Smoothing for discrete-valued time series

We deal with smoothed estimators for conditional probability functions of discrete-valued time series { Y_t } under two different settings. When the conditional distribution of Y_t given its lagged values falls in a parametric family and depends on exogenous random variables, a smoothed maximum (partial) likelihood estimator for the unknown parameter is proposed. While there is no prior information on the distribution, various nonparametric estimation methods have been compared and the adjusted Nadaraya–Watson estimator stands out as it shares the advantages of both Nadaraya–Watson and local linear regression estimators. The asymptotic normality of the estimators proposed has been established in the manner of sparse asymptotics, which shows that the smoothed methods proposed outperform their conventional, unsmoothed, parametric counterparts under very mild conditions. Simulation results lend further support to this assertion. Finally, the new method is illustrated via a real data set concerning the relationship between the number of daily hospital admissions and the levels of pollutants in Hong Kong in 1994–1995. An ad hoc model selection procedure based on a local Akaike information criterion is proposed to select the significant pollutant indices.     

Confidence intervals for the difference in paired Youden indices

Comparison of accuracy between two diagnostic tests can be implemented by investigating the difference in paired Youden indices. However, few literature articles have discussed the inferences for the difference in paired Youden indices. In this paper, we propose an exact confidence interval for the difference in paired Youden indices based on the generalized pivotal quantities. For comparison, the maximum likelihood estimate‐based interval and a bootstrap‐based interval are also included in the study for the difference in paired Youden indices. Abundant simulation studies are conducted to compare the relative performance of these intervals by evaluating the coverage probability and average interval length. Our simulation results demonstrate that the exact confidence interval outperforms the other two intervals even with small sample size when the underlying distributions are normal. A real application is also used to illustrate the proposed intervals. Copyright © 2012 John Wiley & Sons, Ltd.     

Functional sliced inverse regression analysis

Most of the usual multivariate methods have been extended to the context of functional data analysis. Our contribution concerns the study of sliced inverse regression (SIR) when the response variable is real but the regressor is a function. In the first part, we show how the relevant properties of SIR remain essentially the same in the functional context under suitable conditions. Unfortunately, the estimation procedure used in the multivariate case cannot be directly transposed to the functional one. Then, we propose a solution that overcomes this difficulty and we show the consistency of the estimates of the parameters of the model.     

A lower bound for the centred L 2-discrepancy on combined designs under the asymmetric factorials

The foldover is a useful technique in the construction of two-level factorial designs for follow-up experiments. To search an optimal foldover plans is an important issue. In this paper, for a set of asymmetric fractional factorials such as the original designs, a lower bound for centred L ₂-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. All of our results are the extended ones of Ou et al. [Lower bounds of various discrepancies on combined designs, Metrika 74 (2011), pp. 109–119] for symmetric designs to asymmetric designs. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.     

A Shrinkage Estimation of Central Subspace in Sufficient Dimension Reduction

Sliced regression is an effective dimension reduction method by replacing the original high-dimensional predictors with its appropriate low-dimensional projection. It is free from any probabilistic assumption and can exhaustively estimate the central subspace. In this article, we propose to incorporate shrinkage estimation into sliced regression so that variable selection can be achieved simultaneously with dimension reduction. The new method can improve the estimation accuracy and achieve better interpretability for the reduced variables. The efficacy of proposed method is shown through both simulation and real data analysis.     

Kernel Density-Based Linear Regression Estimate

For linear regression models with non normally distributed errors, the least squares estimate (LSE) will lose some efficiency compared to the maximum likelihood estimate (MLE). In this article, we propose a kernel density-based regression estimate (KDRE) that is adaptive to the unknown error distribution. The key idea is to approximate the likelihood function by using a nonparametric kernel density estimate of the error density based on some initial parameter estimate. The proposed estimate is shown to be asymptotically as efficient as the oracle MLE which assumes the error density were known. In addition, we propose an EM type algorithm to maximize the estimated likelihood function and show that the KDRE can be considered as an iterated weighted least squares estimate, which provides us some insights on the adaptiveness of KDRE to the unknown error distribution. Our Monte Carlo simulation studies show that, while comparable to the traditional LSE for normal errors, the proposed estimation procedure can have substantial efficiency gain for non normal errors. Moreover, the efficiency gain can be achieved even for a small sample size.     

Inference for a Linear Functional of Cumulative Hazard Function Via Empirical Likelihood

This article discusses sampling plans, that is, the allocation of sampling units, for computing tolerance limits in a balanced one--way random-effects model. The expected width of the tolerance interval is derived and used as the basis for comparing different sampling plans. A well-known cost function and examples are used to facilitate the discussion.     

Semiparametric Smooth Coefficient Stochastic Frontier Model With Panel Data

ABSTRACT

We investigate the semiparametric smooth coefficient stochastic frontier model for panel data in which the distribution of the composite error term is assumed to be of known form but depends on some environmental variables. We propose multi-step estimators for the smooth coefficient functions as well as the parameters of the distribution of the composite error term and obtain their asymptotic properties. The Monte Carlo study demonstrates that the proposed estimators perform well in finite samples. We also consider an application and perform model specification test, construct confidence intervals, and estimate efficiency scores that depend on some environmental variables. The application uses a panel data on 451 large U.S. firms to explore the effects of computerization on productivity. Results show that two popular parametric models used in the stochastic frontier literature are likely to be misspecified. Compared with the parametric estimates, our semiparametric model shows a positive and larger overall effect of computer capital on the productivity. The efficiency levels, however, were not much different among the models. Supplementary materials for this article are available online.     

改进的投影寻踪分类模型及其在区域经济评价中的应用

作为多元数据的一种分析方法,投影寻踪分类模型已被一些研究者应用到实践中,并取得了良好的效果.然而,投影寻踪分类模型没有严格意义上的分类标准.通过引入有序样本聚类法,可以对投影寻踪分类模型得到的一维投影值进行客观分类.根据改进的模型,对江苏省区域经济的发展进行了综合评价,结果表明:改进的投影寻踪分类模型切实可行,为多元数据分类提供了新途径.