Nichtparametrische statistische Methoden

For testing normality we investigate the power of several tests, first of all, the well known test of Jarque and Bera (1980) and furthermore the tests of Kuiper (1960) and Shapiro and Wilk (1965) as well as tests of Kolmogorov-Smirnov and Cramér-von Mises type. The tests on normality are based, first, on independent random variables (model I) and, second, on the residuals in the classical linear regression (model II). We investigate the exact critical values of the Jarque-Bera test and the Kolmogorov-Smirnov and Cramér-von Mises tests, in the latter case for the original and standardized observations where the unknown parameters µ and σ have to be estimated. The power comparison is carried out via Monte Carlo simulation assuming the model of contaminated normal distributions with varying parameters µ and σ and different proportions of contamination. It turns out that for the JarqueBera test the approximation of critical values by the chi-square distribution does not work very well. The test is superior in power to its competitors for symmetric distributions with medium up to long tails and for slightly skewed distributions with long tails. The power of the Jarque-Bera test is poor for distributions with short tails, especially if the shape is bimodal, sometimes the test is even biased. In this case a modification of the Cramér-von Mises test or the Shapiro-Wilk test may be recommended.

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“…Exact critical values k 1−α are reported by Büning and Trenkler (1994), where the asymptotic null distribution of KS is given, too.…”

Section: Tests Of Kolmogorov-smirnov Typementioning

confidence: 99%

Jarque–Bera Test and its Competitors for Testing Normality – A Power Comparison

Thadewald¹,

Büning²

2007

Journal of Applied Statistics

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“…Fisher's test exploits the exact distribution of the test statistic, but computation can take a very long time for larger tables. See, for example, Büning and Trenkler (1994) or any other monograph on non-parametric statistics. Source: CBI Industrial Trends Survey.…”

Section: Association Analysis For Capacity Restrictions and Financialmentioning

confidence: 99%

Financial Constraints and Capacity Adjustment in the United Kingdom: Evidence from a Large Panel of Survey Data

Kalckreuth

Murphy

2005

SSRN Journal

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Abstract:The interrelationship between financial constraints and firm activity is a hotly debated issue. The way firms cope with financial constraints is fundamental to the analysis of monetary transmission, of financial stability and of growth and development. The CBI Industrial Trends Survey contains detailed information on the financial constraints faced by a large sample of UK manufacturers. This paper uses the quarterly CBI Industrial Trends Survey firm level data between January 1989 and October 1999. The cleaned sample contains 49,244 quarterly observations on 5,196 firms. As more than 63% of the observations refer to firms with less than 200 employees, the data set is especially well suited for comparing large and small companies. The data set is presented and a new method of checking the informational content of the data is developed. Whereas the relationship between investment activity and financial constraints is theoretically ambivalent due to simultaneity, the link between financial constraints on the one hand and the prevalence and duration of capacity gaps on the other should be unambiguously positive. Looking at the relationship between both types of constraints, two important results emerge. First, there is shown to be informational content in the survey data on financial constraints. Specifically, financially constrained firms take longer to close capacity gaps. This indicates that financial constraints do indeed play a part in the investment process. Second, small firms close their capacity gaps faster than large firms do, but financial constraints seem to be of higher relevance to their adjustment dynamics. Keywords:Financial constraints, investment, capacity adjustment, small firm finance, duration analysis. We are able to explore the data base for the CBI Industrial Trends Survey (ITS), which is an important survey for business cycle analysis in the United Kingdom. For the 11 years between January 1989 and October 1999, the cleaned, unbalanced panel contains 49,244 quarterly observations on 5,196 firms. According to the CBI, the ITS represents around 33% of the total current employment within UK manufacturing. The data set covers all size ranges but specifically small firms are represented well, on which very little information is available from micro data sets based on quoted companies. More than 63% of the ITS observations refer to firms with less than 200 employees. On average, around 20.8% of respondents state that they are constrained by the lack of either internal or external financial resources, and that these constraints have an influence on their investment behaviour. JEL-Classification: D21, D92, C33, C41 Non Technical SummaryAfter describing the financing environment for small firms in the UK during the nineties, we present the data set by means of descriptive statistics. At this level of analysis, the differences between large and small firms appear modest. We proceed to examine the informational content of our data on financial constraints. Our focus is on capacity adjustment, ...

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“…Among others, the problems are biasedness, choice of a kernel, and optimal choice of the smoothing parameter (cf. [68], p. 215ff.).…”

Section: Estimation Of Cpe φmentioning

confidence: 99%

Cumulative Paired φ-Entropy

Klein

Mangold

Doll

2016

Entropy

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Abstract:A new kind of entropy will be introduced which generalizes both the differential entropy and the cumulative (residual) entropy. The generalization is twofold. First, we simultaneously define the entropy for cumulative distribution functions (cdfs) and survivor functions (sfs), instead of defining it separately for densities, cdfs, or sfs. Secondly, we consider a general "entropy generating function" φ, the same way Burbea et al. (IEEE Trans. Inf. Theory 1982, 28, 489-495) and Liese et al. (Convex Statistical Distances; Teubner-Verlag, 1987) did in the context of φ-divergences. Combining the ideas of φ-entropy and cumulative entropy leads to the new "cumulative paired φ-entropy" (CPE φ ). This new entropy has already been discussed in at least four scientific disciplines, be it with certain modifications or simplifications. In the fuzzy set theory, for example, cumulative paired φ-entropies were defined for membership functions, whereas in uncertainty and reliability theories some variations of CPE φ were recently considered as measures of information. With a single exception, the discussions in the scientific disciplines appear to be held independently of each other. We consider CPE φ for continuous cdfs and show that CPE φ is rather a measure of dispersion than a measure of information. In the first place, this will be demonstrated by deriving an upper bound which is determined by the standard deviation and by solving the maximum entropy problem under the restriction of a fixed variance. Next, this paper specifically shows that CPE φ satisfies the axioms of a dispersion measure. The corresponding dispersion functional can easily be estimated by an L-estimator, containing all its known asymptotic properties. CPE φ is the basis for several related concepts like mutual φ-information, φ-correlation, and φ-regression, which generalize Gini correlation and Gini regression. In addition, linear rank tests for scale that are based on the new entropy have been developed. We show that almost all known linear rank tests are special cases, and we introduce certain new tests. Moreover, formulas for different distributions and entropy calculations are presented for CPE φ if the cdf is available in a closed form.

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Nichtparametrische statistische Methoden

Cited by 124 publications

References 0 publications

Jarque–Bera Test and its Competitors for Testing Normality – A Power Comparison

Jarque–Bera Test and its Competitors for Testing Normality – A Power Comparison

Financial Constraints and Capacity Adjustment in the United Kingdom: Evidence from a Large Panel of Survey Data

Cumulative Paired φ-Entropy

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