Admissibility of a variance estimator in finite population sampling under Warner's randomized response plan with multiple responses

ABSTRACT

Let P be the proportion of individuals in a finite population possessing a sensitive attribute. We consider the problem of unbiased estimation of (i) the variance of a linear unbiased estimator of P and (ii) the population variance P (1—P) for a given probability sampling design under Warner's (1965 Warner, S.L. (1965). Randomized response - A survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc. 60:63–69.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) randomized response (RR) plan when independent responses are obtained from each sampled individual as many times as he/she is selected in the sample and prove the admissibility of a quadratic unbiased estimator for each.     

Optimal Bayesian strategies for the infinite-armed Bernoulli bandit

We consider the bandit problem with an infinite number of Bernoulli arms, of which the unknown parameters are assumed to be i.i.d. random variables with a common distribution F. Our goal is to construct optimal strategies of choosing “arms” so that the expected long-run failure rate is minimized. We first review a class of strategies and establish their asymptotic properties when F is known. Based on the results, we propose a new strategy and prove that it is asymptotically optimal when F is unknown. Finally, we show that the proposed strategy performs well for a number of simulation scenarios.     

Horvitz-Thompson estimator and generalized πPS designs

Generalized πPS designs were defined by T.J. Rao (1972). Working with a general super-population model θ(g), the strategy consisting of GπPS design together with the associated Horvitz-Thompson estimator of the population total was shown to be better than two other well known strategies in T.J. Rao (1971,1972). In this note we prove the θ(g)-optimality of the strategy consisting of GπPS design together with the associated Horvitz-Thompson estimator in the entire class of p-unbiased strategies of the population total with expected sample size fixed. In view of our theorem the results of T.J. Rao follow as special cases.     

A unified class of penalties with the capability of producing a differentiable alternative to l1 norm penalty

Abstract

This article presents a class of novel penalties that are defined under a unified framework, which includes lasso, SCAD and ridge as special cases, and novel functions, such as the asymmetric quantile check function. The proposed class of penalties is capable of producing alternative differentiable penalties to lasso. We mainly focus on this case and show its desirable properties, propose an efficient algorithm for the parameter estimation and prove the theoretical properties of the resulting estimators. Moreover, we exploit the differentiability of the penalty function by deriving a novel Generalized Information Criterion (GIC) for model selection. The method is implemented in the R package DLASSO freely available from CRAN, http://CRAN.R-project.org/package=DLASSO.     

Time-consistent strategies for multi-period mean-variance portfolio optimization with the serially correlated returns

Abstract

In this paper, we discuss several different styles of multi-period mean-variance portfolio optimization problems under the serially correlated returns. We derive the time-consistent strategies for the classical multi-period mean-variance optimization with and without risk-free asset using a backward induction approach. We also propose an alternative multi-period mean-variance model, and the corresponding time-consistent strategies are derived. Whereafter, we provide some portfolio evaluation indexes and perform extensive empirical studies based on real data, aiming to provide useful advice for investors. To a large extent, the empirical results answer one important and practical question: in actual investment situations, which strategy is preferred by different investors?     

Admissible unbiased estimation of finite population variance under a randomized response model

We consider the problem of estimation of a finite population variance related to a sensitive character under a randomized response model and prove (i) the admissibility of an estimator for a given sampling design in a class of quadratic unbiased estimators and (ii) the admissibility of a sampling strategy in a class of comparable quadratic unbiased strategies.     

Optimal investment-consumption and life insurance with capital constraints

Abstract

The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal strategy and the optimal martingale measure and we obtain the explicit solutions for the power utility functions.     

A classifier under the strongly spiked eigenvalue model in high-dimension,low-sample-size context

Abstract

We consider the classification of high-dimensional data under the strongly spiked eigenvalue (SSE) model. We create a new classification procedure on the basis of the high-dimensional eigenstructure in high-dimension, low-sample-size context. We propose a distance-based classification procedure by using a data transformation. We also prove that our proposed classification procedure has consistency property for misclassification rates. We discuss performances of our classification procedure in simulations and real data analyses using microarray data sets.     

Superiority of the r-k class estimator over some estimators in a misspecified linear model

ABSTRACT

In this article, we discuss the superiority of r-k class estimator over some estimators in a misspecified linear model. We derive the necessary and sufficient conditions for the superiority of the r-k class estimator over each of these estimators under the Mahalanobis loss function by the average loss criterion in the misspecified linear model.     

Upper bounds for ruin probabilities under model uncertainty

Abstract

In this paper, we investigate some ruin problems for risk models that contain uncertainties on both claim frequency and claim size distribution. The problems naturally lead to the evaluation of ruin probabilities under the so-called G-expectation framework. We assume that the risk process is described as a class of G-compound Poisson process, a special case of the G-Lévy process. By using the exponential martingale approach, we obtain the upper bounds for the two-sided ruin probability as well as the ruin probability involving investment. Furthermore, we derive the optimal investment strategy under the criterion of minimizing this upper bound. Finally, we conclude that the upper bound in the case with investment is less than or equal to the case without investment.     

Optimal control strategies for dividend payments and capital injections in compound Markov binomial risk model with penalties for deficits

We consider the compound Markov binomial risk model. The company controls the amount of dividends paid to the shareholders as well as the capital injections in order to maximize the cumulative expected discounted dividends minus the discounted capital injections and the discounted penalties for deficits prior to ruin. We show that the optimal value function is the unique solution of an HJB equation, and the optimal control strategy is a two-barriers strategy given the current state of the Markov chain. We obtain some properties of the optimal strategy and the optimal condition for ruining the company. We offer a high-efficiency algorithm for obtaining the optimal strategy and the optimal value function. In addition, we also discuss the optimal control problem under a restriction of bounded dividend rates. Numerical results are provided to illustrate the algorithm and the impact of the penalties.     

On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with associated errors

ABSTRACT

The purpose of this paper is to prove, under mild conditions, the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows from a uniform linearity property for linear rank statistics that we establish under general conditions on the dependence of the errors. We prove also a tightness criterion for weighted empirical process constructed from associated triangular arrays. This criterion is needed for the proofs which are based on that of Koul [Behavior of robust estimators in the regression model with dependent errors. Ann Stat. 1977;5(4):681–699] and of Louhichi [Louhichi S. Weak convergence for empirical processes of associated sequences. Ann Inst Henri Poincaré Probabilités Statist. 2000;36(5):547–567].     

Searching effective rotation patterns for population median using exponential type estimators in two-occasion rotation sampling

ABSTRACT

The present article is an attempt to explore the rotation patterns using exponential ratio type estimators for the estimation of finite population median at current occasion in two occasion rotation sampling. Properties of the proposed estimators including the optimum replacement strategies have been elaborated. The proposed estimators have been compared with sample median estimator when there is no matching from previous occasion as well with the ratio type estimator proposed by Singh et al. (2007 Singh, H.P., Tailor, R., Singh, S., Kim, Jong-Min. (2007). Quintile estimation in successive sampling. J. Kor. Stat. Soc. 36(4):543–556. [Google Scholar]) for second quantile. The behaviors of the proposed estimators are justified by empirical interpretations and validated by means of simulation study with the help of some natural populations.     

On the Expressions of Estimability in Testing General Linear Hypotheses

In testing a general linear hypothesis of the form K ′β ? ( W ′) under a general linear model, an equivalent hypothesis involving only estimable parametric functions is provided, and then an explicit test statistic in terms of the model matrices is given. The corresponding results are expanded to the case of a general linear model with a restriction and are illustrated by an example.     

Bayesian estimation and prediction for the inverse weibull distribution under general progressive censoring

Abstract

This paper deals with Bayesian estimation and prediction for the inverse Weibull distribution with shape parameter α and scale parameter λ under general progressive censoring. We prove that the posterior conditional density functions of α and λ are both log-concave based on the assumption that λ has a gamma prior distribution and α follows a prior distribution with log-concave density. Then, we present the Gibbs sampling strategy to estimate under squared-error loss any function of the unknown parameter vector (α, λ) and find credible intervals, as well as to obtain prediction intervals for future order statistics. Monte Carlo simulations are given to compare the performance of Bayesian estimators derived via Gibbs sampling with the corresponding maximum likelihood estimators, and a real data analysis is discussed in order to illustrate the proposed procedure. Finally, we extend the developed methodology to other two-parameter distributions, including the Weibull, Burr type XII, and flexible Weibull distributions, and also to general progressive hybrid censoring.     

Using logistic regression for semiparametric comparison of population means and variances

Abstract

We propose to compare population means and variances under a semiparametric density ratio model. The proposed method is easy to implement by employing logistic regression procedures in many statistical software, and it often works very well when data are not normal. In this paper, we construct semiparametric estimators of the differences of two population means and variances, and derive their asymptotic distributions. We prove that the proposed semiparametric estimators are asymptotically more efficient than the corresponding non parametric ones. In addition, a simulation study and the analysis of two real data sets are presented. Finally, a short discussion is provided.     

Empirical likelihood inference for a semiparametric hazards regression model

ABSTRACT

We investigated the empirical likelihood inference approach under a general class of semiparametric hazards regression models with survival data subject to right-censoring. An empirical likelihood ratio for the full 2p regression parameters involved in the model is obtained. We showed that it converged weakly to a random variable which could be written as a weighted sum of 2p independent chi-squared variables with one degree of freedom. Using this, we could construct a confidence region for parameters. We also suggested an adjusted version for the preceding statistic, whose limit followed a standard chi-squared distribution with 2p degrees of freedom.     

Approximation of distributions by using the Anderson Darling statistic

ABSTRACT

In practice, it is often not possible to find an appropriate family of distributions which can be used for fitting the sample distribution with high precision. In these cases, it seems to be opportune to search for the best approximation by a family of distributions instead of an exact fit. In this paper, we consider the Anderson–Darling statistic with plugged-in minimum distance estimator for the parameter vector. We prove asymptotic normality of the Anderson–Darling statistic which is used for a test of goodness of approximation. Moreover, we introduce a measure of discrepancy between the sample distribution and the model class.     

Empirical likelihood ratio tests for the linear regression model with inequality constraints

Abstract

In this article, empirical likelihood is applied to the linear regression model with inequality constraints. We prove that asymptotic distribution of the adjusted empirical likelihood ratio test statistic is a weighted mixture of chi-square distribution.     

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.