Improved orthogonal polynomial density estimates

Density estimates that are expressible as the product of a base density function and a linear combination of orthogonal polynomials are considered in this paper. More specifically, two criteria are proposed for determining the number of terms to be included in the polynomial adjustment component and guidelines are suggested for the selection of a suitable base density function. A simulation study reveals that these stopping rules produce density estimates that are generally more accurate than kernel density estimates or those resulting from the application of the Kronmal–Tarter criterion. Additionally, it is explained that the same approach can be utilized to obtain multivariate density estimates. The proposed orthogonal polynomial density estimation methodology is applied to several univariate and bivariate data sets, some of which have served as benchmarks in the statistical literature on density estimation.     

Robust logistic regression modelling via the elastic net-type regularization and tuning parameter selection

The penalized logistic regression is a useful tool for classifying samples and feature selection. Although the methodology has been widely used in various fields of research, their performance takes a sudden turn for the worst in the presence of outlier, since the logistic regression is based on the maximum log-likelihood method which is sensitive to outliers. It implies that we cannot accurately classify samples and find important factors having crucial information for classification. To overcome the problem, we propose a robust penalized logistic regression based on a weighted likelihood methodology. We also derive an information criterion for choosing the tuning parameters, which is a vital matter in robust penalized logistic regression modelling in line with generalized information criteria. We demonstrate through Monte Carlo simulations and real-world example that the proposed robust modelling strategies perform well for sparse logistic regression modelling even in the presence of outliers.     

Hierarchically penalized quantile regression with multiple responses

We study variable selection in quantile regression with multiple responses. Instead of applying conventional penalized quantile regression to each response separately, it is desired to solve them simultaneously when the sparsity patterns of the regression coefficients for different responses are similar, which is often the case in practice. In this paper, we propose employing a hierarchical penalty that enables us to detect a common sparsity pattern shared between different responses as well as additional sparsity patterns within the selected variables. We establish the oracle property of the proposed method and demonstrate it offers better performance than existing approaches.     

Maximum likelihood estimators in regression models with infinite variance innovations

In this paper we consider the problem of maximum likelihood (ML) estimation in the classical AR(1) model with i.i.d. symmetric stable innovations with known characteristic exponent and unknown scale parameter. We present an approach that allows us to investigate the properties of ML estimators without making use of numerical procedures. Finally, we introduce a generalization to the multivariate case.     

An essentially complete class of multiple decision procedures

Let π₁,…, π_k represent k(?2) independent populations. The quality of the ith population π_i is characterized by a real-valued parameter θ_i, usually unknown. We define the best population in terms of a measure of separation between θ_i's. A selection of a subset containing the best population is called a correct selection (CS). We restrict attention to rules for which the size of the selected subset is controlled at a given point and the infimum of the probability of correct selection over the parameter space is maximized. The main theorem deals with construction of an essentially complete class of selection rules of the above type. Some classical subset selection rules are shown to belong to this class.     

Conditional quantile estimation with auxiliary information for left-truncated and dependent data

In this paper, the empirical likelihood method is used to define a new estimator of conditional quantile in the presence of auxiliary information for the left-truncation model. The asymptotic normality of the estimator is established when the data exhibit some kind of dependence. It is assumed that the lifetime observations with multivariate covariates form a stationary α‐mixing sequence. The result shows that the asymptotic variance of the proposed estimator is not larger than that of standard kernel estimator. Finite sample behavior of the estimator is investigated via simulations too.     

Statistical scoring procedures applicable to laboratory performance evaluation

Two statistical scoring procedures based on p$p$-values have been developed to evaluate the overall performance of analytical laboratories performing environmental measurements. The overall scores of bias and standing are used to determine how consistently a laboratory is able to measure the true (unknown) value correctly over time. The overall scores of precision and standing are used to determine how well a laboratory is able to reproduce its measurements in the long run. Criteria are established for qualitatively labeling measurements as Acceptable, Warning, and Not Acceptable and for identifying areas where laboratories should re-evaluate their measurement procedures. These statistical scoring procedures are applied to two real environmental data sets.     

On the distribution of the adaptive LASSO estimator

We study the distribution of the adaptive LASSO estimator [Zou, H., 2006. The adaptive LASSO and its oracle properties. J. Amer. Statist. Assoc. 101, 1418–1429] in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results in consistent model selection. We show that the finite-sample as well as the large-sample distributions are typically highly nonnormal, regardless of the choice of the tuning parameter. The uniform convergence rate is also obtained, and is shown to be slower than n^-1/2$n^{-1/2}$ in case the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the ‘oracle’ property of the adaptive LASSO estimator established in Zou [2006. The adaptive LASSO and its oracle properties. J. Amer. Statist. Assoc. 101, 1418–1429]. Moreover, we also provide an impossibility result regarding the estimation of the distribution function of the adaptive LASSO estimator. The theoretical results, which are obtained for a regression model with orthogonal design, are complemented by a Monte Carlo study using nonorthogonal regressors.     

基于备件需求优先级的随机库存控制模型研究

根据所安装设备发生故障时对生产过程的影响,备件的需求可划分为关键需求和非关键需求。基于此,研究了需求服从泊松分布、提前期等于常数、基于(S-1,S)订货策略的随机库存模型,提出当库存降低到预定水平,则预留存货以满足关键需求的控制策略,并给出了不同优先级备件服务水平的计算方法。最后结合某核电站库存管理中的一个实例,验证了本文所设计模型的优点和准确性。