区间时变时滞线性系统稳定性准则的改进

研究了区间时变时滞线性系统的稳定性问题,基于Lyapunov泛函方法,使用新的处理技术估计Lyapunov泛函导数的上界,以线性矩阵不等式形式给出了系统稳定性准则的改进结果。所给稳定性准则比已有结果具有更低的保守性,数值实例表明了结果的有效性。     

Some Decompositions of OLSEs and BLUEs Under a Partitioned Linear Model

We consider in this paper a partitioned linear model { y , X ₁ β ₁ + X ₂ β ₂ , σ ² σ } and two corresponding small models { y , X ₁ β ₁ , σ ² σ } and { y , X ₂ β ₂ , σ ² σ } . We derive necessary and sufficient conditions for (i) the ordinary least squares estimator under the full model to be the sum of the ordinary least squares estimators under the two small models; (ii) the best linear unbiased estimator under the full model to be the sum of the best linear unbiased estimators under the two small models; (iii) the best linear unbiased estimator under the full model to be the sum of the ordinary least squares estimators under the two small models. The proofs of the main results in this paper also demonstrate how to use the matrix rank method for characterizing various equalities of estimators under general linear models.     

Evaluating expectations of <Emphasis Type="Italic">L</Emphasis>-statistics by the Steffensen inequality

By combining the Moriguti and Steffensen inequalities, we obtain sharp upper bounds for the expectations of arbitrary linear combinations of order statistics from iid samples. The bounds are expressed in terms of expectations of the left truncated parent distribution and constants that depend only on the coefficients of the linear combination. We also present analogous results for dependent id samples. The bounds are especially useful for L-estimates of the scale parameter of the distribution.     

Investment limit cycles in a socialist economy

The present paper generalizes a linear cycle model of the socialist economy studied in Simonovits (1990): the two equations describing the reproduction of the tensions are retained, while the two linear reaction equations are confined to the interval of lower and upper bounds; outside these intervals the decisions are given by the corresponding bounds (cf. Hicks, 1950).The main result is the following: If a certain linear system of equations and inequalities has a solution, then there exists a limit cycle with period 4, the amplitude of which is independent of the initial states.     

A Bayesian-like estimator of the process capability index Cpmk

Pearn et al. (1992) proposed the capability index C_pmk, and investigated the statistical properties of its natural estimator for stable normal processes with constant mean μ. Chen and Hsu (1995) showed that under general conditions the asymptotic distribution of is normal if μ≠m, and is a linear combination of the normal and the folded-normal distributions if μ=m, where m is the mid-point between the upper and the lower specification limits. In this paper, we consider a new estimator for stable processes under a different (more realistic) condition on process mean, namely, P (μ≥m)=p, 0≤p≤1. We obtain the exact distribution, the expected value, and the variance of under normality assumption. We show that for P (μ≥m)=0, or 1, the new estimator is the MLE of C_pmk, which is asymptotically efficient. In addition, we show that under general conditions is consistent and is asymptotically unbiased. We also show that the asymptotic distribution of is a mixture of two normal distributions. RID="*" ID="*"  The research was partially supported by National Science Council of the Republic of China (NSC-89-2213-E-346-003).     

Another look at the naive estimator in a regression model

We consider the linear regression model where only a particular linear function of the dependent variables is observed, Stahlecker and Schmidt (1987) proposed a naive least squares (LS) estimator for regression coefficients in such a case. In this note we represent their estimator as a general ridge estimator. This observation leads to a view different from the previous work and provides an easy way of obtaining many important properties of the naive LS estimator. Our approach also gives some insight into the relationship between the naive LS estimator and the generalized least squares estimator.     

Kantorovich inequalities and efficiency comparisons for several classes of estimators in linear models

New matrix, determinant and trace versions of the Kantorovich inequality (KI) involving two positive definite matrices are presented. Some of these are used to study the efficiencies of minimum-distance (MD) estimators, generalized method-of-moments (GMM) estimators and several estimators specific to longitudinal or panel-data analysis. They are also used to give upper bounds for the determinant and trace of the asymptotic variance matrix of a weighted least-squares (WLS) estimator in the generalized linear model.     

Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement error of certain types and can also handle non-synchronous trading. It is the first estimator which has these three properties which are all essential for empirical work in this area. We derive the large sample asymptotics of this estimator and assess its accuracy using a Monte Carlo study. We implement the estimator on some US equity data, comparing our results to previous work which has used returns measured over 5 or 10 min intervals. We show that the new estimator is substantially more precise.     

On the performance of the ordinary least squares method under an error component model

Starting from the one-dimensional results by Wang et al (1994) we consider the performance of the ordinary least squares estimator in comparison to the best linear unbiased estimator under an error component model with random effects in units and time. Upper bounds are derived for the first-order approximation to the difference between both estimators and for the spectral norm of the difference between their dispersion matrices.     

Strong Consistency of the Maximum Likelihood Estimator in Generalized Linear and Nonlinear Mixed-Effects Models

Generalized linear and nonlinear mixed-effects models are used extensively in biomedical, social, and agricultural sciences. The statistical analysis of these models is based on the asymptotic properties of the maximum likelihood estimator. However, it is usually assumed that the maximum likelihood estimator is consistent, without providing a proof. A rigorous proof of the consistency by verifying conditions from existing results can be very difficult due to the integrated likelihood. In this paper, we present some easily verifiable conditions for the strong consistency of the maximum likelihood estimator in generalized linear and nonlinear mixed-effects models. Based on this result, we prove that the maximum likelihood estimator is consistent for some frequently used models such as mixed-effects logistic regression models and growth curve models.     

Best constants in Chebyshev inequalities with various applications

In this article we describe some ways to significantly improve the Markov-Gauss-Camp-Meidell inequalities and provide specific applications. We also describe how the improved bounds are extendable to the multivariate case. Applications include explicit finite sample construction of confidence intervals for a population mean, upper bounds on a tail probability P(X>k) by using the density at k, approximation of P-values, simple bounds on the Riemann Zeta function, on the series , improvement of Minkowski moment inequalities, and construction of simple bounds on the tail probabilities of asymptotically Poisson random variables. We also describe how a game theoretic argument shows that our improved bounds always approximate tail probabilities to any specified degree of accuracy. Received: April 1999     

THE ROLE OF CONDITIONAL HETEROSKEDASTICITY IN IDENTIFYING AND ESTIMATING LINEAR TRIANGULAR SYSTEMS,WITH APPLICATIONS TO ASSET PRICING MODELS THAT INCLUDE A MISMEASURED FACTOR

A new estimator is proposed for linear triangular systems, where identification results from the model errors following a bivariate and diagonal GARCH(1,1) process with potentially time‐varying error covariances. This estimator applies when traditional instruments are unavailable. I demonstrate its usefulness on asset pricing models like the capital asset pricing model and Fama–French three‐factor model. In the context of a standard two‐pass cross‐sectional regression approach, this estimator improves the pricing performance of both models. Set identification bounds and an associated estimator are also provided for cases where the conditions supporting point identification fail. Copyright © 2013 John Wiley & Sons, Ltd.     

Model‐Assisted Estimation of a Spatial Population Mean

This paper deals with the estimation of the mean of a spatial population. Under a design‐based approach to inference, an estimator assisted by a penalized spline regression model is proposed and studied. Proof that the estimator is design‐consistent and has a normal limiting distribution is provided. A simulation study is carried out to investigate the performance of the new estimator and its variance estimator, in terms of relative bias, efficiency, and confidence interval coverage rate. The results show that gains in efficiency over standard estimators in classical sampling theory may be impressive.     

Small sample corrections for LTS and MCD

The least trimmed squares estimator and the minimum covariance determinant estimator [6] are frequently used robust estimators of regression and of location and scatter. Consistency factors can be computed for both methods to make the estimators consistent at the normal model. However, for small data sets these factors do not make the estimator unbiased. Based on simulation studies we therefore construct formulas which allow us to compute small sample correction factors for all sample sizes and dimensions without having to carry out any new simulations. We give some examples to illustrate the effect of the correction factor.     

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.     

Estimation and optimal designs for linear Haar-wavelet models

This paper gives an analytical expression for the best linear unbiased estimator (BLUE) of the unknown parameters in the linear Haar-wavelet model. From the analytical expression, we solve for the eigenvalues of the covariance matrix of the BLUE in analytical form. Further, we use these eigenvalues to construct some conventional discrete optimal designs for the model. The equivalences among these optimal designs are demonstrated and some examples are also given.      

Linear programming-based estimators in simple linear regression

In this paper we introduce a linear programming estimator (LPE) for the slope parameter in a constrained linear regression model with a single regressor. The LPE is interesting because it can be superconsistent in the presence of an endogenous regressor and, hence, preferable to the ordinary least squares estimator (LSE). Two different cases are considered as we investigate the statistical properties of the LPE. In the first case, the regressor is assumed to be fixed in repeated samples. In the second, the regressor is stochastic and potentially endogenous. For both cases the strong consistency and exact finite-sample distribution of the LPE is established. Conditions under which the LPE is consistent in the presence of serially correlated, heteroskedastic errors are also given. Finally, we describe how the LPE can be extended to the case with multiple regressors and conjecture that the extended estimator is consistent under conditions analogous to the ones given herein. Finite-sample properties of the LPE and extended LPE in comparison to the LSE and instrumental variable estimator (IVE) are investigated in a simulation study. One advantage of the LPE is that it does not require an instrument.     

Fast Kernel Smoothing of Point Patterns on a Large Network using Two‐dimensional Convolution

We propose a computationally efficient and statistically principled method for kernel smoothing of point pattern data on a linear network. The point locations, and the network itself, are convolved with a two‐dimensional kernel and then combined into an intensity function on the network. This can be computed rapidly using the fast Fourier transform, even on large networks and for large bandwidths, and is robust against errors in network geometry. The estimator is consistent, and its statistical efficiency is only slightly suboptimal. We discuss bias, variance, asymptotics, bandwidth selection, variance estimation, relative risk estimation and adaptive smoothing. The methods are used to analyse spatially varying frequency of traffic accidents in Western Australia and the relative risk of different types of traffic accidents in Medellín, Colombia.     

Bounds for the variance of an inverse binomial estimator

Summary  B est [1] found the variance of the minimum variance unbiased estimator of the parameter p of the negative binomial distribution. M ikulski and Sm [2] gave an upper bound to it, easier to calculate than B est's expression and a good approximation for small values of p and large values of r (the number of successes). In this paper both lower bounds and closer upper bounds are derived.     

Constrained Kalman Filtering: Additional Results

This paper deals with linear state space modelling subject to general linear constraints on the state vector. The discussion concentrates on four topics: the constrained Kalman filtering versus the recursive restricted least squares estimator; a new proof of the constrained Kalman filtering under a conditional expectation framework; linear constraints under a reduced state space modelling; and state vector prediction under linear constraints. The techniques proposed are illustrated in two real problems. The first problem is related to investment analysis under a dynamic factor model, whereas the second is about making constrained predictions within a GDP benchmarking estimation.