In data anaysis concerning the investigation of the relationship between a dependent variable Y and an independent variable X, one may wish to determine whether this relationship is monotone or not. This determination may be of interest in itself, or it may form part of a (nonparametric) regression analysis which relies on monotonicity of the true regression function. In this paper we generalize the test of positive correlation by proposing a test statistic for monotonicity based on fitting a parametric model, say a higher order polynomial, to the data with and without the monotonicity constraint. The statistic has an asymptotic chi-bar-squared distribution under the null hypothesis that the true regression function is on the boundary of the space of monotone functions. Based on the theoretical results, an algorithm is developed for testing the significance of the statistic, and it is shown to perform well in several null and non-null settings. Extensions to fitting regression splines ...

To test whether the model fits the data well, a goodness-of-fit (GOF) test can be used. The chi-square GOF test is often used to test the null hypothesis that a function describes the mean of the data well. The null hypothesis with this test is rejected too often, however, because the nominal significance level (usually 0.05) is exceeded. Alternatively, the level of Hotelling’s test is accurate if a fixed hypothesis for the mean is available. In many situations, however, only an estimate of the mean is available, and so the level of Hotelling’s test may also be incorrect. An approximate version of Hotelling’s test is suggested as a GOF test. It is shown that this requires only an adjustment of the degrees of freedom of Hotelling’s original test. GOF tests assume that the model is either correct or incorrect whereas in model specification it is often assumed that the model is an approximation. Consequently, for approximate models a GOF test will mostly indicate that the model does not fit. It is therefore suggested that a measure of approximation to the true model could be used to get an indication of how bad the approximate model is. It is also shown that correct confidence intervals can be obtained from when using an approximate model. The results are applied to data from the daily news memory test. 1

Abstract—By using signal processing techniques, an estimate of activity in the brain from the electro- or magneto-encephalogram (EEG or MEG) can be obtained. For a proper analysis, a test is required to indicate whether the model for brain activity fits. A problem in using such tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald test for these cases. One of the advantages of the Wald test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald tests in electromagnetic source analysis (EMSA) are examined: a test on source amplitudes and a test on the closeness of source pairs. The Wald test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Cramér–Rao bound (CRB) is required for the use of the Wald test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald test are still good, with a moderate number of trials. Additionally, the CRB and Wald test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude. Index Terms—Approximate model, constrained optimization, Fisher information with constraints, model checking, parameter covariance, separable least squares, source localization. I.

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The world banking industry is undergoing a large-scale transformation. Banking systems and financial markets, both domestic and international, have been undergoing a series of profound changes. One of the main driving forces of these worldwide changes is the introduction of innovations in new information technologies. Against these trends, industrial structure in the banking industry and banking regulation have sometimes encouraged these trends and sometimes adapted to them. The aim of this paper is to present research findings and the main arguments in the literature on technological change and industrial organisation in the banking industry. The last section of the paper focuses on the role of information technologies in the banking industry. We present research findings of functional studies on IT investment in the banking industry. These studies have analysed the relationship between IT and corporate performance by examining specific IT applications in the context of corporate strategies.

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the author and does not necessarily represent the views of the Federal Reserve

This paper aims at investigating the efficiency of European and U.S. commercial banks. Scale and scope economies indicators, as well as a measurement of X-efficiency are derived from three cost functions: Fourier flexible form, translog and Box-Cox. This allows checking the stability and the robustness of the evidence across the different specifications. Our results over the period 1995-98 show that overall the average cost curve is relatively flat with some evidence of scale efficiency gains. More puzzling are the results on the presence of scope economies.

In many situations in econometrics, data possibly contaminated by recording errors are the only sources available. Even in situations in which the data are themselves clean, observations may occasionally be