Asymptotic Properties of Error Density Estimator in Regression Model Under α-Mixing Assumptions

This paper aims at working out economic groupscreening plans to sort out defective items from a population which consists of tems with unequal a-priori probabilities of being defective. It is shown that in the case of group-screening from a population with unequal a-priori probabilities of factors being defective, the number of obseruations needed on the average is considerably smaller than that required in the case of a population with factors having the same a-priori probability of being defective. Tables at the end give some group-screening plans as illustrations.     

Conditional Score Tests for Heteroscedasticity in the Two-Way Error Components Model

This paper extends the one-way heteroskedasticity score test of Holly and Gardiol (2000, In: Krishnakumar, J, Ronchetti, E (Eds.), Panel Data Econometrics: Future Directions, North-Holland, Amsterdam, pp. 199–211) to two conditional Lagrange Multiplier (LM) tests of heteroskedasticity under contiguous alternatives within the two-way error components model framework. In each case, the derivation of Rao's efficient score statistics for testing heteroskedasticity is first obtained. Then, based on a specific set of assumptions, the asymptotic distribution of the score under contiguous alternatives is established. Finally, the expression for the score test statistic in the presence of heteroskedasticity and related asymptotic local powers of these score test statistics are derived and discussed.     

Asymptotic Properties of Conditional Quantile Estimator Under Left-Truncated and α-Mixing Conditions

In this article, we establish strong uniform convergence and asymptotic normality of estimators of conditional quantile and conditional distribution function for a left truncated model when the data exhibit some kind of dependence. It is assumed that the observations form a stationary α-mixing sequence. The results of Lemdani et al. (2009 Lemdani , M. , Ould-Saïd , E. , Poulin , N. ( 2009 ). Asymptotic properties of a conditional quantile estimator with randomly truncated data . J. Multivariate Anal. 100 : 546 – 559 .[Crossref], [Web of Science ®] , [Google Scholar]) are relaxed from the i.i.d. assumption to α-mixing setting. Finite sample behavior of the estimators is investigated via simulations as well.     

The Effect of Estimation of Unknown Degrees of Freedom on Estimation of Remaining Parameters in Spanos’ Conditional t Heteroskedastic Model

This article investigates the effect of estimation of unknown degrees of freedom on efficient estimation of remaining parameters in Spanos’ conditional t heteroskedastic model. We compare by simulation three maximum likelihood estimators (MLEs) of the remaining parameters in the model: the MLE of the remaining parameters when all the parameters are estimated by the MLE, when the degrees of freedom is estimated by a method of moments estimator, and when the degrees of freedom is erroneously specified. The latter two methods are found to perform poorly compared to the former method for the inference of variance parameters in the model. Thus, efficient estimation of degrees of freedom by the MLE is important to estimate efficiently the remaining variance parameters.     

Transformed Logit Confidence Intervals for Small Populations in Single Capture–Recapture Estimation

The good performance of logit confidence intervals for the odds ratio with small samples is well known. This is true unless the actual odds ratio is very large. In single capture–recapture estimation the odds ratio is equal to 1 because of the assumption of independence of the samples. Consequently, a transformation of the logit confidence intervals for the odds ratio is proposed in order to estimate the size of a closed population under single capture–recapture estimation. It is found that the transformed logit interval, after adding .5 to each observed count before computation, has actual coverage probabilities near to the nominal level even for small populations and even for capture probabilities near to 0 or 1, which is not guaranteed for the other capture–recapture confidence intervals proposed in statistical literature. Thus, given that the .5 transformed logit interval is very simple to compute and has a good performance, it is appropriate to be implemented by most users of the single capture–recapture method.     

Survival Estimation with Missing Censoring Times for the Generalized Koziol–Green Model

ABSTRACT

When analyzing time-to-event data, there are various situations in which right censoring times for unfailed units are missing. In that context, by taking a supplementary sample of a convenient percentage of unfailed units, we propose a semi-parametric method for estimating a survival function under the natural extension of the Koziol–Green model to double random censoring. Some large sample properties of this estimator are derived. We prove uniform strong consistency and asymptotic weak convergence to a Gaussian process. A simulation study is also presented in order to analyze the behavior of the proposed estimator.     

Asymptotic Normality for Regression Function Estimate Under Truncation and α-Mixing Conditions

In this article we establish pointwise asymptotic normality of nonparametric kernel estimator of regression function for a left truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. Also, the asymptotic normality of the estimation of the covariable's density is considered. As a by-product, we obtain a uniform weak convergence rate for the product-limit estimator of the lifetime and truncated distributions under dependence, which is interesting independently. Finite sample behavior of the estimator of the regression function is investigated as well.     

Aalen’s Additive Risk Model for Left-Truncated and Right-Censored Data

We analyze left-truncated and right-censored (LTRC) data using Aalen’s linear models. The integrated square error (ISE) is used to select an optimal bandwidth of the weighted least-squared estimator. We also consider a semiparametric approach for the case when the distribution of the left-truncated variable is parameterized. A simulation study is conducted to investigate the performance of the proposed estimators. The approaches are illustrated with the data of Stanford heart transplant.     

Conditional Akaike information criterion in the Fay–Herriot model

The Fay–Herriot model, a popular approach in small area estimation, uses relevant covariates to improve the inference for quantities of interest in small sub-populations. The conditional Akaike information (AI) (Vaida and Blanchard, 2005 [23]) in linear mixed-effect models with i.i.d. errors can be extended to the Fay–Herriot model for measuring prediction performance. In this paper, we derive the unbiased conditional AIC (cAIC) for three popular approaches to fitting the Fay–Herriot model. The three cAIC have closed forms and are convenient to implement. We conduct a simulation study to demonstrate their accuracy in estimating the conditional AI and superior performance in model selection than the classic AIC. We also apply the cAIC in estimating county-level prevalence rates of obesity for working-age Hispanic females in California.     

What Level of Statistical Model Should We Use in Small Area Estimation?

If unit‐level data are available, small area estimation (SAE) is usually based on models formulated at the unit level, but they are ultimately used to produce estimates at the area level and thus involve area‐level inferences. This paper investigates the circumstances under which using an area‐level model may be more effective. Linear mixed models (LMMs) fitted using different levels of data are applied in SAE to calculate synthetic estimators and empirical best linear unbiased predictors (EBLUPs). The performance of area‐level models is compared with unit‐level models when both individual and aggregate data are available. A key factor is whether there are substantial contextual effects. Ignoring these effects in unit‐level working models can cause biased estimates of regression parameters. The contextual effects can be automatically accounted for in the area‐level models. Using synthetic and EBLUP techniques, small area estimates based on different levels of LMMs are investigated in this paper by means of a simulation study.     

Linear Prediction Sufficiency for New Observations in the General Gauss–Markov Model

We consider the prediction of new observations in a general Gauss–Markov model. We state the fundamental equations of the best linear unbiased prediction, BLUP, and consider some properties of the BLUP. Particularly, we focus on such linear statistics, which preserve enough information for obtaining the BLUP of new observations as a linear function of them. We call such statistics linearly prediction sufficient for new observations, and introduce some equivalent characterizations for this new concept.     

Nonparametric Estimation of Sojourn Time Distributions for Truncated Serial Event Data—a Weight-adjusted Approach

In follow-up studies, survival data often include subjects who have had a certain event at recruitment and may potentially experience a series of subsequent events during the follow-up period. This kind of survival data collected under a cross-sectional sampling criterion is called truncated serial event data. The outcome variables of interest in this paper are serial sojourn times between successive events. To analyze the sojourn times in truncated serial event data, we need to confront two potential sampling biases arising simultaneously from a sampling criterion and induced informative censoring. In this study, nonparametric estimation of the joint probability function of serial sojourn times is developed by using inverse probabilities of the truncation and censoring times as weight functions to accommodate these two sampling biases under various situations of truncation and censoring. Relevant statistical properties of the proposed estimators are also discussed. Simulation studies and two real data are presented to illustrate the proposed methods.     

Confidence Intervals for Conditional Tail Risk Measures in ARMA–GARCH Models

ABSTRACT

ARMA–GARCH models are widely used to model the conditional mean and conditional variance dynamics of returns on risky assets. Empirical results suggest heavy-tailed innovations with positive extreme value index for these models. Hence, one may use extreme value theory to estimate extreme quantiles of residuals. Using weak convergence of the weighted sequential tail empirical process of the residuals, we derive the limiting distribution of extreme conditional Value-at-Risk (CVaR) and conditional expected shortfall (CES) estimates for a wide range of extreme value index estimators. To construct confidence intervals, we propose to use self-normalization. This leads to improved coverage vis-à-vis the normal approximation, while delivering slightly wider confidence intervals. A data-driven choice of the number of upper order statistics in the estimation is suggested and shown to work well in simulations. An application to stock index returns documents the improvements of CVaR and CES forecasts.     

Measuring Tail Thickness to Estimate the Stable Index α: A Critique

A generalized Pareto or simple Pareto tail-index estimate above 2 has frequently been cited as evidence against infinite-variance stable distributions. It is demonstrated that this inference is invalid; tail index estimates greater than 2 are to be expected for stable distributions with α as low as 1.65. The nonregular distribution of the likelihood ratio statistic for a null of normality and an alternative of symmetric stability is tabulated by Monte Carlo methods and appropriately adjusted for sampling error in repeated tests. Real stock returns yield a stable α of 1.845 and reject iid normality at the .996 level.     

Bayesian Estimation of the Log–linear Exponential Regression Model with Censorship and Collinearity

In this work, a simulation study is conducted to evaluate the performance of Bayesian estimators for the log–linear exponential regression model under different levels of censoring and degrees of collinearity for two covariates. The diffuse normal, independent Student-t and multivariate Student-t distributions are considered as prior distributions and to draw from the posterior distributions, the Metropolis algorithm is implemented. Also, the results are compared with the maximum likelihood estimators in terms of the mean squared error, coverages and length of the credibility and confidence intervals.     

On the α-risks for shewhart control charts

The performance of the usual Shewhart control charts for monitoring process means and variation can be greatly affected by nonnormal data or subgroups that are correlated. Define the α_k-risk for a Shewhart chart to be the probability that at least one “out-of-control” subgroup occurs in k subgroups when the control limits are calculated from the k subgroups. Simulation results show that the α_k-risks can be quite large even for a process with normally distributed, independent subgroups. When the data are nonnormal, it is shown that the α_k-risk increases dramatically. A method is also developed for simulating an “in-control” process with correlated subgroups from an autoregressive model. Simulations with this model indicate marked changes in the α_k-risks for the Shewhart charts utilizing this type of correlated process data. Therefore, in practice a process should be investigated thoroughly regarding whether or not it is generating normal, independent data before out-of-control points on the control charts are interpreted to be due to some real assignable cause.