Books on probability ideas are reviewed

In this paper, semiparametric methods are applied to estimate multivariate volatility functions, using a residual approach as in [J. Fan and Q. Yao, Efficient estimation of conditional variance functions in stochastic regression, Biometrika 85 (1998), pp. 645–660; F.A. Ziegelmann, Nonparametric estimation of volatility functions: The local exponential estimator, Econometric Theory 18 (2002), pp. 985–991; F.A. Ziegelmann, A local linear least-absolute-deviations estimator of volatility, Comm. Statist. Simulation Comput. 37 (2008), pp. 1543–1564], among others. Our main goal here is two-fold: (1) describe and implement a number of semiparametric models, such as additive, single-index and (adaptive) functional-coefficient, in volatility estimation, all motivated as alternatives to deal with the curse of dimensionality present in fully nonparametric models; and (2) propose the use of a variation of the traditional cross-validation method to deal with model choice in the class of adaptive functional-coefficient models, choosing simultaneously the bandwidth, the number of covariates in the model and also the single-index smoothing variable. The modified cross-validation algorithm is able to tackle the computational burden caused by the model complexity, providing an important tool in semiparametric volatility estimation. We briefly discuss model identifiability when estimating volatility as well as nonnegativity of the resulting estimators. Furthermore, Monte Carlo simulations for several underlying generating models are implemented and applications to real data are provided.     

Quantile regression and variable selection for the single-index model

In this paper, we propose a new full iteration estimation method for quantile regression (QR) of the single-index model (SIM). The asymptotic properties of the proposed estimator are derived. Furthermore, we propose a variable selection procedure for the QR of SIM by combining the estimation method with the adaptive LASSO penalized method to get sparse estimation of the index parameter. The oracle properties of the variable selection method are established. Simulations with various non-normal errors are conducted to demonstrate the finite sample performance of the estimation method and the variable selection procedure. Furthermore, we illustrate the proposed method by analyzing a real data set.     

Pseudo-Bayes and pseudo-empirical Bayes estimators in randomized response sampling

In this article, new pseudo-Bayes and pseudo-empirical Bayes estimators for estimating the proportion of a potentially sensitive attribute in a survey sampling have been introduced. The proposed estimators are compared with the recent estimator proposed by Odumade and Singh [Efficient use of two decks of cards in randomized response sampling, Comm. Statist. Theory Methods 38 (2009), pp. 439–446] and Warner [Randomized response: A survey technique for eliminating evasive answer bias, J. Amer. Statist. Assoc. 60 (1965), pp. 63–69].     

A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter

ABSTRACT

A statistical test can be seen as a procedure to produce a decision based on observed data, where some decisions consist of rejecting a hypothesis (yielding a significant result) and some do not, and where one controls the probability to make a wrong rejection at some prespecified significance level. Whereas traditional hypothesis testing involves only two possible decisions (to reject or not a null hypothesis), Kaiser’s directional two-sided test as well as the more recently introduced testing procedure of Jones and Tukey, each equivalent to running two one-sided tests, involve three possible decisions to infer the value of a unidimensional parameter. The latter procedure assumes that a point null hypothesis is impossible (e.g., that two treatments cannot have exactly the same effect), allowing a gain of statistical power. There are, however, situations where a point hypothesis is indeed plausible, for example, when considering hypotheses derived from Einstein’s theories. In this article, we introduce a five-decision rule testing procedure, equivalent to running a traditional two-sided test in addition to two one-sided tests, which combines the advantages of the testing procedures of Kaiser (no assumption on a point hypothesis being impossible) and Jones and Tukey (higher power), allowing for a nonnegligible (typically 20%) reduction of the sample size needed to reach a given statistical power to get a significant result, compared to the traditional approach.     

Bayesian Design of Special Type of Double Sampling Plans for Compliance Testing

Bayesian acceptance sampling plans, which utilize prior information on the process variation, can be employed as an alternative to conventional types of plans for taking decisions on the disposition of submitted lots. A special type of double sampling inspection plans by attributes with small acceptance numbers using Bayesian methodology is presented in this paper emphasizing its significance over small acceptance number single sampling plans. The procedures for designing such sampling plans for specified degree of discrimination which would ensure protection to the producer and consumer are discussed with illustrations under the conditions for the application of gamma-Poisson distribution.     

Negotiating Tensions between Methodology and Procedural Ethics

In this commentary, I consider what can go wrong in research when tensions arise between methodology and procedural ethics. I recount difficulties negotiating and implementing a participant recruitment strategy during my doctoral research project, which aimed to explore the experiences of people affected by dementia in the United Kingdom who were disengaged from services. To access this hard-to-reach population, I intended to adopt an informal recruitment strategy, snowball sampling from personal contacts and striking up conversations in public places. The procedural ethics committee were unhappy with this approach, deeming it potentially coercive. They suggested a more formal recruitment strategy enacted via emailing community organisations and churches. This approach entailed practical consequences that ultimately weakened the study sample, data and findings. This case raises questions about the negotiation of tensions between methodology and procedural ethics in gerontological research.     

菲利普斯曲线在中国的有效性研究

从基本的菲利普斯曲线理论出发,提出了新的适应性预期模型,并以此为基础建立附加预期的菲利普斯曲线方程,进而估计出我国近年来的自然失业率水平,由此证明了菲利普斯曲线在我国的有效性,并描述了预期因素对实际通货膨胀水平的影响。最后结合实证分析结果提出解决我国通货膨胀和失业问题的建议,如保证货币政策的连贯性、加强信息披露、解决结构性失业问题等。     

Power comparison of the Kolmogorov–Smirnov test under ranked set sampling and simple random sampling

Many studies have been used to compare the power of several goodness-of-fit (GOF) tests under simple random sampling (SRS) and ranked set sampling (RSS). In our study, a different design procedure and ranking process in RSS are thoroughly investigated. A simulation study is conducted to compare the power of the Kolmogorov–Smirnov test under SRS and RSS with different sets and cycle sizes for several distributions. Level-2 sampling design and partially rank-ordered sets are used. Also, we benefited from auxiliary variables in the ranking process. Finally, results are presented with tables and figures. Under these conditions we show that the RSS has better performance against the SRS in finite population.     

Bayesian ratemaking under Dirichlet process mixtures

Experience ratemaking plays a crucial role in general insurance in determining future premiums of individuals in a portfolio by assessing observed claims from the whole portfolio. This paper investigates this problem in which claims can be modeled by certain parametric family of distributions. The Dirichlet process mixtures are employed to model the distributions of the parameters so as to make two advantages: to produce exact Bayesian experience premiums for a class of premium principles generated from generic error functions and, at the same time, provide robust and flexible ways to avoid possible bias caused by traditionally used priors such as non informative priors or conjugate priors. In this paper, the Bayesian experience ratemaking under Dirichlet process mixture models are investigated and due to the lack of analytical forms of the conditional expectations of the quantities concerned, the Gibbs sampling schemes are designed for the purpose of approximations.     

Estimating the population proportion in modified ranked set sampling methods

In this paper, proportion estimators and associated variance estimators are proposed for a binary variable with a concomitant variable based on modified ranked set sampling methods, which are extreme ranked set sampling (ERSS), median ranked set sampling (MRSS), percentile ranked set sampling (Per-RSS) and L ranked set sampling (LRSS) methods. The Monte Carlo simulation study is performed to compare the performance of the estimators based on bias, mean squared error, and relative efficiency for different levels of correlation coefficient, set and cycle sizes under normal and log-normal distributions. Moreover, the study is supported with real data application.