to measure multivariate predictive ability of financial market movements

In this paper we develop a structural equation model with latent variables in an ordinal setting which allows us to test broker-dealer predictive ability of financial market movements. We use a multivariate logit model in a latent factor framework, develop a tractable estimator based on a Laplace approximation, and show its consistency and asymptotic normality. Monte Carlo experiments reveal that both the estimation method and the testing procedure perform well in small samples. An empirical illustration is given for mid-term forecasts simultaneously made by two broker-dealers for several countries.structural equation model, latent variable, generalised linear model, factor analysis, multinomial logit, forecasts, LAMLE, canonical correlation

Can One Estimate the Conditional Distribution of Post-Model-Selection Estimators?

We consider the problem of estimating the conditional distribution of a post-model-selection estimator where the conditioning is on the selected model. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion like AIC or by a hypothesis testing procedure) and second estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate this distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower bounds on the performance of estimators for this distribution. Similar impossibility results are also obtained for the conditional distribution of linear functions (e.g., predictors) of the post-model-selection estimator.Inference after model selection, Post-model-selection estimator, Pre-test estimator, Selection of regressors, Akaikeis information criterion AIC, Model uncertainty, Consistency, Uniform consistency, Lower risk bound