Simulating non‐normal distributions with specified L‐moments and L‐correlations

This paper derives a procedure for simulating continuous non‐normal distributions with specified L‐moments and L‐correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product‐moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L‐moment‐based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L‐skew and L‐kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. Further, the L‐correlation also demonstrated to be less biased and more stable than the Pearson correlation. It is also shown how the proposed L‐moment‐based procedure can be extended to the larger class of power method distributions associated with polynomials of order five.     

The effect of response scaling on the detection of linear dependencies among multiresponse data

Summary Box and Draper (1965) introduced a criterion for the estimation of parameters from a multiresponse model. This criterion can lead to misleading results in the presence of linear relationships among the responses. Box et al. (1973) proposed a procedure for detecting the existence of such relationships when the multiresponse data are subject to round-off errors. The procedure is applicable only when the round-off errors are identically distributed as uniform random variates. In many situations, however, the round-off errors can vary considerably. For example, the responses may have distinct physical meanings, and hence distinct scales of measurement with possibly widely different orders of magnitude. This article extends Box et al.’s procedure to cover these situations. Two examples are given to illustrate the implementation of the proposed methodology.     

Analysis of Intertemporal Efficiency Trends Using Rank Statistics With an Application Evaluating the Macro Economic Performance of OECD Nations

This paper presents two applications of rank statistics to evaluate efficiency performance trends using productive efficiency measures derived through various Data Envelopment Analysis (DEA) models. The paper starts with a discussion of the difficulties in obtaining consistent ranks from DEA efficiency ratings. Next, a procedure is proposed to identify intertemporal performance trends using any one of several possible efficiency measures. Another procedure is then developed to test the stability over time of the rank positions of the analyzed units. For each statistical procedure, a small numerical example involving DEA efficiency measures is provided to illustrate the proposed technique. Finally, the new procedures are applied to data reflecting the macro-economic performance of 17 OECD nations in 1979–1988. The outcomes of the application are discussed and contrasted with previous research in this area.     

Statistical inference on restricted partial linear regression models with partial distortion measurement errors

We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed under the null hypothesis. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure, and a real example is analyzed for an illustration.     

Applying lot-by-lot double sampling plan to reform Taiwan National Health Insurance auditing system

This paper seeks to design an elaborate and effective “sampling audit and payment process” for a single-payer system of national health insurance. Furthermore, contrive incentive mechanisms in the “sampling audit and payment process” to make the healthcare providers willing to apply for their medical claim payments straightforwardly. A framework of “medical claim payment auditing by double sampling plan (MCPAD)” procedure based on the lot-by-lot double sampling plan was proposed to curb the growth of medical expenses. The proposed procedure entertains several advantages, including: (1) it meets international standards of sampling plan; (2) it simplifies the auditing process; (3) it reduces sample size and auditing costs; and (4) it encourages healthcare providers using an honest medical claim payment through the incentive mechanisms. This study successfully reduces the sampling cost and effectively audits the claimed medical fees as well as encourages healthcare providers to straightforwardly apply for their medical claim payments. Practically, the proposed MCPAD procedure is also applied to healthcare provider. It is anticipated that the proposed procedure in other nations in the future.     

Discrimination of Observations into One of Two Elliptic Populations based on Monotone Training Samples

In this paper we deal with the problem of classifying a p-dimensional random vector into one of two elliptically contoured populations with unknown and distinct mean vectors and a common, but unknown, scale matrix. The classification procedure is based on two-step monotone training samples, one from each population, with the same monotone pattern. Our aim is to extend the classification procedure, which proposed recently by Chung and Han (Ann Ins Stat Math 52:544–556, 2000). This procedure is a linear combination of two discriminant functions, one based on the complete samples and the other on the incomplete samples. The performance of the proposed classification rule is compared with the plug-in method, this means with the classification rule which arises if the unknown parameters are substituted, into the usual classification rule, by their estimators. In order to apply the plug-in method, the MLE of the location parameters and of the common scale matrix of g ≥ 2 elliptically contoured populations are analytically obtained on the basis of two-step monotone training samples.     

Sequential estimation in generalized linear models when covariates are subject to errors

Sequential methods have been used for many applications; especially, when fixed sample procedures are not possible and/or when “early stopping” of sampling is beneficial for applications. At the same time, the issue of how to make correct inferences when measurement errors are present has drawn considerable attention from statisticians. In this paper, the problems of sequential estimation of generalized linear models when there are measurement errors in both adaptive and fixed design cases are studied. The proposed sequential procedure is proved to be asymptotically consistent and efficient in the sense of Chow and Robbins [Ann Math Stat 36(2):457–462, 1965] when measurement errors decay gradually as the number of sequentially selected design points increases. This assumption is useful in sequentially designed experiments, and can also be fulfilled in the case when replicate measurements are available. Some numerical studies based on a Rasch model and a logistic regression model are conducted to evaluate the performance of the proposed procedure.     

The raise method. An alternative procedure to estimate the parameters in presence of collinearity

Recently, Feng-Jeng (Qual Quant 42:417–426, 2008) has proposed the nested estimation procedure as another alternative from the practical point of view of the problem of multicollinearity. Although the nested estimation procedure can promise to avoid multicollinearity, it can also avoid important information by eliminating variables. We are presenting another alternative called the raise method, which keeps all the information which could be highly recommended in some cases. We apply our proposal to a known example and compare the results with the nested estimation procedure, the ridge regression and the principal components.     

LAD variable selection for linear models with randomly censored data

The least absolute deviations (LAD) variable selection for linear models with randomly censored data is studied through the Lasso. The proposed procedure can select significant variables in the parameters. With appropriate selection of the tuning parameters, we establish the consistency of this procedure and the oracle property of the resulting estimators. Simulation studies are conducted to compare the proposed procedure with an inverse-censoring-probability weighted LAD LASSO-estimator.     

Bayes estimates of muIti-criteria decision alternatives using Monte Carlo integration

A Bayesian procedure is proposed for the estimation of the weights of the alternatives in a multi-criteria decision model with data that stem from pair-wise comparison of alternatives. The prior information restricts the weights to the unit simplex. The posterior results are computed by Monte Carlo integration procedures based on importance sampling. The Bayesian procedure is applied to a case study concerning the choice of a professor of Operations Research (OR). Results are: (1) according to the Bayesian procedure a different candidate would be chosen as professor of OR than according to the maximum likelihood procedure; (2) given the prior and data information, there exists a substantial probability of taking the wrong decision; (3) there exists a ranking of the candidates with a posterior probability greater than one half.     

Consistency vs Flexibility: The Impact of Employee Voice in Rule-Based and Discretionary Decision Procedures

Consistency and flexibility are desirable, but incompatible, features of decision-making procedures. A comparison of a rule-based decision procedure (maximizing consistency) with a discretionary decision procedure (maximizing flexibility) was conducted. Employee voice was predicted to interact with decision procedure in impacting fairness perceptions. Student participants (N = 128) in a 2 × 2 laboratory simulation viewed videotaped depictions of a supervisor discussing a positive drug test result with an employee. The employee was given, or not given, an opportunity to explain; the supervisor was permitted discretion in determining the consequence or was completely bound by company policy. The proposed advantages of each decision procedure were obtained under contrasting levels of employee voice. Voice was desirable when the supervisor had discretionary authority; voice was unnecessary or even detrimental when a rule-based procedure was used. No overall preference between these two decision procedures was evident.     

基于Sieve Bootstrap方法的季节时间序列模型检验问题研究

研究目标：完善季节时间序列模型建模理论,解决建模过程烦琐、各类检验方法的结论差异大以及模型误设定问题。研究方法：基于对各季节时间序列模型的数理分析及比较,提出合理的模型检验程序;再运用Sieve Bootstrap方法,给出季节性单位根检验及确定性季节过程检验的统计量的临界值,并比较基于Sieve Bootstrap的检验方法与HEGY检验、BT检验的异同。研究发现：本文提出的检验程序能有效识别模型,检验统计量有限样本性质优良;实证分析表明,本文提出的检验程序及方法能更有效地识别中国宏观经济数据中的季节性。研究创新：将Sieve Bootstrap方法应用于季节时间序列的平稳性检验及趋势性检验中。研究价值：提出季节时间序列模型检验程序及检验方法,促进其在季节性经济数据中的应用。     

Semiparametric quantile regression estimation in dynamic models with partially varying coefficients

We study quantile regression estimation for dynamic models with partially varying coefficients so that the values of some coefficients may be functions of informative covariates. Estimation of both parametric and nonparametric functional coefficients are proposed. In particular, we propose a three stage semiparametric procedure. Both consistency and asymptotic normality of the proposed estimators are derived. We demonstrate that the parametric estimators are root-n$n$ consistent and the estimation of the functional coefficients is oracle. In addition, efficiency of parameter estimation is discussed and a simple efficient estimator is proposed. A simple and easily implemented test for the hypothesis of a varying-coefficient is proposed. A Monte Carlo experiment is conducted to evaluate the performance of the proposed estimators.     

Nonparametric Employment Subcenter Identification

A two-stage procedure is proposed for identifying urban employment subcenters. The first stage identifies candidate subcenters as significant positive residuals in a smoothed employment density function. Subcenters are those sites that provide significant explanatory power in the second-stage, semiparametric employment density function estimation. The procedure can be applied to either aggregated or disaggregated data, does not require detailed knowledge of the study area, and is easily reproducible by other researchers. Results are presented for five previously studied cities—Chicago, Dallas, Houston, Los Angeles, and San Francisco—and a new one, New Orleans.     

Test of Bernoulli success probability in inverse sampling for nearer alternatives using adaptive allocation

This paper provides a test procedure for the problem of testing Bernoulli success probability in the case of costly trials when an inverse sampling is carried out. The proposed test is based on a two population adaptive sampling scheme used in clinical trials. Some exact and asymptotic results related to the test are studied. The proposed procedure is applicable where the alternatives are not too far from the null hypothetical value.     

Quasi-isotonic regression and stochastic approximation

Summary Mukerjee’s stochastic approximation procedure on a lattice is modified: at each stage of the procedure, a sample quasi-isotonic regression is calculated instead of the isotonic one, the former being defined as the least-squares fit of observations within the class of functions that are nonpositive on the left and nonnegative on the right of some point. An effective algorithm is given and a convergence theorem proven. A multidimensional version of the procedure is proposed, the question of its convergence being left open. Research supported by the Deutsche Forschungsgemeinschaft, SFB 72.     

Distribution free estimation of heteroskedastic binary response models using Probit/Logit criterion functions

In this paper estimators for distribution free heteroskedastic binary response models are proposed. The estimation procedures are based on relationships between distribution free models with a conditional median restriction and parametric models (such as Probit/Logit) exhibiting (multiplicative) heteroskedasticity. The first proposed estimator is based on the observational equivalence between the two models, and is a semiparametric sieve estimator (see, e.g. Gallant and Nychka (1987), Ai and Chen (2003) and Chen et al. (2005)) for the regression coefficients, based on maximizing standard Logit/Probit criterion functions, such as NLLS and MLE. This procedure has the advantage that choice probabilities and regression coefficients are estimated simultaneously. The second proposed procedure is based on the equivalence between existing semiparametric estimators for the conditional median model (,  and ) and the standard parametric (Probit/Logit) NLLS estimator. This estimator has the advantage of being implementable with standard software packages such as Stata. Distribution theory is developed for both estimators and a Monte Carlo study indicates they both perform well in finite samples.     

Semiparametric time series regression modeling with a diverging number of parameters

Variable selection and error structure determination of a partially linear model with time series errors are important issues. In this paper, we investigate the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation penalty for a partially linear model with a divergent number of covariates and finite order autoregressive time series errors. Both consistency and asymptotic normality of the proposed penalized estimators are derived. The oracle property of the resultant estimators is proved. Simulation studies are carried out to assess the finite‐sample performance of the proposed procedure. A real data analysis is made to illustrate the usefulness of the proposed procedure as well.     

An extremal quotient test for exponential distributions

Summary A procedure based on the extremal quotient is proposed for testing the null hypothesis H ₀: the population of the sample has an exponential distribution against H _a : it does not have an exponential distribution.The proposed procedure is a nonparametric test which could lead to an early decision for the rejection ofH ₀     

Determining the optimal scheme of zoned effluent charges for the control of air pollution

A minimum costly zoned effluent charge program for the control of air pollution is considered paying attention to the general situation where polluters' cost functions of treating pollutant are unknown to the policy authority, and an iterative procedure by which the authority can attain a set of optimal charges is presented. The algorithm consists of steps of estimating the unknown treatment cost functions by observing polluter behavior and steps of revising charges based on the estimated cost functions. In the latter steps, a newly developed solution procedure for the zoned charge programming problem is involved. Simulated use of the algorithm indicates that the iterative charge revision procedure proposed in this paper can effectively provide the optimal scheme of zoned effluent charges.