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91.
Toxicologists and pharmacologists often describe toxicity of a chemical using parameters of a nonlinear regression model. Thus estimation of parameters of a nonlinear regression model is an important problem. The estimates of the parameters and their uncertainty estimates depend upon the underlying error variance structure in the model. Typically, a priori the researcher would not know if the error variances are homoscedastic (i.e., constant across dose) or if they are heteroscedastic (i.e., the variance is a function of dose). Motivated by this concern, in this paper we introduce an estimation procedure based on preliminary test which selects an appropriate estimation procedure accounting for the underlying error variance structure. Since outliers and influential observations are common in toxicological data, the proposed methodology uses M-estimators. The asymptotic properties of the preliminary test estimator are investigated; in particular its asymptotic covariance matrix is derived. The performance of the proposed estimator is compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using a data set obtained from the National Toxicology Program. 相似文献
92.
A comparison of maximum likelihood and least squares for the estimation of a cumulative distribution
《Journal of Statistical Computation and Simulation》2012,82(3-4):229-239
Monte Carlo methods are used to compare the methods of maximum likelihood and least squares to estimate a cumulative distribution function. When the probabilistic model used is correct or nearly correct, the two methods produce similar results with the MLE usually slightly superior When an incorrect model is used, or when the data is contaminated, the least squares technique often gives substantially superior results. 相似文献
93.
《Journal of Statistical Computation and Simulation》2012,82(8):1621-1643
When a spatial point process model is fitted to spatial point pattern data using standard software, the parameter estimates are typically biased. Contrary to folklore, the bias does not reflect weaknesses of the underlying mathematical methods, but is mainly due to the effects of discretization of the spatial domain. We investigate two approaches to correcting the bias: a Newton–Raphson-type correction and Richardson extrapolation. In simulation experiments, Richardson extrapolation performs best. 相似文献
94.
95.
《Journal of Statistical Computation and Simulation》2012,82(18):3701-3714
ABSTRACTConsiderable effort has been spent on the development of confidence intervals for process capability indices (PCIs) based on the sampling distribution of the PCI or the transferred PCI. However, there is still no definitive way to construct a closed interval for a PCI. The aim of this study is to develop closed intervals for the PCIs Cpu, Cpl, and Spk based on Boole's inequality and de Morgan's laws. The relationships between different sample sizes, the significance levels, and the confidence intervals of the PCIs Cpu, Cpl, and Spk are investigated. Then, a testing model for interval estimation for the PCIs Cpu, Cpl, and Spk is built as a powerful tool for measuring the quality performance of a product. Finally, an applied example is given to demonstrate the effectiveness and applicability of the proposed method and the testing model. 相似文献
96.
《Journal of Statistical Computation and Simulation》2012,82(3):211-224
A problem of testing of hypotheses on the mean vector of a multivariate normal distribution with unknown and positive definite covariance matrix is considered when a sample with a special, though not unusual, pattern of missing observations from that population is available. The approximate percentage points of the test statistic are obtained and their accuracy has been checked by comparing them with some exact percentage points which are calculated for complete samples and some special incomplete samples. The approximate percentage points are in good agreement with exact percentage points. The above work is extended to the problem of testing the hypothesis of equality of two mean vectors of two multivariate normal distributions with the same, unknown covariance matrix 相似文献
97.
Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing transductive prediction procedures that are able to take advantage of the sparsity in the high dimensional linear regression. More precisely, we define transductive versions of the LASSO (Tibshirani, 1996) and the Dantzig Selector (Candès and Tao, 2007). These procedures combine labeled and unlabeled observations of the training dataset to produce a prediction for the unlabeled observations. We propose an experimental study of the transductive estimators that shows that they improve the LASSO and Dantzig Selector in many situations, and particularly in high dimensional problems when the predictors are correlated. We then provide non-asymptotic theoretical guarantees for these estimation methods. Interestingly, our theoretical results show that the Transductive LASSO and Dantzig Selector satisfy sparsity inequalities under weaker assumptions than those required for the “original” LASSO. 相似文献
98.
《Journal of Statistical Computation and Simulation》2012,82(2-3):87-92
The standard frequency domain approximation to the Gaussian likelihood of a sample from an ARMA process is considered. The Newton-Raphson and Gauss-Newton numerical maximisation algorithms are evaluated for this approximate likelihood and the relationships between these algorithms and those of Akaike and Hannan explored. In particular it is shown that Hannan's method has certain computational advantages compared to the other spectral estimation methods considered 相似文献
99.
《Statistics》2012,46(6):1396-1436
ABSTRACTThe paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting. 相似文献
100.
《Journal of Statistical Computation and Simulation》2012,82(10):2233-2247
In this paper, we develop modified versions of the likelihood ratio test for multivariate heteroskedastic errors-in-variables regression models. The error terms are allowed to follow a multivariate distribution in the elliptical class of distributions, which has the normal distribution as a special case. We derive the Skovgaard-adjusted likelihood ratio statistics, which follow a chi-squared distribution with a high degree of accuracy. We conduct a simulation study and show that the proposed tests display superior finite sample behaviour as compared to the standard likelihood ratio test. We illustrate the usefulness of our results in applied settings using a data set from the WHO MONICA Project on cardiovascular disease. 相似文献