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Analysis of textile materials often includes measurement of structural anisotropy or directional orientation of textile object systems. To that purpose, the real-world objects are replaced by their images, which are analyzed, and the results of this analysis are used for decisions about the product(s). Study of the image data allows one to understand the image contents and to perform quantitative and qualitative description of objects of interest. This paper deals in particular with the problem of estimating the main orientation of fiber systems. Firstly, we present a concise survey of the methods suitable for estimating orientation of fiber systems stemming from the image analysis. The methods we consider are based on the two-dimensional discrete Fourier transform combined with the method of moments. Secondly, we suggest abandoning the currently used global, that is, all-at-once, analysis of the whole image, which typically leads to just one estimate of the characteristic of interest, and advise replacing it with a “local analysis”. This means splitting the image into many small, non-overlapping pieces, and estimating the characteristic of interest for each piece separately and independently of the others. As a result we obtain many estimates of the characteristic of interest, one for each sub-window of the original image, and – instead of averaging them to get just one value – we suggest analyzing the distribution of the estimates obtained for the respective sub-images. The proposed approach seems especially appealing when analyzing nonwoven textiles and nanofibrous layers, which may often exhibit quite a large anisotropy of the characteristic of interest.

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The detection of (structural) breaks or the so called change point problem has drawn increasing attention from the theoretical, applied economic and financial fields. Much of the existing research concentrates on the detection of change points and asymptotic properties of their estimators in panels when N, the number of panels, as well as T , the number of observations in each panel are large. In this paper we pursue a different approach, i.e., we consider the asymptotic properties when N → ∞ while keeping T fixed. This situation is typically related to large (firm-level) data containing financial information about an immense number of firms/stocks across a limited number of years/quarters/months. We propose a general approach for testing for break(s) in this setup. In particular, we obtain the asymptotic behavior of test statistics. We also propose a wild bootstrap procedure that could be used to generate the critical values of the test statistics. The theoretical approach is supplemented by numerous simulations and by an empirical illustration. We demonstrate that the testing procedure works well in the framework of the four factors CAPM model. In particular, we estimate the breaks in the monthly returns of US mutual funds during the period January 2006 to February 2010 which covers the subprime crises.

Change point, Data driven test, Model selection, Rank test,

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