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51.
《统计学通讯:理论与方法》2013,42(10):1989-2004
We consider a linear regression with the error term that obeys an autoregressive model of infinite order and estimate parameters of the models. The parameters of the autoregressive model should be estimated based on estimated residuals obtained by means of the method of ordinary least squares, because the errors are unobservable. The consistency of the coefficients, variance and spectral density of the model obeyed by the error term is shown. Further, we estimate the coefficients of the linear regression by means of the method of estimated generalized least squares. We also show the consistency of the estimator. 相似文献
52.
Hay and Olsen (1984) incorrectly argue that a multi-part model, the two-part model used in Duan et al. (1982,1983), is nested within the sample-selection model. Their proof relies on an unmentioned restrictive assumption that cannot be satisfied. We provide a counterexample to show that the propensity to use medical care and the level of expense can be positively associated in the two-part model, contrary to their assertion. The conditional specification in the multi-part model is preferable to the unconditional specification in the selection model for modeling actual (v. potential) outcomes. The selection model also has poor statistical and numerical properties and relies on untestable assumptions. Empirically the multi-part estimators perform as well as or better than the sample selection estimator for the data set analyzed in Duan et al. (1982, 1983). 相似文献
53.
In this article, we consider the problems of testing the goodness of fit of the parametric accelerated failure time model and the Cox proportional hazards model. We consider omnibus test statistics based on residuals. The statistical distributions of Kolmogorov, Cramer-von Mises–Smirnov, and Anderson–Darling statistics are all investigated by means of Monte Carlo simulations. Type-I, Type-II, and independent random censoring situations are all considered in this study. A Monte Carlo power study has also been carried out for these tests to distinguish between various baseline models, which reveals that the Anderson–Darling test performs better than the others. 相似文献
54.
Renhao Jin 《统计学通讯:模拟与计算》2017,46(3):1781-1795
In spatial statistics, the correct identification of a variogram model when fitted to an empirical variogram depends on many factors. Here, simulation experiments show fitting based on the variogram cloud is preferable to that based on Matheron's and Cressie–Hawkins empirical variogram estimators. For correct model specification, a number of models should be fitted to the empirical variogram using a grid of cut-off values, and recommendations are given for best choice. A design where roughly half the maximum distance between points equals the practical range works well for correct variogram identification of any model, with varying nugget sizes and sample sizes. 相似文献
55.
The purpose of this note is to spell out the conditions for the existence of the mean of the coefficient; estimator in seemingly unrelated regressions. 相似文献
56.
The likelihood ratio is used for measuring the strength of statistical evidence. The probability of observing strong misleading evidence along with that of observing weak evidence evaluate the performance of this measure. When the corresponding likelihood function is expressed in terms of a parametric statistical model that fails, the likelihood ratio retains its evidential value if the likelihood function is robust [Royall, R., Tsou, T.S., 2003. Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions. J. Roy. Statist. Soc. Ser. B 65, 391–404]. In this paper, we extend the theory of Royall and Tsou [2003. Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions. J. Roy. Statist. Soc., Ser. B 65, 391–404] to the case when the assumed working model is a characteristic model for two-way contingency tables (the model of independence, association and correlation models). We observe that association and correlation models are not equivalent in terms of statistical evidence. The association models are bounded by the maximum of the bump function while the correlation models are not. 相似文献
57.
Hillel Bar-Gera 《The American statistician》2017,71(2):112-119
R-squared (R2) and adjusted R-squared (R2Adj) are sometimes viewed as statistics detached from any target parameter, and sometimes as estimators for the population multiple correlation. The latter interpretation is meaningful only if the explanatory variables are random. This article proposes an alternative perspective for the case where the x’s are fixed. A new parameter is defined, in a similar fashion to the construction of R2, but relying on the true parameters rather than their estimates. (The parameter definition includes also the fixed x values.) This parameter is referred to as the “parametric” coefficient of determination, and denoted by ρ2*. The proposed ρ2* remains stable when irrelevant variables are removed (or added), unlike the unadjusted R2, which always goes up when variables, either relevant or not, are added to the model (and goes down when they are removed). The value of the traditional R2Adj may go up or down with added (or removed) variables, either relevant or not. It is shown that the unadjusted R2 overestimates ρ2*, while the traditional R2Adj underestimates it. It is also shown that for simple linear regression the magnitude of the bias of R2Adj can be as high as the bias of the unadjusted R2 (while their signs are opposite). Asymptotic convergence in probability of R2Adj to ρ2* is demonstrated. The effects of model parameters on the bias of R2 and R2Adj are characterized analytically and numerically. An alternative bi-adjusted estimator is presented and evaluated. 相似文献
58.
A weighted bootstrap approximation for comparing the error distributions in nonparametric regression
Gustavo I. Rivas Martínez 《Journal of Statistical Computation and Simulation》2017,87(18):3503-3520
Several procedures have been proposed for testing the equality of error distributions in two or more nonparametric regression models. Here we deal with methods based on comparing estimators of the cumulative distribution function (CDF) of the errors in each population to an estimator of the common CDF under the null hypothesis. The null distribution of the associated test statistics has been approximated by means of a smooth bootstrap (SB) estimator. This paper proposes to approximate their null distribution through a weighted bootstrap. It is shown that it produces a consistent estimator. The finite sample performance of this approximation is assessed by means of a simulation study, where it is also compared to the SB. This study reveals that, from a computational point of view, the proposed approximation is more efficient than the one provided by the SB. 相似文献
59.
Li-Fei Huang 《统计学通讯:模拟与计算》2017,46(7):5763-5771
The ordinary Wilcoxon signed rank test table provides confidence intervals for the median of one population. Adjusted Wilcoxon signed rank test tables which can provide confidence intervals for the median and the 10th percentile of one population are created in this paper. Base-(n + 1) number system and theorems about property of symmetry of the adjusted Wilcoxon signed rank test statistic are derived for programming. Theorem 1 states that the adjusted Wilcoxon signed rank test statistic are symmetric around n(n + 1)/4. Theorem 2 states that the adjusted Wilcoxon signed rank test statistic with the same number of negative ranks m are symmetric around m(n+1)/2. 87.5% and 85% confidence intervals of the median are given in the table for n = 12, 13,…, 29 to create approximated 95% confidence intervals of the ratio of medians for two independent populations. 95% and 92.5% confidence intervals of the 10th percentile are given in the table for n = 26, 27, 28, 29 to create approximated 95% confidence regions of the ratio of the 10th percentiles for two independent populations. Finally two large datasets from wood industry will be partitioned to verify the correctness of adjusted Wilcoxon signed rank test tables for small samples. 相似文献
60.
The aim of this paper is to introduce a new method which corrects residual variances for the butterfly distributed residuals (BDR). Distribution theory, confidence intervals, and tests of hypotheses are valid and meaningful only if the standard regression assumptions are satisfied. Heteroskedasticity is one of the violations of these assumptions and BDR is another type of heteroskedasticity. This study reveals an alternative approach to correct the BDR type of heteroskedasticity by the weighting re-estimated absolute residuals (WRAR). After giving brief information about heteroskedasticity and BDR type of heteroskedasticity, WRAR is introduced. WRAR and the usual variance stabilizing techniques are compared on multiple and simple regression models. 相似文献