On Semiparametric Mode Regression Estimation

It has been found that, for a variety of probability distributions, there is a surprising linear relation between mode, mean, and median. In this article, the relation between mode, mean, and median regression functions is assumed to follow a simple parametric model. We propose a semiparametric conditional mode (mode regression) estimation for an unknown (unimodal) conditional distribution function in the context of regression model, so that any m-step-ahead mean and median forecasts can then be substituted into the resultant model to deliver m-step-ahead mode prediction. In the semiparametric model, Least Squared Estimator (LSEs) for the model parameters and the simultaneous estimation of the unknown mean and median regression functions by the local linear kernel method are combined to infer about the parametric and nonparametric components of the proposed model. The asymptotic normality of these estimators is derived, and the asymptotic distribution of the parameter estimates is also given and is shown to follow usual parametric rates in spite of the presence of the nonparametric component in the model. These results are applied to obtain a data-based test for the dependence of mode regression over mean and median regression under a regression model.     

On Mean Squared Prediction Error Estimation in Small Area Estimation Problems

For a general linear mixed normal model, a new linearized weighted jackknife method is proposed to estimate the mean squared prediction error (MSPE) of an empirical best linear unbiased predictor (EBLUP) of a general mixed effect. Different MSPE estimators are compared using a Monte Carlo simulation study.     

On the Simultaneous Estimation of Scale Parameters

This note is an extension of Das Gupta's results (1986) on the estimation of multiparameter gamma distribution. Consider p (p ? 2) independent positive random variables with possibly different scale-parameter densities. For the estimation of the powers of the scale parameters it is shown that the “best multiple estimator” is inadmissible with respect to a large class of weighted quadratic loss functions.     

On Variance Estimation in Semiparametric Regression Models

ABSTRACT

This article considers estimation of the error variance in a semiparametric regression model. The estimator, based on the semiparametric residuals, is shown to be consistent (with certain rate) for the error variance.     

On Variance-Stabilizing Multivariate Non Parametric Regression Estimation

The mean squared error (MSE)-minimizing local variable bandwidth for the univariate local linear estimator (the LL) is well-known. This bandwidth does not stabilize variance over the domain. Moreover, in regions where a regression function has zero curvature, the LL estimator is discontinuous. In this paper, we propose a variance-stabilizing (VS) local variable diagonal bandwidth matrix for the multivariate LL estimator. Theoretically, the VS bandwidth can outperform the multivariate extension of the MSE-minimizing local variable scalar bandwidth in terms of asymptotic mean integrated squared error and can avoid discontinuity created by the MSE-minimizing bandwidth. We present an algorithm for estimating the VS bandwidth and simulation studies.     

On Nonparametric Estimation of a Reliability Function

This article considers the properties of a nonparametric estimator developed for a reliability function which is used in many reliability problems. Properties such as asymptotic unbiasedness and consistency are proven for the estimator and using U-statistics, weak convergence of the estimator to a normal distribution is shown. Finally, numerical examples based on an extensive simulation study are presented to illustrate the theory and compare the estimator developed in this article with another based directly on the ratio of two empirical distributions studied in Zardasht and Asadi (2010 Zardasht , V. , Asadi , M. ( 2010 ). Evaluation of P(X _t  > Y _t ) when both X _t and Y _t are residual lifetimes of two systems . Statistica Neerlandica 64 : 460 – 481 .[Crossref], [Web of Science ®] , [Google Scholar]).     

On Estimation of the Bivariate Poisson INAR Process

In a recent article, Pedeli and Karlis (2010 Pedeli, X. and Karlis, D. 2010. A Bivariate INAR(1) Process with Application. Statistical Modelling: An international Journal, 11: 325–349. [Crossref], [Web of Science ®] , [Google Scholar]) examined the extension of the classical Integer–valued Autoregressive (INAR) model to the bivariate case. In the present article, we examine estimation methods for the case of bivariate Poisson innovations. This is a simple extension of the classical INAR model allowing for two discrete valued time series to be correlated. Properties of different estimators are given. We also compare their properties via a small simulation experiment. Extensions to incorporate covariate information is discussed. A real data application is also provided.     

On Improvement in Variance Estimation Using Auxiliary Information

Kadilar and Cingi (2006 Kadilar , C. , Cingi , H. ( 2006 ). Improvement in variance estimation using auxiliary information . Hacett. J. Math. Statist. 35 ( 1 ): 111 – 115 . [Google Scholar]) have introduced an estimator for the population variance using an auxiliary variable in simple random sampling. We propose a new ratio-type exponential estimator for population variance which is always more efficient than usual ratio and regression estimators suggested by Isaki (1983 Isaki , C. T. ( 1983 ). Variance estimation using auxiliary information . J. Amer. Statist. Assoc. 78 : 117 – 123 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and by Kadilar and Cingi (2006 Kadilar , C. , Cingi , H. ( 2006 ). Improvement in variance estimation using auxiliary information . Hacett. J. Math. Statist. 35 ( 1 ): 111 – 115 . [Google Scholar]). Efficiency comparison is carried out both mathematically and numerically.     

On Efficient AR Spectral Estimation for Long-Range Predictions

ABSTRACT

This article discusses the concept of asymptotic efficiency from the frequency domain point of view making use of the direct method for multiple prediction. In particular, it is shown that with the use of a new autoregressive model selection at each prediction time h, the asymptotic lower bound of the integrated relative squared error of an AR spectral estimate is attained by the order selected for multistep prediction by the AIC selection procedure Akaike (1973 Akaike , H. ( 1973 ). Information theory and an extension of the maximum likelihood principle . In Petrov , B. N. , Csaki , F. eds. Proc. 2nd Int. Symp. on Information Theory. Budapest : Akademia Kiado , 267 – 281 . [Google Scholar]) and its alike when the underlying process is a non zero mean infinite order not necessarily Gaussian AR process.     

On the Estimation of Parameters of Kumaraswamy-G Distributions

Cordeiro and de Castro proposed a new family of generalized distributions based on the Kumaraswamy distribution (denoted as Kw-G). Nadarajah et al. showed that the density function of the new family of distributions can be expressed as a linear combination of the density of exponentiated family of distributions. They derived some properties of Kw-G distributions and discussed estimation of parameters using the maximum likelihood (ML) method. Cheng and Amin and Ranneby introduced a new method of estimating parameters based on Kullback–Leibler divergence (the maximum spacing (MSP) method). In this article, the estimates of parameters of Kw-G distributions are obtained using the MSP method. For some special Kw-G distributions, the new estimators are compared with ML estimators. It is shown by simulations and a real data application that MSP estimators have better properties than ML estimators.     

Dynamic Conditional Correlation: On Properties and Estimation

This article addresses some of the issues that arise with the Dynamic Conditional Correlation (DCC) model. It is proven that the DCC large system estimator can be inconsistent, and that the traditional interpretation of the DCC correlation parameters can result in misleading conclusions. Here, we suggest a more tractable DCC model, called the cDCC model. The cDCC model allows for a large system estimator that is heuristically proven to be consistent. Sufficient stationarity conditions for cDCC processes of interest are established. The empirical performances of the DCC and cDCC large system estimators are compared via simulations and applications to real data.     

On Estimation of Hurst Parameter Under Noisy Observations

It is widely accepted that some financial data exhibit long memory or long dependence, and that the observed data usually possess noise. In the continuous time situation, the factional Brownian motion B^H and its extension are an important class of models to characterize the long memory or short memory of data, and Hurst parameter H is an index to describe the degree of dependence. In this article, we estimate the Hurst parameter of a discretely sampled fractional integral process corrupted by noise. We use the preaverage method to diminish the impact of noise, employ the filter method to exclude the strong dependence, and obtain the smoothed data, and estimate the Hurst parameter by the smoothed data. The asymptotic properties such as consistency and asymptotic normality of the estimator are established. Simulations for evaluating the performance of the estimator are conducted. Supplementary materials for this article are available online.     

On Rates of Convergence for Bayesian Density Estimation

Abstract.  We consider the problem of estimating a compactly supported density taking a Bayesian nonparametric approach. We define a Dirichlet mixture prior that, while selecting piecewise constant densities, has full support on the Hellinger metric space of all commonly dominated probability measures on a known bounded interval. We derive pointwise rates of convergence for the posterior expected density by studying the speed at which the posterior mass accumulates on shrinking Hellinger neighbourhoods of the sampling density. If the data are sampled from a strictly positive, α -Hölderian density, with α  ∈ ( 0,1] , then the optimal convergence rate n^{− α / (2 α +1)} is obtained up to a logarithmic factor. Smoothing histograms by polygons, a continuous piecewise linear estimator is obtained that for twice continuously differentiable, strictly positive densities satisfying boundary conditions attains a rate comparable up to a logarithmic factor to the convergence rate n ^−4/5 for integrated mean squared error of kernel type density estimators.     

On Sensitivity of Inverse Response Plot Estimation and the Benefits of a Robust Estimation Approach

Abstract. Inverse response plots are a useful tool in determining a response transformation function for response linearization in regression. Under some mild conditions it is possible to seek such transformations by plotting ordinary least squares fits versus the responses. A common approach is then to use nonlinear least squares to estimate a transformation by modelling the fits on the transformed response where the transformation function depends on an unknown parameter to be estimated. We provide insight into this approach by considering sensitivity of the estimation via the influence function. For example, estimation is insensitive to the method chosen to estimate the fits in the initial step. Additionally, the inverse response plot does not provide direct information on how well the transformation parameter is being estimated and poor inverse response plots may still result in good estimates. We also introduce a simple robustified process that can vastly improve estimation.     

On the Derivation of Efficiency Results in Linear Estimation

This paper proposes a simple rank condition for determining whether or not certain limited information estimators based on common data transformations in linear models are efficient. Examples which illustrate the use of the condition are presented.     

On the Estimation of the Probability Density by Trigonometric Series

We present in this article an estimator based on a new orthogonal trigonometric series. We give its statistical properties (bias, variance, mean square error, and mean integrated square error) and the asymptotic properties (convergence of variance, convergence of the mean square error, convergence of the mean integrated square error, uniform convergence in probability, and the rate of convergence of the mean integrated square error). The comparison by simulation on a test density between the estimator obtained from a new trigonometric series with Fejer estimator also based on orthogonal trigonometric series, shows that our estimator is more performant in the sense of the mean integrated square error.     

PPS抽样设计的比估计及其模拟分析

本文在介绍简单随机抽样比估计的基础上,对PPS抽样设计的比估计进行了系统的研究,并使用了第一次农业普查数据对方法进行了模拟。从模拟结果可以看到,比估计方法可以解决一些调查精度和多目标调查的问题。     

On Sampling Designs for Integral Estimation of a Random Process

Abstract

In this paper the problem of finding exactly optimal sampling designs for estimating the weighted integral of a stochastic process with a product covariance structure (R(s,t)=u(s)v(t), s<t) is discussed. The sampling designs for certain standard processes belonging to the product class are calculated. An asymptotic solution to the design problem also follows as a consequence.     

On the Estimation Accuracy of Causal Effects using Supplementary Variables

This paper focuses on a situation in which a set of treatments is associated with a response through a set of supplementary variables in linear models as well as discrete models. Under the situation, we demonstrate that the causal effect can be estimated more accurately from the set of supplementary variables. In addition, we show that the set of supplementary variables can include selection variables and proxy variables as well. Furthermore, we propose selection criteria for supplementary variables based on the estimation accuracy of causal effects. From graph structures based on our results, we can judge certain situations under which the causal effect can be estimated more accurately by supplementary variables and reliably evaluate the causal effects from observed data.