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Monod模型中的高效实验设计AI 解读

Summary Estimation and experimental design in a non-linear regression model that is used in microbiology are studied. The Monod model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, water research, pharmacokinetics and plant physiology. It is proved that least squares estimates are asymptotically unbiased and normally distributed. The asymptotic covariance matrix of the estimator is the basis for the construction…

高度分层研究中协变量缺失的似然方法AI 解读

Summary The paper considers canonical link generalized linear models with stratum-specific nuisance intercepts and missing covariate data. This family includes the conditional logistic regression model. Existing methods for this problem, each of which uses a conditioning argu- ment to eliminate the nuisance intercept, model either the missing covariate data or the missingness process. The paper compares these methods under a common likelihood framework. The semiparametric…

时间序列的经验似然拟合优度检验AI 解读

Summary Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α-mixing process to formulate a test statistic that…

最小条件下 U 统计量的 Edgeworth 展开AI 解读

Berry-Esseen bounds for U -statistics under the optimal moment conditions were derived by Koroljuk and Borovskich and Friedrich.Under the same optimal moment assumptions with an additional nonlattice condition, we establish a one-term Edgeworth expansion with remainder o(n -1/2 ) for U -statistics.

长记忆参数半参数 Whittle 估计的 Edgeworth 展开AI 解读

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate and the original untapered one. For the tapered estimate, our higher-order correction…

扰乱网数值积分的渐近分布AI 解读

Recently, in a series of articles, Owen proposed the use of scrambled (t.m.s) nets and (t.s) sequences in high-dimensional numerical integration. These scrambled nets and sequences achieve the superior accuracy of equidistribution methods while allowing for the simpler error estimation techniques of Monte Carlo methods. The main aim of this article is to use Stein's method to study the asymptotic distribution of the scrambled (0.m.s) net integral estimate. In particular, it…

加速随机化随机优化AI 解读

We propose a general class of randomized gradient estimates to be employed in a recursive search for the minimum of an unknown multivariate regression function. Here only two observations per iteration step are used. Special cases include random direction stochastic approximation (Kushner and Clark), simultaneous perturbation stochastic approximation (Spall) and a special kernel based stochastic approximation method (Polyak and Tsybakov). If the unknown regression is…

非独立同分布双重删失数据的回归 M 估计AI 解读

Considering the linear regression model with fixed design, the usual M-estimator} with a complete sample of the response variables is expressed as a functional of a generalized weighted bivariate empirical process, and its asymptotic normality is directly derived through the Hadamard differentiability property of this functional and the weak convergence of this generalized weighted empirical process. The result reveals the direct relationship between the M-estimator and the…

M 估计量与正态分位数AI 解读

This paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles. Our estimators are linear combinations of M-estimators. Their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators. Compared with empirical quantiles, the new estimators offer considerable reduction of variance at near normal probability distributions.

基于多元 M 估计的鞍点近似与检验AI 解读

We consider multidimensional M-functional parameters defined by expectations of score functions associated with multivariate M-estimators and tests for hypotheses concerning multidimensional smooth functions of these parameters. We propose a test statistic suggested by the exponent in the saddlepoint approximation to the density of the function of the M-estimates. This statistic is analogous to the log likelihood ratio in the parametric case. We show that this statistic is…

关于线性泛函非参数估计的一则札记AI 解读

Precise asymptotic descriptions of the minimax affine risks and bias-variance tradeoffs for estimating linear functionals are given for a broad class of moduli. The results are complemented by illustrative examples including one where it is possible to construct an estimator which is fully adaptive over a range of parameter spaces.

结果依赖两阶段抽样下半参数回归的大样本理论AI 解读

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch and Wild (1999) under two-phase sampling designs. We show that the maximum likelihood…

完全标记信息下多点连锁分析的渐近估计理论AI 解读

We consider estimation of a disease susceptibility locus $\tau$ at a chromosome. With perfect marker data available, the estimator $\htau_N$ of $\tau$ based on $N$-pedigrees has a rate of convergence $N^{-1}$ under mild regularity conditions. The limiting distribution is the arg max of a certain compound Poisson process. Our approach is conditional on observed phenotypes, and therefore treats parametric and nonparametric linkage, as well as quantitative trait loci methods…

解复合：泊松随机和的估计问题AI 解读

Given a sample from a compound Poisson distribution, we consider estimation of the corresponding rate parameter and base distribution. This has applications in insurance mathematics and queueing theory. We propose a plug-in type estimator that is based on a suitable inversion of the compounding operation. Asymptotic results for this estimator are obtained via a local analysis of the decompounding functional.

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潜变量框架下处理效应参数的简便估计量AI 解读

This note derives simply computed closed-form expressions for the average treatment effect, the effect of treatment on the treated, the local average treatment effect, and the marginal treatment effect in a latent-variable framework for both normal and nonnormal models. Asymptotic standard errors for versions of these parameters that average over observed characteristics are also obtained. The performances of the derived estimators are also evaluated in Monte Carlo…

动态模型参数化条件分布的检验AI 解读

This paper proposes a nonparametric test for parametric conditional distributions of dynamic models. The test is of the Kolmogorov type coupled with Khmaladze's martingale transformation. It is asymptotically distribution-free and has nontrivial power against root-n local alternatives. The method is applicable for various dynamic models, including autoregressive and moving average models, generalized autoregressive conditional heteroskedasticity (GARCH), integrated GARCH,…

02.4.2 结构方程模型拟合优度检验中一个矩阵的秩：解答AI 解读

On the rank of a matrix useful in goodness-of-fit testing of structural equation models—solution.An excellent solution was independently proposed by A. Satorra and H. Neudecker, the posers of the problem.

The asymptotic distribution of the Dickey–Fuller statistic under nonnegativity constraint.

E-Gini 指数的渐近估计AI 解读

Under minimal assumptions on the distribution of income, we demonstrate that Chakravarty's empirical (1988, International Economic Review 29, 147–156) E-Gini index is consistent and asymptotically normal. We also derive an explicit formula for the asymptotic variance of the index and then construct a consistent and computationally straightforward estimator for it.Sincere thanks are due to the co-editor Oliver B. Linton and two anonymous referees whose constructive criticism,…

具有 GARCH(1,1) 误差的单位根过程渐近推断AI 解读

This paper investigates the so-called one-step local quasi–maximum likelihood estimator for the unit root process with GARCH(1,1) errors. When the scaled conditional errors (the ratio of the disturbance to the conditional standard deviation) follow a symmetric distribution, the asymptotic distribution of the estimated unit root is derived only under the second-order moment condition. It is shown that this distribution is a functional of a bivariate Brownian motion as in Ling…

分段协整的推断AI 解读

A cointegration relation is often interpreted as a long-run equilibrium relation whereas short-run deviations are allowed to a certain extent. In practice, however, real data often fail to confirm cointegration for a well understood economic relation. This paper proposes that in many cases failure of confirming cointegration is due to nonstationary deviations in a relatively small portion of the data period (“short-run”) whereas a cointegration relation prevails in the other…

界限置信区域的构造AI 解读

We modify the procedure for constructing exact bounds confidence regions introduced by Dufour (1990, Econometrica 58, 475–494) so as to drop the requirement that the confidence regions for the nuisance parameters are marginal with respect to the parameters of interest, i.e., that they are the same for all values of the parameters of interest. We illustrate this modified procedure with an application to a dependent variable heteroskedasticity model and, using a Monte Carlo…