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1.
The Kolmogorov-Smirnov (K–S) one-sided and two-sided tests of goodness of fit based on the test statistics D+ n D? n and Dn are equivalent to tests based on taking the cumulative probability of the i–th order statistic of a sample of size n to be (i–.5)/n. Modified test statistics C+ n, C? n and Cn are obtained by taking the cumulative probability to be i/(n+l). More generally, the cumula-tive probability may be taken to be (i?δ)/(n+l?2δ), as suggested by Blom (1958), where 0 less than or equal δ less than or equal .5. Critical values of the test statis-tics can be found by interpolating inversely in tables of the proba-bility integrals obtained by setting a=l/(n+l?2δ) in an expression given by Pyke (1959). Critical values for the D's (corresponding to δ=.5) have been tabulated to 5DP by Miller (1956) for n=1(1)100. The authors have made analogous tabulations for the C's (corresponding to δ=0) [previously tabulated by Durbin (1969) for n=1(1)60(2)100] and for the test statistics E+ n, E? n and En corresponding to δ f.3. They have also made a Monte Carlo comparison of the power of the modified tests with that of the K–S test for several hypothetical distributions. In a number of cases, the power of the modified tests is greater than that of the K–S test, especially when the standard deviation is greater under the alternative than under the null hypo-thesis. 相似文献
2.
The smooth goodness of fit tests are generalized to singly censored data and applied to the problem of testing Weibull (or extreme value) fit. Smooth tests, Pearson-type tests, and the spacings tests proposed by Mann, Schemer, and Fertig (1973) are compared on the basis of local asymptotic relative efficiency with respect to the asymptotic best test against generalized gamma alternatives, The smooth test of order one Is found to be most efficient for the generalized gamma alternatives. 相似文献
3.
Adel I Bargal 《统计学通讯:理论与方法》2013,42(2):537-549
In this paper properties of two estimators of Cpm are investigated in terms of changes in the process mean and variance. The bias and mean squared error of these estimators are derived. It can be shown that the estimate of Cpm proposed by Chan, Cheng and Spiring (1988) has smaller bias than the one proposed by Boyles (1991) and also has a smaller mean squared error under certain conditions. Various approximate confidence intervals for Cpm are obtained and are compared in terms of coverage probabilities, missed rate and average interval width. 相似文献
4.
《Journal of Statistical Computation and Simulation》2012,82(1-4):43-61
This paper investigates a new family of goodness-of-fit tests based on the negative exponential disparities. This family includes the popular Pearson's chi-square as a member and is a subclass of the general class of disparity tests (Basu and Sarkar, 1994) which also contains the family of power divergence statistics. Pitman efficiency and finite sample power comparisons between different members of this new family are made. Three asymptotic approximations of the exact null distributions of the negative exponential disparity famiiy of tests are discussed. Some numerical results on the small sample perfomance of this family of tests are presented for the symmetric null hypothesis. It is shown that the negative exponential disparity famiiy, Like the power divergence family, produces a new goodness-of-fit test statistic that can be a very attractive alternative to the Pearson's chi-square. Some numerical results suggest that, application of this test statistic, as an alternative to Pearson's chi-square, could be preferable to the I 2/3 statistic of Cressie and Read (1984) under the use of chi-square critical values. 相似文献
5.
Steven G. From 《统计学通讯:理论与方法》2013,42(12):3167-3183
In this paper, a new test statistic is presented for testing the null hypothesis of equal multinomial cell probabilities versus various trend alternatives. Exact asymptotic critical values are obtained, The power of the test is compared with several other statistics considered by Choulakian et al (1995), The test is shown to have better power for certain trend alternatives. 相似文献
6.
The proportional hazards regression model of Cox(1972) is widely used in analyzing survival data. We examine several goodness of fit tests for checking the proportionality of hazards in the Cox model with two-sample censored data, and compare the performance of these tests by a simulation study. The strengths and weaknesses of the tests are pointed out. The effects of the extent of random censoring on the size and power are also examined. Results of a simulation study demonstrate that Gill and Schumacher's test is most powerful against a broad range of monotone departures from the proportional hazards assumption, but it may not perform as well fail for alternatives of nonmonotone hazard ratio. For the latter kind of alternatives, Andersen's test may detect patterns of irregular changes in hazards. 相似文献
7.
E. González-Estrada J. A. Villaseñor 《Journal of Statistical Computation and Simulation》2018,88(4):726-751
This R package implements three types of goodness-of-fit tests for some widely used probability distributions where there are unknown parameters, namely tests based on data transformations, on the ratio of two estimators of a dispersion parameter, and correlation tests. Most of the considered tests have been proved to be powerful against a wide range of alternatives and some new ones are proposed here. The package's functionality is illustrated with several examples by using some data sets from the areas of environmental studies, biology and finance, among others. 相似文献
8.
Kishan G. Mehrotra 《统计学通讯:理论与方法》2013,42(8):869-878
A class of tests based on spacings is obtained for milticensored samples. Their asymptotic null as well as alternative distributions are obtained. 相似文献
9.
Divergence measures play an important role in statistical theory, especially in large sample theories of estimation and testing.
The underlying reason is that they are indices of statistical distance between probability distributions P and Q; the smaller
these indices are the harder it is to discriminate between P and Q. Many divergence measures have been proposed since the
publication of the paper of Kullback and Leibler (1951). Renyi (1961) gave the first generalization of Kullback-Leibler divergence,
Jeffreys (1946) defined the J-divergences, Burbea and Rao (1982) introduced the R-divergences, Sharma and Mittal (1977) the
(r,s)-divergences, Csiszar (1967) the ϕ-divergences, Taneja (1989) the generalized J-divergences and the generalized R-divergences
and so on. In order to do a unified study of their statistical properties, here we propose a generalized divergence, called
(h,ϕ)-divergence, which include as particular cases the above mentioned divergence measures. Under different assumptions, it is
shown that the asymptotic distributions of the (h,ϕ)-divergence statistics are either normal or chi square. The chi square and the likelihood ratio test statistics are particular
cases of the (h,ϕ)-divergence test statistics considered. From the previous results, asymptotic distributions of entropy statistics are derived
too. Applications to testing statistical hypothesis in multinomial populations are given. The Pitman and Bahadur efficiencies
of tests of goodness of fit and independence based on these statistics are obtained. To finish, apendices with the asymptotic
variances of many well known divergence and entropy statistics are presented.
The research in this paper was supported in part by DGICYT Grants N. PB91-0387 and N. PB91-0155. Their financial support is
gratefully acknowledged. 相似文献
10.
A gamma regression model with an exponential link function for the means Is considered. Moment properties of the deviance statistics based on maximum likelihood and weighted least squares fits are used to define modified deviance statistics which provide alternative global goodness of fit tests. The null distribution properties of the deviances and modified deviances are compared with those of the approximating chi-square distribution and It is shown that the use of the modified deviances gives much better control over the significance levels of the tests. 相似文献
11.
We obtain the asymptotic distributions of certain forms in observations that are possible Type I and Type II censored. This result is directly applicable to the study of asympototic distributions for censored data versions of the Shapiro- wilk test for normality. Moreove, it applies more generally than just to the null hypothesis of normality. 相似文献
12.
Elena Kulinskaya 《统计学通讯:理论与方法》2013,42(5):1121-1150
This paper deals with the asymptotics of a class of tests for association in 2-way contingency tables based on square forms in cell frequencies, given the total number of observations (multinomial sampling) or one set of marginal totals (stratified sampling). The case when both row and column marginal totals are fixed (hypergeometric sampling) was studied in Kulinskaya (1994), The class of tests under consideration includes a number of classical measures for association, Its two subclasses are the tests based on statistics using centralized cell frequencies (asymptotically distributed as weighted sums of central chi-squares) and those using the non-centralized cell frequencies (asymptotically normal). The parameters of asymptotic distributions depend on the sampling model and on true marginal probabilities. Maximum efficiency for asymptotically normal statistics is achieved under hypergeometric sampling, If the cell frequencies or the statistic as a whole are centralized using marginal proportions as estimates for marginal probabilities, the asymptotic distribution does not differ much between models and it is equivalent to that under hypergeometric sampling. These findings give an extra justification for the use of permutation tests for association (which are based on hypergeometric sampling). As an application, several well known measures of association are analysed. 相似文献
13.
In this paper we propose an application of N-distance theory [Klebanov, L.B., 2005. N-distances and their applications. Karolinum, Prague] for testing simple hypotheses of goodness of fit and homogeneity. The asymptotic null distribution of test statistics is established and coincides with the distribution of infinite quadratic form of independent standard normal random variables. A construction of multivariate free-of-distribution homogeneity test is considered. The power of proposed criteria is compared with classical tests using Monte-Carlo simulations. 相似文献
14.
Shimizu Kunio 《统计学通讯:理论与方法》2013,42(9):975-985
Suppose that the function f is of recursive type and the random variable X is normally distributed with mean μ and variance α2. We set C = f(x). Neyman & Scott (1960) and Hoyle (1968) gave the UMVU estimators for the mean E(C) and for the variance Var(C) from independent and identically distributed random variables X1,…, Xn(n ≧ 2) having a normal distribution with mean μ and variance σ2, respectively. Shimizu & Iwase (1981) gave the variance of the UMVU estimator for E(C). In this paper, the variance of the UMVU estimator for Var(C) is given. 相似文献
15.
In previous literature the effects of rounding on fixed sample hypothesis tests have been considered. However sequential tests have received little attention. In this paper the robustness of these tests under rounding is considered. The results indicate that in terms of significance level and power the sequential tests were less affected by rounding than the fixed sample tests. 相似文献
16.
Al though mixtures form a rich class of probability models, they often present difficulties for statistical inference. Likelihood functions are sometimes unbounded at certain values of the parameters, and densities often have no closed form. These features complicate hoth maximum-likelihood estimation and tests of fit based on the empirical distribution function. New inferential methods using sample characteristic functions (Cfs) and moment generating functions (MGFs) seem well-suited to mixtures. since these transforms often take simple form/ This paper reports a simulation study of the properties of estimators and tests of fit based on CFs, MGFs, and sample moments when applied to three specific families of thick tailed mixture distributios. 相似文献
17.
Ludger Ruschendorf 《Statistics》2013,47(2):221-230
It is shown that the coupling of distributions by their quantile transforms leads to simple and unifying proofs of monotonicity and unbiasedness properties of tests in many nonparametric testing problems 相似文献
18.
Received: January 12, 2000; revised version: July 26, 2000 相似文献
19.
In this article we have presented some of the asymptotic theorems related to one-truncation parameter family of distributions ? Comparison of performance of different estimators and other inferential problems have been tackled - Also applications of the main results have been given and illustrated their uses with examples. 相似文献
20.
John W. Pratt 《统计学通讯:理论与方法》2013,42(8):779-787
The author believes that tests provide a poor model of most real problems, usually so poor that their objectivity is tangential and often too poor to be useful. 相似文献