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28
Testing multivariate uniformity and its applications
 Math. Comp
, 2001
"... Abstract. Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0, 1] d (d ≥ 2). These statistics are derived from numbertheoretic or quasiMonte Carlo methods for measuring the discrepancy of points in [0, 1] d. Under the null hypothesis that ..."
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Abstract. Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0, 1] d (d ≥ 2). These statistics are derived from numbertheoretic or quasiMonte Carlo methods for measuring the discrepancy of points in [0, 1] d. Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in [0, 1] d, we obtain some asymptotic properties of the new statistics. By Monte Carlo simulation, it is found that the finitesample distributions of the new statistics are well approximated by the standard normal distribution, N(0, 1), or the chisquared distribution, χ 2 (2). A power study is performed, and possible applications of the new statistics to testing general multivariate goodnessoffit problems are discussed. 1.
1061 “The distribution of households consumptionexpenditure budget shares” by
, 2009
"... In 2009 all ECB publications feature a motif taken from the €200 banknote. This paper can be downloaded without charge from ..."
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In 2009 all ECB publications feature a motif taken from the €200 banknote. This paper can be downloaded without charge from
Tests for breaks in the conditional comovements of asset returns. Working paper. http://www.unc.edu/˜eghysels
 Econometrica
, 1998
"... Abstract: We propose procedures designed to uncover structural breaks in the comovements of financial markets. A reduced form approach is introduced that can be considered as a twostage method for reducing the dimensionality of multivariate heteroskedastic conditional volatility models through ma ..."
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Abstract: We propose procedures designed to uncover structural breaks in the comovements of financial markets. A reduced form approach is introduced that can be considered as a twostage method for reducing the dimensionality of multivariate heteroskedastic conditional volatility models through marginalization. The main advantage is that one can use returns normalized by volatility filters that are purely datadriven and construct general conditional covariance dynamic specifications. The main thrust of our procedure is to examine changepoints in the comovements of normalized returns. The tests allow for strong and weak dependent as well as leptokurtic processes. We document, using a ten year period of two representative high frequency FX series, that regression models with nonGaussian errors adequately describe their comovements. Changepoints are detected in the conditional covariance of the DM/US $ and YN/US $ normalized returns over the decade 19861996. Key words and phrases: Changepoint tests, conditional covariance, highfrequency financial data, multivariate GARCH models. 1.
Comparison of Tests for Univariate Normality
 Proc. Interstat
, 2002
"... Tests for univariate normality, some of them not included in previous comparisons, are compared according to their power and simplicity, the validity of their reported pvalues, their behavior under rounding, the information they provide and their availability in software. The power of each test wa ..."
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Tests for univariate normality, some of them not included in previous comparisons, are compared according to their power and simplicity, the validity of their reported pvalues, their behavior under rounding, the information they provide and their availability in software. The power of each test was estimated by computer simulation for small, moderate and large sample sizes and a wide range of symmetric, skewed, contaminated and mixed distributions. A new omnibus test based on skewness and kurtosis is discussed. Key Words: Skewness, kurtosis, Lskewness, scale contaminated, mixed distributions. 1
GoodnessOfFit For The Generalized Exponential Distribution By
"... Recently a new distribution called generalized exponential or exponentiated exponential distribution was introduced and studied quite extensively by the authors (see Gupta and Kundu, 1999, 2001a, 2001b, 2002, 2003). A class of goodnessoffit tests for the generalized exponential distribution with e ..."
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Recently a new distribution called generalized exponential or exponentiated exponential distribution was introduced and studied quite extensively by the authors (see Gupta and Kundu, 1999, 2001a, 2001b, 2002, 2003). A class of goodnessoffit tests for the generalized exponential distribution with estimated parameter is proposed. The tests are based on the empirical distribution function. These test statistics are available when the hypothesized distribution is completely specified. When the parameters of the generalized exponential distribution are not known and must be estimated from the sample data, the standard tables for these test statistics are not valid. This article uses Monte Carlo and Pearson system techniques to create tables of critical values for such situations. Moreover, the power of the proposed test statistics is investigated for a number of alternative distributions. The results of the power studies showed that the test statistic proposed by Liao and Shimokawa (1999) is the most powerful goodnessoffit test among the competitors.
Computer Simulation of Clostridium botulinum Strain 56A Behavior at
, 2002
"... It is generally assumed that spore behavior is independent of spore concentration, but recently published mathematical models indicate that this is not the case. A Monte Carlo simulation was employed in this study to further examine the independence assumption by evaluating the inherent variance in ..."
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It is generally assumed that spore behavior is independent of spore concentration, but recently published mathematical models indicate that this is not the case. A Monte Carlo simulation was employed in this study to further examine the independence assumption by evaluating the inherent variance in spore germination data. All simulations were carried out with @Risk software. A total of 500 to 4,000 iterations were needed for each simulation to reach convergence. Lag time and doubling time from a higher inoculum concentration were used to simulate the time to detection (TTD) at a lower inoculum concentration under otherwise identical environmental conditions. The point summaries of the simulated and observed TTDs were recorded for the 26 simulations, with kinetic data at the target inoculum concentration. The ratios of the median (R m � median obs/ median sim) and 90 % range (R r � 90 % range obs/90 % range sim) were calculated. Most R m and R r values were greater than one, indicating that the simulated TTDs were smaller and more homogeneous than the observed ones. R r values departed farther from one than R m values. Ratios obtained when simulating 1 spore with 10,000 spores deviated the farthest from one. Neither ratio was significantly different from the other when simulating 1 spore with 100 spores or simulating 100 spores with 10,000 spores. When kinetic data were not available, the percent positive observed at the 95th percentile of the simulated TTDs was obtained. These simulation results confirmed that the assumption of independence between spores is not valid.
Evaluating Predictive Densities of U.S. Output Growth and In‡ation in a Large Macroeconomic Data Set
, 2013
"... We evaluate conditional predictive densities for U.S. output growth and inflation using a number of commonly used forecasting models that rely on a large number of macroeconomic predictors. More specifically, we evaluate how well conditional predictive densities based on the commonly used normality ..."
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We evaluate conditional predictive densities for U.S. output growth and inflation using a number of commonly used forecasting models that rely on a large number of macroeconomic predictors. More specifically, we evaluate how well conditional predictive densities based on the commonly used normality assumption fit actual realizations outofsample. Our focus on predictive densities acknowledges the possibility that, although some predictors can improve or deteriorate point forecasts, they might have the opposite effect on higher moments. We find that normality is rejected for most models in some dimension according to at least one of the tests we use. Interestingly, however, combinations of predictive densities appear to be correctly approximated by a normal density: the simple, equal average when predicting output growth and Bayesian model average when predicting inflation. Keywords:
Goodnessoffit for the ToppLeone distribution with unknown parameters
 Applied Mathematical Sciences
, 2012
"... Abstract A class of goodnessoffit tests for the ToppLeone distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. KolomogorovSminrov, CramervonMises, AndersonDarling, Watson, and LiaoShimokawa are proposed. Numerical simulations are pe ..."
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Abstract A class of goodnessoffit tests for the ToppLeone distribution with estimated parameters is proposed. The tests are based on the empirical distribution function. KolomogorovSminrov, CramervonMises, AndersonDarling, Watson, and LiaoShimokawa are proposed. Numerical simulations are performed to calculate the critical values for the proposed tests. Finally, the power estimate is performed with the hypothesized ToppLeone distribution versus widely used alternates.
NONPARAMETRIC STATISTICAL ANALYSIS FOR MULTIPLE COMPARISON OF MACHINE LEARNING REGRESSION ALGORITHMS
"... In the paper we present some guidelines for the application of nonparametric statistical tests and posthoc procedures devised to perform multiple comparisons of machine learning algorithms. We emphasize that it is necessary to distinguish between pairwise and multiple comparison tests. We show that ..."
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In the paper we present some guidelines for the application of nonparametric statistical tests and posthoc procedures devised to perform multiple comparisons of machine learning algorithms. We emphasize that it is necessary to distinguish between pairwise and multiple comparison tests. We show that the pairwise Wilcoxon test, when employed to multiple comparisons, will lead to overoptimistic conclusions. We carry out intensive normality examination employing ten different tests showing that the output of machine learning algorithms for regression problems does not satisfy normality requirements. We conduct experiments on nonparametric statistical tests and posthoc procedures designed for multiple 1×N and N ×N comparisons with six different neural regression algorithms over 29 benchmark regression data sets. Our investigation proves the usefulness and strength of multiple comparison statistical procedures to analyse and select machine learning algorithms.