Testing for lack of fit in linear multiresponse models based on exact or near replicates

Three procedures for testing the adequacy of a proposed linear multiresponse regression model against unspecified general alternatives are considered. The model has an error structure with a matrix normal distribution which allows the vector of responses for a particular run to have an unknown covariance matrix while the responses for different runs are uncorrelated. Furthermore, each response variable may be modeled by a separate design matrix. Multivariate statistics corresponding to the classical univariate lack of fit and pure error sums of squares are defined and used to determine the multivariate lack of fit tests. A simulation study was performed to compare the power functions of the test procedures in the case of replication. Generalizations of the tests for the case in which there are no independent replicates on all responses are also presented.     

Nonparametric density deconvolution by weighted kernel estimators

Nonparametric density estimation in the presence of measurement error is considered. The usual kernel deconvolution estimator seeks to account for the contamination in the data by employing a modified kernel. In this paper a new approach based on a weighted kernel density estimator is proposed. Theoretical motivation is provided by the existence of a weight vector that perfectly counteracts the bias in density estimation without generating an excessive increase in variance. In practice a data driven method of weight selection is required. Our strategy is to minimize the discrepancy between a standard kernel estimate from the contaminated data on the one hand, and the convolution of the weighted deconvolution estimate with the measurement error density on the other hand. We consider a direct implementation of this approach, in which the weights are optimized subject to sum and non-negativity constraints, and a regularized version in which the objective function includes a ridge-type penalty. Numerical tests suggest that the weighted kernel estimation can lead to tangible improvements in performance over the usual kernel deconvolution estimator. Furthermore, weighted kernel estimates are free from the problem of negative estimation in the tails that can occur when using modified kernels. The weighted kernel approach generalizes to the case of multivariate deconvolution density estimation in a very straightforward manner.     

Confidence intervals for secondary parameters following a sequential test

In sequential studies, formal interim analyses are usually restricted to a consideration of a single null hypothesis concerning a single parameter of interest. Valid frequentist methods of hypothesis testing and of point and interval estimation for the primary parameter have already been devised for use at the end of such a study. However, the completed data set may warrant a more detailed analysis, involving the estimation of parameters corresponding to effects that were not used to determine when to stop, and yet correlated with those that were. This paper describes methods for setting confidence intervals for secondary parameters in a way which provides the correct coverage probability in repeated frequentist realizations of the sequential design used. The method assumes that information accumulates on the primary and secondary parameters at proportional rates. This requirement will be valid in many potential applications, but only in limited situations in survival analysis.     

The academic attitudes of American teenagers, 1990–2002: Cohort and gender effects on math achievement

Using data from the National Education Longitudinal Study of 1988 and the Education Longitudinal Study of 2002, I compare the academic attitudes of high school students from Generation X and the Millennial Generation. I then analyze the effects these attitudes have on mathematics achievement test scores. Compared to the earlier group, students in the later cohort were less likely to indicate academic reasons for attending school and largely perceived their friends as being less engaged academically. Students in both cohorts whose friends held academic values experienced an increase in math scores. The more students in the earlier cohort disagreed that they came to school for academic reasons, the more their math scores decreased; this relationship did not appear for the later cohort. Females in each cohort showed stronger academic attitudes than males; additionally, believing that popularity was important was associated with lower test scores for females, but not males, in the Millennial cohort.     

Improved Monte Carlo inference for models with additive error

Some statistical models defined in terms of a generating stochastic mechanism have intractable distribution theory, which renders parameter estimation difficult. However, a Monte Carlo estimate of the log-likelihood surface for such a model can be obtained via computation of nonparametric density estimates from simulated realizations of the model. Unfortunately, the bias inherent in density estimation can cause bias in the resulting log-likelihood estimate that alters the location of its maximizer. In this paper a methodology for radically reducing this bias is developed for models with an additive error component. An illustrative example involving a stochastic model of molecular fragmentation and measurement is given.     

专业化市场在产业集群发展中的作用

中国产业集群的发展往往与一个或者多个专业批发市场相联系。中国的流通体制改革是中国专业化市场出现的重要原因。专业化市场对产业集群发展所起的作用可以说是中国特有的现象。先前的研究很少对中国这个特有现象给予重视。在产业集群和专业化市场的相互作用中,这些和产业集群有着密切联系的市场演变出不同的类型。专业化市场可以服务单个产业集群也可以服务多个产业集群。专业化市场可以细分为：房地产式,集群衍生式,中枢式和孵化器式。     

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations

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.     

Validation of Nonparametric Two-sample Bootstrap in ROC Analysis on Large Datasets

The nonparametric two-sample bootstrap is applied to computing uncertainties of measures in receiver operating characteristic (ROC) analysis on large datasets in areas such as biometrics, speaker recognition, etc. when the analytical method cannot be used. Its validation was studied by computing the standard errors of the area under ROC curve using the well-established analytical Mann–Whitney statistic method and also using the bootstrap. The analytical result is unique. The bootstrap results are expressed as a probability distribution due to its stochastic nature. The comparisons were carried out using relative errors and hypothesis testing. These match very well. This validation provides a sound foundation for such computations.     

The Local Power of the CADF and CIPS Panel Unit Root Tests

Very little is known about the local power of second generation panel unit root tests that are robust to cross-section dependence. This article derives the local asymptotic power functions of the cross-section argumented Dickey–Fuller Cross-section Augmented Dickey-Fuller (CADF) and CIPS tests of Pesaran (2007), which are among the most popular tests around.