Finite population estimation under generalized linear model assistance

Finite population estimation is the overall goal of sample surveys. When information regarding auxiliary variables are available, one may take advantage of general regression estimators (GREG) to improve sample estimates precision. GREG estimators may be derived when the relationship between interest and auxiliary variables is represented by a normal linear model. However, in some cases, such as when estimating class frequencies or counting processes means, Bernoulli or Poisson models are more suitable than linear normal ones. This paper focuses on building regression type estimators under a model-assisted approach, for the general case in which the relationship between interest and auxiliary variables may be suitably described by a generalized linear model. The finite population distribution of the variable of interest is viewed as if generated by a member of the exponential family, which includes Bernoulli, Poisson, gamma and inverse Gaussian distributions, among others. The resulting estimator is a generalized linear model regression estimator (GEREG). Its general form and basic statistical properties are presented and studied analytically and empirically, using Monte Carlo simulation experiments. Three applications are presented in which the GEREG estimator shows better performance than the GREG one.     

Decentralized estimation of regression coefficients in sensor networks

Consider a wireless sensor network with a fusion center deployed to estimate a common non-random parameter vector. Each sensor obtains a noisy observation vector of the non-random parameter vector according to a linear regression model. The observation noise is correlated across the sensors. Due to power, bandwidth and complexity limitations, each sensor linearly compresses its data. The compressed data from the sensors are transmitted to the fusion center, which linearly estimates the non-random parameter vector. The goal is to design the compression matrices at the sensors and the linear unbiased estimator at the fusion center such that the total variance of the estimation error is minimized. In this paper, we provide necessary and sufficient conditions for achieving the performance of the centralized best linear unbiased estimator. We also provide the optimal compression matrices and the optimal linear unbiased estimator when these conditions are satisfied. When these conditions are not satisfied, we propose a sub-optimal algorithm to determine the compression matrices and the linear unbiased estimator. Simulation results are provided to illustrate the effectiveness of the proposed algorithm.     

Bias-adjusted estimation in the ARX(1) model

A new point estimator for the AR(1) coefficient in the linear regression model with arbitrary exogenous regressors and stationary AR(1) disturbances is developed. Its construction parallels that of the median-unbiased estimator, but uses the mode as a measure of central tendency. The mean-adjusted estimator is also considered, and saddlepoint approximations are used to lower the computational burden of all the estimators. Large-scale simulation studies for assessing their small-sample properties are conducted. Their relative performance depends almost exclusively on the value of the autoregressive parameter, with the new estimator dominating over a large part of the parameter space.     

Local polynomial estimation in partial linear regression models under dependence

A regression model whose regression function is the sum of a linear and a nonparametric component is presented. The design is random and the response and explanatory variables satisfy mixing conditions. A new local polynomial type estimator for the nonparametric component of the model is proposed and its asymptotic normality is obtained. Specifically, this estimator works on a prewhitening transformation of the dependent variable, and the results show that it is asymptotically more efficient than the conventional estimator (which works on the original dependent variable) when the errors of the model are autocorrelated. A simulation study and an application to a real data set give promising results.     

Fuzzy entropy in fuzzy weighted linear regression model under linear restrictions with simulation study

In fuzzy set theory, it is well known that a fuzzy number can be uniquely determined through its position and entropy. Hence, by using the concept of fuzzy entropy the estimators of the fuzzy regression coefficients may be estimated. In the present communication, a fuzzy linear regression (FLR) model with some restrictions in the form of prior information has been considered. The estimators of regression coefficients have been obtained with the help of fuzzy entropy for the restricted/unrestricted FLR model by assigning some weights in the distance function. Some numerical examples have also been provided in order to illustrate the proposed model along with the obtained weighted estimators. Further, in order to compare the performance of unrestricted estimator and restricted estimator, a simulation study has been conducted by using two fundamental criteria of dominance – mean squared error matrix (MSEM) and absolute bias.     

Improved Liu-type estimator in partial linear model

In this article, a Liu-type estimation is proposed for the vector-parameter in a partial linear model. This new estimator can be regarded as generalization of the restricted least-squares estimator, the restricted ridge estimator and the restricted Liu estimator. We also obtain the asymptotic distributional bias and risk of these estimators and we also discuss some properties of the new estimator. The selection of the tuning parameter in the proposed estimator is also presented. Finally, a simulation study is presented to explain the performance of the new estimator.     

Small area estimation using a nonparametric model-based direct estimator

Nonparametric regression is widely used as a method of characterizing a non-linear relationship between a variable of interest and a set of covariates. Practical application of nonparametric regression methods in the field of small area estimation is fairly recent, and has so far focussed on the use of empirical best linear unbiased prediction under a model that combines a penalized spline (p-spline) fit and random area effects. The concept of model-based direct estimation is used to develop an alternative nonparametric approach to estimation of a small area mean. The suggested estimator is a weighted average of the sample values from the area, with weights derived from a linear regression model with random area effects extended to incorporate a smooth, nonparametrically specified trend. Estimation of the mean squared error of the proposed small area estimator is also discussed. Monte Carlo simulations based on both simulated and real datasets show that the proposed model-based direct estimator and its associated mean squared error estimator perform well. They are worth considering in small area estimation applications where the underlying population regression relationships are non-linear or have a complicated functional form.     

Fuzzy linear regression model based on fuzzy scalar product

The new concept and method of imposing imprecise (fuzzy) input and output data upon the conventional linear regression model is proposed in this paper. We introduce the fuzzy scalar (inner) product to formulate the fuzzy linear regression model. In order to invoke the conventional approach of linear regression analysis for real-valued data, we transact the α-level linear regression models of the fuzzy linear regression model. We construct the membership functions of fuzzy least squares estimators via the form of “Resolution Identity” which is a well-known formula in fuzzy sets theory. In order to obtain the membership value of any given least squares estimate taken from the fuzzy least squares estimator, we transform the original problem into the optimization problems. We also provide two computational procedures to solve the optimization problems.     

Computational aspects of robust estimators for linear regressions

This paper presents estimation procedures for some robust regression methods: the Bounded-Influence estimator for both a single linear equation (Krasker and Welsch, 1982) and a linear simultaneous equation model (Krasker and Welsch, 1985); the linear version of the Huber estimator for both a single equation (Huber, 1973, 1981) and a simultaneous equations model.The procedures are written in the RATS econometric language, which is widely available on microcomputers and mainframes.     

Conditional mean estimation under asymmetric and heteroscedastic error by linear combination of quantile regressions

In this paper we propose a new estimator for regression problems in the form of the linear combination of quantile regressions. The proposed estimator is helpful for the conditional mean estimation when the error distribution is asymmetric and heteroscedastic.It is shown that the proposed estimator has the consistency under heteroscedastic regression model: Y=μ(X)+σ(X)·e, where X is a vector of covariates, Y is a scalar response, e is a zero mean random variable independent of X and σ(X) is a positive value function. When the error term e is asymmetric, we show that the proposed estimator yields better conditional mean estimation performance than the other estimators. Numerical experiments both in synthetic and real data are shown to illustrate the usefulness of the proposed estimator.     

Absolute penalty and shrinkage estimation in partially linear models

In the context of a partially linear regression model, shrinkage semiparametric estimation is considered based on the Stein-rule. In this framework, the coefficient vector is partitioned into two sub-vectors: the first sub-vector gives the coefficients of interest, i.e., main effects (for example, treatment effects), and the second sub-vector is for variables that may or may not need to be controlled. When estimating the first sub-vector, the best estimate may be obtained using either the full model that includes both sub-vectors, or the reduced model which leaves out the second sub-vector. It is demonstrated that shrinkage estimators which combine two semiparametric estimators computed for the full model and the reduced model outperform the semiparametric estimator for the full model. Using the semiparametric estimate for the reduced model is best when the second sub-vector is the null vector, but this estimator suffers seriously from bias otherwise. The relative dominance picture of suggested estimators is investigated. In particular, suitability of estimating the nonparametric component based on the B-spline basis function is explored. Further, the performance of the proposed estimators is compared with an absolute penalty estimator through Monte Carlo simulation. Lasso and adaptive lasso were implemented for simultaneous model selection and parameter estimation. A real data example is given to compare the proposed estimators with lasso and adaptive lasso estimators.     

Simulation-based two-stage estimation for multiple nonparametric regression

To reduce the curse of dimensionality arising from nonparametric estimation procedures for multiple nonparametric regression, in this paper we suggest a simulation-based two-stage estimation. We first introduce a simulation-based method to decompose the multiple nonparametric regression into two parts. The first part can be estimated with the parametric convergence rate and the second part is small enough so that it can be approximated by orthogonal basis functions with a small trade-off parameter. Then the linear combination of the first and second step estimators results in a two-stage estimator for the multiple regression function. Our method does not need any specified structural assumption on the regression function and it is proved that the newly proposed estimation is always consistent even if the trade-off parameter is designed to be small. Thus when the common nonparametric estimator such as local linear smoothing collapses because of the curse of dimensionality, our estimator still works well.     

Stochastic observability in network state estimation and control

A hidden Markov model for the traffic congestion control problem in transmission control protocol (TCP) networks is developed, and the question of observability of this system is posed. Of specific interest are the dependence of observability on the congestion control law and the interaction between observability ideas and the effectiveness of feedback control. Analysis proceeds with a survey of observability concepts and an extension of some available definitions for linear and nonlinear stochastic systems. The key idea is to link the improvement of state estimator performance to the conditioning on the output data sequence. The observability development proceeds from linear deterministic systems to linear Gaussian systems, nonlinear systems, etc., with backwards compatibility to deterministic ideas. The principal concepts relate to the entropy decrease of scalar functions of the state, which in the linear case are describable in terms of covariance matrices. A feature of nonlinear systems is that the estimator properties may affect the closed-loop control performance. Results are derived linking stochastic reconstructibility to strict improvement of the optimal closed-loop control performance over open-loop control for the hidden Markov model. The entropy provides a means to quantify and thus order simulation results for a simplified TCP network. Motivated by the link between feedback control and reconstructibility, the entropy formulation is also explored as a means to discriminate between different control strategies for improving estimator performance. This approach has connections to dual-adaptive control ideas, where the control has the simultaneous and opposing goals of regulating the system and of exciting the system to prevent estimator divergence.     

Genetic adaptive state estimation

A genetic algorithm (GA) uses the principles of evolution, natural selection, and genetics to offer a method for parallel search of complex spaces. This paper describes a GA that can perform on-line adaptive state estimation for linear and nonlinear systems. First, it shows how to construct a genetic adaptive state estimator where a GA evolves the model in a state estimator in real time so that the state estimation error is driven to zero. Next, several examples are used to illustrate the operation and performance of the genetic adaptive state estimator. Its performance is compared to that of the conventional adaptive Luenberger observer for two linear system examples. Next, a genetic adaptive state estimator is used to predict when surge and stall occur in a nonlinear jet engine. Our main conclusion is that the genetic adaptive state estimator has the potential to offer higher performance estimators for nonlinear systems over current methods.     

Neural networks for bandwidth selection in local linear regression of time series

The problem of automatic bandwidth selection in nonparametric regression is considered when a local linear estimator is used to derive nonparametrically the unknown regression function. A plug-in method for choosing the smoothing parameter based on the use of the neural networks is presented. The method applies to dependent data generating processes with nonlinear autoregressive time series representation. The consistency of the method is shown in the paper, and a simulation study is carried out to assess the empirical performance of the procedure.     

OFDM系统中线性插值信道估计器的性能研究

为了得到由线性插值信道估计器本身精度造成的插值误差与噪声所带来的误差间的定量关系,通过基于一阶线性插值的OFDM系统梳状导频信道估计器和块状导频信道估计器误差性能的分析,推导出了插值误差和高斯噪声对估计器性能影响的数学表示式,并得出了线性插值信道估计器导频间距的选择规范;最后,在IEEE802.11 a环境下进行了系统仿真,仿真结果表明,插值误差与插值带来的噪声降低二者存在折衷,并且在室内环境中具有相同导频间距的梳状导频估计器比块状导频信道估计器性能优越。     

Option valuation based on the neural regression model

In this article, a neural regression (NR) model, which produces nonlinear coefficients of multiple regression model based on neural networks, is introduced to capture the option valuation’s nonlinear characteristics effectively. The traditional linear regression uses the least-squares estimator to estimate the coefficient of a linear regression and thus may only produce suboptimal solutions. However, Applying neural networks to forecast volatility in option pricing has increased in popularity in recent years since many studies have indicated that the conventional option pricing models are not accurate enough. Our proposed neural regression model devotes to evaluate option values to improve on the tracking error in the measurement of hedging capability. The NR model uses the variables introduced by the Black–Scholes Model and applies the multiple regressions (MR) model to re-price option values. It is worth noting that each corresponding weight coefficient in MR is constructed by a complete neural network rather than by a scalar value. By capturing the nonlinear behaviors of option pricing, our proposed NR model has lower tracking error and better hedging capability than the BS model and other studies.     

Receding horizon output feedback control for constrained uncertain systems using periodic invariance

In this article, we consider a receding horizon output feedback control (RHOC) method for linear discrete-time systems with polytopic model uncertainties and input constraints. First, we derive a set of estimator gains and then we obtain, on the basis of the periodic invariance, a series of state feedback gains stabilising the augmented output feedback system with these estimator gains. These procedures are formulated as linear matrix inequalities. An RHOC strategy is proposed based on these state feedback and state estimator gains in conjunction with their corresponding periodically invariant sets. The proposed RHOC strategy enhances the performance in comparison with the case in which static periodic gains are used, and increases the size of the stabilisable region by introducing a degree of freedom to steer the augmented state into periodically invariant sets.     

Nonparametric density estimation for positive time series

The Gaussian kernel density estimator is known to have substantial problems for bounded random variables with high density at the boundaries. For independent and identically distributed data, several solutions have been put forward to solve this boundary problem. In this paper, we propose the gamma kernel estimator as a density estimator for positive time series data from a stationary α-mixing process. We derive the mean (integrated) squared error and asymptotic normality. In a Monte Carlo simulation, we generate data from an autoregressive conditional duration model and a stochastic volatility model. We study the local and global behavior of the estimator and we find that the gamma kernel estimator outperforms the local linear density estimator and the Gaussian kernel estimator based on log-transformed data. We also illustrate the good performance of the h-block cross-validation method as a bandwidth selection procedure. An application to data from financial transaction durations and realized volatility is provided.     

Linear Regression Constrained to a Ball

Stoica, P., and Ganesan, G., Linear Regression Constrained to a Ball, Digital Signal Processing11 (2001), 80–90.A worst case lower bound (WCLB) result obtained by Nemirovskii suggests that a potentially significant estimation accuracy enhancement may be achieved provided the true parameter vector is known to belong to a ball. In this paper we discuss the many facets and implications of Nemirovskiirs result by using linear regression as a vehicle for illustration. In particular, we address briefly such issues as biased versus unbiased estimation, minimax optimal estimation, tightness of the WCLB, and comparison of WCLB with the performance of the least squares estimator constrained to the ball and that of the linear minimax estimator.