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1.
Circular data are observations that are represented as points on a unit circle. Times of day and directions of wind are two such examples. In this work, we present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is useful especially when the likelihood surface is ill behaved. Markov chain Monte Carlo techniques are used to fit the proposed model and to generate predictions. The method is illustrated using an environmental data set. 相似文献
2.
M. Kaluszka 《统计学通讯:理论与方法》2013,42(9-10):1899-1910
ABSTRACT Sharp bounds on expected values of L-statistics based on a sample of possibly dependent, identically distributed random variables are given in the case when the sample size is a random variable with values in the set {0, 1, 2,…}. The dependence among observations is modeled by copulas and mixing. The bounds are attainable and provide characterizations of some non trivial distributions. 相似文献
3.
In this paper, we propose two multimodal circular distributions which are suitable for modeling circular data sets with two or more modes. Both distributions belong to the regular exponential family of distributions and are considered as extensions of the von Mises distribution. Hence, they possess the highly desirable properties, such as the existence of non-trivial sufficient statistics and optimal inferences for their parameters. Fine particulates (PM2.5) are generally emitted from activities such as industrial and residential combustion and from vehicle exhaust. We illustrate the utility of our proposed models using a real data set consisting of fine particulates (PM2.5) pollutant levels in Houston region during Fall season in 2019. Our results provide a strong evidence that its diurnal pattern exhibits four modes; two peaks during morning and evening rush hours and two peaks in between. 相似文献
4.
Rafael Pérez-Ocón Juan Eloy Ruiz-Castro & M. Luz Gámiz-Pérez 《Journal of the Royal Statistical Society. Series C, Applied statistics》2001,50(1):111-124
A cohort of 300 women with breast cancer who were submitted for surgery is analysed by using a non-homogeneous Markov process. Three states are onsidered: no relapse, relapse and death. As relapse times change over time, we have extended previous approaches for a time homogeneous model to a non omogeneous multistate process. The trends of the hazard rate functions of transitions between states increase and then decrease, showing that a changepoint can be considered. Piecewise Weibull distributions are introduced as transition intensity functions. Covariates corresponding to treatments are incorporated in the model multiplicatively via these functions. The likelihood function is built for a general model with k changepoints and applied to the data set, the parameters are estimated and life-table and transition probabilities for treatments in different periods of time are given. The survival probability functions for different treatments are plotted and compared with the corresponding function for the homogeneous model. The survival functions for the various cohorts submitted for treatment are fitted to the mpirical survival functions. 相似文献
5.
Soujin Wang 《Revue canadienne de statistique》1990,18(3):255-264
It is well known that saddlepoint expansions lead to accurate approximations to the cumulative distributions and densities of a sample mean and other simple linear statistics. The use of such expansions is explored in a broader situation. The saddlepoint formula for the tail probability of a certain type of nonlinear statistic is derived. The relative error of O(n–1), as in the linear case, is retained. A simple example is considered, to illustrate the great accuracy of the approximation. 相似文献
6.
《Journal of Statistical Computation and Simulation》2012,82(4):319-332
The maximum entropy characterization of the von Mises distribution on the circle is exploited to derive a consistent goodness of fit test for the von Mises distribution. Monte Carlo simulation results are tabulated giving critical values of the test statistic for various sample sizes and values of the concentration parameter. A power analysis is presented for various alternative hypotheses, comparing this entropy statistic to two other competing goodness of fit statistics. The entropy statistic is shown to compare favorably and may be more attractive, especially considering its ease of computation. 相似文献
7.
Paul J. Smith 《统计学通讯:理论与方法》2013,42(3):209-220
A nonparametric test for circular symmetry about 0 in a continuous bivariate distribution is proposed. The test is of the von Mises type, based on the empirical cdf of the sample, expressed in polar co-ordinates. However, the test is independent of the choice of the polar axis. The asymptotic form of the test statistic is obtained by considering the weak convergence of the empirical process to a limiting Gaussian process. The asymptotic distribution of the test statistic is found explicitly, both under the null hypothesis and under simple alternatives. The test is shown to be consistent against all alternatives. 相似文献
8.
A comparison of various methods for estimating the parameters in mixtures of von mises distributions
In this paper we compare five methods for estimating the unknown parameters in a mixture of two von Mises distributions. We propose a new method based on the characteristic function and compare it with the classical methods based on maximum likelihood and moments. Thus far these methods have been successfully applied only to linear data. Here we show that the application to circular data is reasonably straightforward and that convergence to the final estimates is fairly rapid. For various simulated known mixtures the results obtained are satisfactory. Finally, we introduce a modification of the method of moments which is considerably faster in CPU time than any of the other methods used and gives good results. 相似文献
9.
Juan Kalemkerian 《统计学通讯:理论与方法》2017,46(10):4671-4685
Given i.i.d. Gaussian random variables and after standardizing the sample by subtracting the sample mean and dividing it by the sample deviation, we obtain an integral formula for the distribution of these self-normalized variables. Using geometrical arguments, we obtain the distribution of each and the joint distribution of two of them. These formulas can be used to calculate the expected value of the particular type of Cramér von Mises statistic to test normality. 相似文献
10.
11.
Adelaide Figueiredo 《统计学通讯:模拟与计算》2013,42(9):1991-2003
The von Mises-Fisher distribution is widely used for modeling directional data. In this article, we derive the discriminant rules based on this distribution to assign objects into pre-existing classes. We determine a distance between two von Mises-Fisher populations and we calculate estimates of the misclassification probabilities. We also analyze the behavior of the distance between two von Mises-Fisher populations and of the estimates of the misclassification probabilities when we modify the parameters of the populations or the samples size or the dimension of the sphere. Finally, we present an example with real spherical data available in the literature. 相似文献
12.
Riccardo Gatto 《Statistics》2013,47(4):409-421
The broad class of generalized von Mises (GvM) circular distributions has certain optimal properties with respect to information theoretic quantities. It is shown that, under constraints on the trigonometric moments, and using the Kullback–Leibler information as the measure, the closest circular distribution to any other is of the GvM form. The lower bounds for the Kullback–Leibler information in this situation are also provided. The same problem is also considered using a modified version of the Kullback–Leibler information. Finally, series expansions are given for the entropy and the normalizing constants of the GvM distribution. 相似文献
13.
Marius Iosifescu 《Journal of statistical planning and inference》1992,30(3):395-400
We derive the Berry-Esséen theorem with optimal convergence rate for U-statistics and von Mises statistics associated with a special class of Markov chains occuring in the theory of dependence with complete connections. 相似文献
14.
This article focuses on estimating an autoregressive regression model for circular time series data. Simulation studies have shown the difficulties involved in obtaining good estimates from low concentration data or from small samples. It presents an application using real data. 相似文献
15.
《Journal of Statistical Computation and Simulation》2012,82(7):1023-1033
We develop an exact Kolmogorov–Smirnov goodness-of-fit test for the Poisson distribution with an unknown mean. This test is conditional, with the test statistic being the maximum absolute difference between the empirical distribution function and its conditional expectation given the sample total. Exact critical values are obtained using a new algorithm. We explore properties of the test, and we illustrate it with three examples. The new test seems to be the first exact Poisson goodness-of-fit test for which critical values are available without simulation or exhaustive enumeration. 相似文献
16.
Kanti V. Mardia John T. Kent Zhengzheng Zhang Charles C. Taylor Thomas Hamelryck 《Journal of applied statistics》2012,39(11):2475-2492
Motivated by examples in protein bioinformatics, we study a mixture model of multivariate angular distributions. The distribution treated here (multivariate sine distribution) is a multivariate extension of the well-known von Mises distribution on the circle. The density of the sine distribution has an intractable normalizing constant and here we propose to replace it in the concentrated case by a simple approximation. We study the EM algorithm for this distribution and apply it to a practical example from protein bioinformatics. 相似文献
17.
The authors develop consistent nonparametric estimation techniques for the directional mixing density. Classical spherical harmonics are used to adapt Euclidean techniques to this directional environment. Minimax rates of convergence are obtained for rotation ally invariant densities verifying various smoothness conditions. It is found that the differences in smoothness between the Laplace, the Gaussian and the von Mises‐Fisher distributions lead to contrasting inferential conclusions. 相似文献
18.
Douglas M. Hawkins 《Journal of applied statistics》2017,44(8):1319-1332
The von Mises distribution is widely used for modeling angular data. When such data are seen in a quality control setting, there may be interest in checking whether the values are in statistical control or have gone out of control. A cumulative sum (cusum) control chart has desirable properties for checking whether the distribution has changed from an in-control to an out-of-control setting. This paper develops cusums for a change in the mean direction and concentration of angular data and illustrates some of their properties. 相似文献
19.
A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations
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Pseudo‐values have proven very useful in censored data analysis in complex settings such as multi‐state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second‐order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo‐values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U‐statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies. 相似文献
20.
Wen-Liang Hung Shou-Jen Chang-Chien Miin-Shen Yang 《Journal of applied statistics》2012,39(10):2259-2274
The EM algorithm is the standard method for estimating the parameters in finite mixture models. Yang and Pan [25] proposed a generalized classification maximum likelihood procedure, called the fuzzy c-directions (FCD) clustering algorithm, for estimating the parameters in mixtures of von Mises distributions. Two main drawbacks of the EM algorithm are its slow convergence and the dependence of the solution on the initial value used. The choice of initial values is of great importance in the algorithm-based literature as it can heavily influence the speed of convergence of the algorithm and its ability to locate the global maximum. On the other hand, the algorithmic frameworks of EM and FCD are closely related. Therefore, the drawbacks of FCD are the same as those of the EM algorithm. To resolve these problems, this paper proposes another clustering algorithm, which can self-organize local optimal cluster numbers without using cluster validity functions. These numerical results clearly indicate that the proposed algorithm is superior in performance of EM and FCD algorithms. Finally, we apply the proposed algorithm to two real data sets. 相似文献