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61.
C. G. Khatri 《Journal of statistical planning and inference》1977,1(3):299-307
In the present paper, the authors obtained exact and asymptotic expressions for the joint distribution of correlated quadratic forms when the underlying distribution is a multivariate normal. 相似文献
62.
An Edgeworth expansion for a linear combination of stratum means in stratified sampling without replacement from a finite population is derived. The expansion is applied to a bootstrap proposed for this context to show that the bootstrap captures the second-order term of the expansion. 相似文献
63.
M-quantile regression is defined as a “quantile-like” generalization of robust regression based on influence functions. This article outlines asymptotic properties for the M-quantile regression coefficients estimators in the case of i.i.d. data with stochastic regressors, paying attention to adjustments due to the first-step scale estimation. A variance estimator of the M-quantile regression coefficients based on the sandwich approach is proposed. Empirical results show that this estimator appears to perform well under different simulated scenarios. The sandwich estimator is applied in the small area estimation context for the estimation of the mean squared error of an estimator for the small area means. The results obtained improve previous findings, especially in the case of heteroskedastic data. 相似文献
64.
Jorge M. Arevalillo 《统计学通讯:理论与方法》2013,42(11):3196-3205
ABSTRACTThis article is concerned with the derivation and study of the Cornish-Fisher expansion for a wide class of estimators of the parameter in the first order autoregressive process. Second and third order Cornish-Fisher approximations to the quantile of the distribution of the corresponding asymptotically normal standardized statistic are stated explicitly and their accuracy is examined, both theoretically and numerically, by comparing them with the exact value of the quantile obtained by Monte Carlo simulation. 相似文献
65.
66.
Mukhter M Ali 《统计学通讯:理论与方法》2013,42(5):1321-1343
It i s well known that even if the sample observations are correlated and not normal, the sample mean is normal in 1arge samples. But how large is large? This question i s investigated in this paper. In particular , the relation between the rate of convergence and the correlation property of the observations i s explored. It i s observed that the correlation, in general, retards the rate of convergence. 相似文献
67.
Consider the D-optimal designs for a combined polynomial and trigonometric regression on a partial circle. It is shown that the optimal design is equally supported and the structure of the optimal design depends only on the length of the design interval and the support points are analytic functions of this parameter. Moreover, the Taylor expansion of the optimal support points can be determined efficiently by a recursive procedure. Examples are presented to illustrate the procedures for computing the optimal designs. 相似文献
68.
In the article, it is shown that in panel data models the Hausman test (HT) statistic can be considerably refined using the bootstrap technique. Edgeworth expansion shows that the coverage of the bootstrapped HT is second-order correct. The asymptotic versus the bootstrapped HT are compared also by Monte Carlo simulations. At the null hypothesis and a nominal size of 0.05, the bootstrapped HT reduces the coverage error of the asymptotic HT by 10–40% of nominal size; for nominal sizes less than or equal to 0.025, the coverage error reduction is between 30% and 80% of nominal size. For the nonnull alternatives, the power of the asymptotic HT fictitiously increases by over 70% of the correct power for nominal sizes less than or equal to 0.025; the bootstrapped HT reduces overrejection to less than one fourth of its value. The advantages of the bootstrapped HT increase with the number of explanatory variables. Heteroscedasticity or serial correlation in the idiosyncratic part of the error does not hamper advantages of the bootstrapped version of HT, if a heteroscedasticity robust version of the HT and the wild bootstrap are used. But, the power penalty is not negligible if a heteroscedasticity robust approach is used in the homoscedastic panel data model. 相似文献
69.
A generalization of the Poisson distribution was defined by Consul and Jain (Ann. Math. Statist., 41, (1970)) and was obtained as a particular family of Lagrange distributions by Consul and Shenton (SIAM. J. Appl. Math., 23, (1972)). The distribution is subsequently named the generalized Poisson distribution (GPD). This GPD reduces to the Poisson distribution for ? = 0. When the data have a one-way layout structure, the asymptotically locally optimal Neyman's C(d) test is constructed and compared with the conditional test on the hypothesis Ho? = 0. Within the framework of the generalized linear models an appropriate link function is given, and the asymptotic distributions of the estimated parameters are derived. 相似文献
70.
Haruhiko Ogasawara 《统计学通讯:模拟与计算》2013,42(1):177-199
ABSTRACT Asymptotic distributions of the standardized estimators of the squared and non squared multiple correlation coefficients under nonnormality were obtained using Edgeworth expansion up to O(1/n). Conditions for the normal-theory asymptotic biases and variances to hold under nonnormality were derived with respect to the parameter values and the weighted sum of the cumulants of associated variables. The condition for the cumulants indicates a compensatory effect to yield the robust normal-theory lower-order cumulants. Simulations were performed to see the usefulness of the formulas of the asymptotic expansions using the model with the asymptotic robustness under nonnormality, which showed that the approximations by Edgeworth expansions were satisfactory. 相似文献