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具有 ARMA 误差的非参数样条回归AI 解读

We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain O(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The…

存在大量干扰参数时的经验贝叶斯与条件推断AI 解读

This paper concerns the use of empirical Bayes methods to improve the efficiency of a parameter of interest, θ, in the presence of many nuisance parameters, {øi}, one from each data stratum. A class of distributions is introduced such that for fixed θ, the minimal sufficient statistic ti(θ) for øi is from an exponential family and hence complete. By imposing the assumption that the øi's are generated from an unspecified distribution function Q, we show that for this class of…

柯西模型中的条件推断AI 解读

Many computations associated with the two-parameter Cauchy model are shown to be greatly simplified if the parameter space is represented by the complex plane rather than the real plane. With this convention we show that the family is closed under Mö bius transformation of the sample space: there is a similar induced transformation on the parameter space. The chief raison d'être of the paper, however, is that the two-parameter Cauchy model provides an example of a nonunique…

指数族中更准确的置信区间AI 解读

Fisher's theory of maximum likelihood estimation routinely provides approximate confidence intervals for a parameter of interest θ, the standard intervals θ ^ ± zασ ^ where θ ^ is the maximum likelihood estimator, ô is an estimate of standard error based on differentiation of the log likelihood function, and zα is a normal percentile point. Recent work has produced systems of better approximate confidence intervals, which look more like exact intervals when exact intervals…

基于参数的渐近方法AI 解读

Fisher's theory of maximum likelihood estimation routinely provides approximate confidence intervals for a parameter of interest θ, the standard intervals θ ^ ± zασ ^ where θ ^ is the maximum likelihood estimator, ô is an estimate of standard error based on differentiation of the log likelihood function, and zα is a normal percentile point. Recent work has produced systems of better approximate confidence intervals, which look more like exact intervals when exact intervals…

半参数模型的投影似然函数AI 解读

In a sequence of papers, McLeish (1984), Hutton & Nelson (1986) and Godambe & Heyde (1987) have motivated the use of the quasi-score function as an estimating function for semiparametric models by showing that it is the projection of the true score into a class of unbiased estimating functions. Thus the quasi-score approximates the score within this class of functions. In this paper, we introduce a class of inference functions for independent observations that contain…

标志点数据的大小与形状分析AI 解读

The paper deals with statistical analysis of landmark data using the exact joint distribution theory for the size and shape of planar Gaussian configurations. This is an extension of earlier work which considered marginal shape analysis. Special cases of the size and shape distribution are examined and the isotropic Gaussian model is investigated in particular detail. Various properties are studied, including conditional distributions and a curve of regression. Finally we…

有序列联表的序约束 RC 模型：估计与拟合检验AI 解读

The RC model has been proposed as a model for ordered contingency tables. It involves parametric scores that are assigned to the rows and columns of the table so that these scores reflect the ordinality of the row and column categories. Efficient estimation of these parameters subject to order constraints remained an open problem mainly due to severe difficulties in computing these estimates and difficulties in deriving an appropriate asymptotic goodness-of-fit test. A…

双重灵活对数样条响应模型的渐近理论AI 解读

Consider a $\mathscr{Y}$-valued response variable having a density function $f(\cdot\mid x)$ that depends on an $\mathscr{X}$-valued input variable $x.$ It is assumed that $\mathscr{X}$ and $\mathscr{Y}$ are compact intervals and that $f(\cdot\mid\cdot)$ is continuous and positive on $\mathscr{X} \times \mathscr{Y}.$ Let $F(\cdot\mid x)$ denote the distribution function of $f(\cdot\mid x)$ and let $Q(\cdot\mid x)$ denote its quantile function. A finite-parameter exponential…

样条平滑参数的交叉验证与最大似然估计性能AI 解读

An important aspect of nonparametric regression by spline smoothing is the estimation of the smoothing parameter. In this article we report on an extensive simulation study that investigates the finite-sample performance of generalized cross-validation, cross-validation, and marginal likelihood estimators of the smoothing parameter in splines of orders 2 and 3. The performance criterion for both the estimate of the function and its first derivative is measured by the square…

利用 EM 获得渐近方差协方差矩阵：SEM 算法AI 解读

The expectation maximization (EM) algorithm is a popular, and often remarkably simple, method for maximum likelihood estimation in incomplete-data problems. One criticism of EM in practice is that asymptotic variance–covariance matrices for parameters (e.g., standard errors) are not automatic byproducts, as they are when using some other methods, such as Newton–Raphson. In this article we define and illustrate a procedure that obtains numerically stable asymptotic…

位置参数的折中最大似然估计量AI 解读

This article describes a new approach for constructing robust location estimators. These estimators are constructed to be nearly optimal in small sample sizes simultaneously for two or more possible underlying shapes of the density of the data. The estimators are weighted averages of the maximum likelihood estimators for the densities considered, where the weights depend on the sample through the likelihood functions. Because of this relationship to the usual MLE's, these…

状态空间模型的自助法：高斯最大似然估计与卡尔曼滤波AI 解读

The bootstrap is proposed as a method for assessing the precision of Gaussian maximum likelihood estimates of the parameters of linear state-space models. Our results also apply to autoregressive moving average models, since they are a special case of state-space models. It is shown that for a time-invariant, stable system, the bootstrap applied to the innovations yields asymptotically consistent standard errors. To investigate the performance of the bootstrap for finite…

单参数情形下最大似然估计与后验均值的比较AI 解读

Consider estimation of a scalar parameter θ of a distribution on the basis of a random sample of size n. Possible estimators include the maximum likelihood estimator, n , and the posterior mean with respect to some prior distribution, n . In this article n and n are compared by considering a large-sample version of the Pitman nearness criterion; conditions are given under which n is preferable to n in this sense. Several examples are provided that show that comparisons of n…

潜在真实时间序列及其指标：一种替代方法AI 解读

de Leeuw and McKelvey proposed a method for using two imperfect indicators to predict the values of an unobserved series. In this article we suggest an alternative method that uses the multiple indicator approach to model the true time series and its indicators. We examine the identification status of the model, estimate the parameters by maximum likelihood, and use the Kalman filter to obtain predictions of the unobserved series. The method is applied to the U.S. gross…

广义线性模型导论AI 解读

Part 1 Background scope notation distributions derived from normal distribution. Part 2 Model fitting: plant growth sample birthweight sample notation for linear models exercises. Part 3 Exponential family of distributions and generalized linear models: exponential family of distributions generalized linear models. Part 4 Estimation: method of maximum likelihood method of least squares estimation for generalized linear models example of simple linear regression for Poisson…

位置参数的折中最大似然估计AI 解读

This article describes a new approach for constructing robust location estimators. These estimators are constructed to be nearly optimal in small sample sizes simultaneously for two or more possible underlying shapes of the density of the data. The estimators are weighted averages of the maximum likelihood estimators for the densities considered, where the weights depend on the sample through the likelihood functions. Because of this relationship to the usual MLE's, these…

样条平滑参数的交叉验证与最大似然估计表现AI 解读

An important aspect of nonparametric regression by spline smoothing is the estimation of the smoothing parameter. In this article we report on an extensive simulation study that investigates the finite-sample performance of generalized cross-validation, cross-validation, and marginal likelihood estimators of the smoothing parameter in splines of orders 2 and 3. The performance criterion for both the estimate of the function and its first derivative is measured by the square…

捕获—再捕获实验中泊松与多项模型的推断AI 解读

Capture-recapture models have been formulated both as Poisson and as multinomial distributions. Maximum likelihood estimates of parameters under the two models are compared. For parameters which do not involve the population size the asymptotic covariances are shown to be the same.

有限总体规模序贯估计中最大似然估计量的不可容许性AI 解读

For the sequential estimation of the size of a finite population, the maximum likelihood estimator is a commonly used estimator but has no explicit expression. In this paper, it is shown that the maximum likelihood estimator is inadmissible. An estimator which is simple in form and dominates the maximum likelihood estimator asymptotically is proposed.

关于Seber环志回收数据模型的说明AI 解读

We provide simple explicit maximum-likelihood estimates for Seber's (1971) model for ring-recovery data, obtaining both the general solution, and the particular estimate satisfying Seber's constraint.

一个实证求职模型的精确似然函数AI 解读

The exact likelihood function for a prototypal job search model is analyzed. The optimality condition implied by the dynamic programming framework is fully imposed. Using the optimality condition allows identification of an offer arrival probability separately from an offer acceptance probability. The estimation problem is nonstandard. The geometry of the likelihood function in finite samples is considered, along with asymptotic properties of the maximum likelihood estimator.

不可逆性与误设 ARMA 模型的伪极大似然估计AI 解读

Recently Tanaka and Satchell [11] investigated the limiting properties of local maximizers of the Gaussian pseudo-likelihood function of a misspecified moving average model of order one in case the spectral density of the data process has a zero at frequency zero. We show that pseudo-maximum likelihood estimators in the narrower sense, that is, global maximizers of the Gaussian pseudo-likelihood function, may exhibit behavior drastically different from that of the local…

高斯向量自回归模型中协整向量的估计与假设检验AI 解读

This paper contains the likelihood analysis of vector autoregressive models allowing for cointegration. The author derives the likelihood ratio test for cointegrating rank and finds it asymptotic distribution. He shows that the maximum likelihood estimator of the cointegrating relations can be found by reduced rank regression and derives the likelihood ratio test of structural hypotheses about these relations. The author shows that the asymptotic distribution of the maximum…