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Meintanis, Simos G.; Allison, James; Santana, Leonard
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1 Citations
We investigate the finitesample properties of certain procedures which employ the novel notion of the probability weighted empirical characteristic function. The procedures considered are: (1) Testing for symmetry in regression, (2) Testing for multivariate normality with independent observations, and (3) Testing for multivariate normality of random effects in mixed models. Along with the new tests alternative methods based on the ordinary empirical characteristic function as well as other more well known procedures are implemented for the purpose of comparison.
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Ng, Hon Keung Tony; Balakrishnan, N.; Panchapakesan, S.
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10 Citations
In this paper, we first give an overview of the precedencetype test procedures. Then we propose a nonparametric test based on early failures for the equality of two lifetime distributions against two alternatives concerning the best population. This procedure utilizes the minimal Wilcoxon ranksum precedence statistic (Ng and Balakrishnan, 2002, 2004) which can determine the difference between populations based on early (100q%) failures. Hence, this procedure can be useful in lifetesting experiments in biological as well as industrial settings. After proposing the test procedure, we derive the exact null distribution of the test statistic in the twosample case with equal or unequal sample sizes. We also present the exact probability of correct selection under the Lehmann alternative. Then, we generalize the test procedure to the ksample situation. Critical values for some sample sizes are presented. Next, we examine the performance of this test procedure under a locationshift alternative through Monte Carlo simulations. Two examples are presented to illustrate our test procedure with selecting the best population as an objective.
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Heuchenne, Cédric; PardoFernández, Juan Carlos
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Assume that we have two populations (X_{1},Y_{1}) and (X_{2},Y_{2}) satisfying two general nonparametric regression models Y_{j}=m_{j}(X_{j})+ε_{j}, j=1,2, where m(⋅) is a smooth location function, ε_{j} has zero location and the response Y_{j} is possibly rightcensored. In this paper, we propose to test the null hypothesis H_{0}:m_{1}=m_{2} versus the onesided alternative H_{1}:m_{1}<m_{2}. We introduce two test statistics for which we obtain the asymptotic normality under the null and the alternative hypotheses. Although the tests are based on nonparametric techniques, they can detect any local alternative converging to the null hypothesis at the parametric rate n^{−1/2}. The practical performance of a bootstrap version of the tests is investigated in a simulation study. An application to a data set about unemployment duration times is also included.
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Melas, Viatcheslav B.; Pepelyshev, Andrey; Shpilev, Petr; Salmaso, Luigi; Corain, Livio; Arboretti, Rosa
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3 Citations
The paper is devoted to the elaboration of an efficient approach for comparison of two regression curves based on the empirical Fourier coefficients of regression functions. For the problem of testing for the equality of the two unknown functions in the case of homoscedastic error structure and observation at equidistant points, we derive a new procedure with adaptive choice of the number of the coefficients used in the hypotheses testing. Our approach is based on approximation of the most powerful test using the full knowledge of the regression functions. The results are justified by theoretical arguments and the superiority of the new procedure is also confirmed by a simulation study.
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Henze, Norbert; Meintanis, Simos G.
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58 Citations
Abstract.
A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of KolmogorovSmirnov and Cramérvon Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace transform and the empirical characteristic function, a method based on entropy as well as tests of the KolmogorovSmirnov and Cramérvon Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodnessoffit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finitesample performance of the tests is investigated in an extensive simulation study.
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Milošević, Bojana
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4 Citations
Two new tests for exponentiality, of integral and Kolmogorovtype, are proposed. They are based on a recent characterization and formed using appropriate Vstatistics. Their asymptotic properties are examined and their local Bahadur efficiencies against some common alternatives are found. A class of locally optimal alternatives for each test is obtained. The powers of these tests, for some small sample sizes, are compared with different exponentiality tests.
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Bingham, Melissa A.; Scray, Marissa L.
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Although there have been fairly recent advances regarding inference for threedimensional rotation data, there are still many areas of interest yet to be explored. One such area involves comparing the rotational symmetry of 3D rotations. In this paper, nonparametric inference is used to test if F_{1}=F_{2}, where F_{i} is the degree of rotational symmetry of distribution i, through a permutation test. The validity of the developed permutation test is examined through a simulation study and the test is applied to a small example in biomechanics.
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Meintanis, S. G.
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6 Citations
In this paper, goodnessoffit tests are constructed for the skew normal law. The proposed tests utilize the fact that the moment generating function of the skew normal variable satisfies a simple differential equation. The empirical counterpart of this equation, involving the empiricalmoment generating function, yields appropriate test statistics. The consistency of the tests is investigated under general assumptions, and the finitesample behavior of the proposed method is investigated via a parametric bootstrap procedure.
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Geng, Pei; Koul, Hira L.
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This article studies a minimum distance regression model checking approach in the presence of Berkson measurement errors in covariates without specifying the measurement error density but when external validation data are available. The proposed tests are based on a class of minimized integrated square distances between a nonparametric estimate of the calibrated regression function and the parametric null model being fitted. The asymptotic distributions of these tests under the null hypothesis and against certain alternatives are established. Surprisingly, these asymptotic distributions are the same as in the case of known measurement error density. In comparison, the asymptotic distributions of the corresponding minimum distance estimators of the null model parameters are affected by the estimation of the calibrated regression function. A simulation study shows desirable performance of a member of the proposed class of estimators and tests.
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Dette, Holger; Wieczorek, Gabriele
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In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the L^{2}distance between the square of the regression function and the variance function. We prove asymptotic normality of a standardized estimate of this distance under the null hypothesis and fixed alternatives. The finite sample properties of a corresponding bootstrap test are investigated by means of a simulation study. The results are applicable to stationary processes with the common mixing conditions and are used to construct tests for ARCH assumptions in financial time series.
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