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使用单侧动态主成分预测多条时间序列AI 解读

We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Usually dynamic principal components have been defined as functions of past and future values of the series and therefore they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this article can be successfully used for forecasting…

广义动态主成分AI 解读

Brillinger defined dynamic principal components (DPC) for time series based on a reconstruction criterion. He gave a very elegant theoretical solution and proposed an estimator which is consistent under stationarity. Here, we propose a new enterally empirical approach to DPC. The main differences with the existing methods—mainly Brillinger procedure—are (1) the DPC we propose need not be a linear combination of the observations and (2) it can be based on a variety of loss…

广义线性模型的投影估计量AI 解读

We introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression. These projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter. We found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction ε of outlier contamination. For small ε, this bias is approximately twice the…

基于最优预测的稳健响应变量变换AI 解读

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are…

多变量数据中的异常值传播AI 解读

We investigate the performance of robust estimates of multivariate location under nonstandard data contamination models such as componentwise outliers (i.e., contamination in each variable is independent from the other variables). This model brings up a possible new source of statistical error that we call “propagation of outliers.” This source of error is unusual in the sense that it is generated by the data processing itself and takes place after the data has been…

一类稳健且具有完全渐近效率的回归估计量AI 解读

This paper introduces a new class of robust estimators for the linear regression model. They are weighted least squares estimators, with weights adaptively computed using the empirical distribution of the residuals of an initial robust estimator. It is shown that under certain general conditions the asymptotic breakdown points of the proposed estimators are not less than that of the initial estimator, and the finite sample breakdown point can be at most $1/n$ less. For the…

一类局部与全局稳健的回归估计量AI 解读

We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1 and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We…

一类局部与全局稳健的回归估计量AI 解读

We present a new class of regression estimates called generalized τ estimates. These estimates are defined by minimizing the τ scale of the weighted residuals, with weights that penalize high-leverage observations. Like the τ estimates, the generalized τ estimates utilize for their definition two loss functions, ρ1 and ρ2, which together with the weights can be chosen to achieve simultaneously high breakdown point, finite gross error sensitivity, and high efficiency. We…

近似线性回归中一步 GM 估计量的泛函稳定性AI 解读

This paper provides a comparative sensitivity analysis of one-step Newton–Raphson estimators for linear regression. Such estimators have been proposed as a way to combine the global stability of high breakdown estimators with the local stability of generalized maximum likelihood estimators. We analyze this strategy, obtaining upper bounds for the maximum bias induced by $\varepsilon$-contamination of the model. These bounds yield break-down points and local rates of…

摘要暂缺

利用影响矩阵识别线性回归中的高影响观测子集AI 解读

SUMMARY This paper presents a new method to identify influential subsets in linear regression problems. The procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentred covariances of the effect on the whole data set of deleting each observation, normalized to include the univariate Cook statistics on the diagonal. It is shown that the eigenstructure of the influence matrix is useful to identify influential subsets and a procedure for…

最小α分位数估计的极小极大偏差性质AI 解读

A natural measure of the degree of robustness of an estimate $\mathbf{T}$ is the maximum asymptotic bias $B_\mathbf{T}(\varepsilon)$ over an $\varepsilon$-contamination neighborhood. Martin, Yohai and Zamar have shown that the class of least $\alpha$-quantile regression estimates is minimax bias in the class of $M$-estimates, that is, they minimize $B_\mathbf{T}(\varepsilon)$, with $\alpha$ depending on $\varepsilon$. In this paper we generalize this result, proving that the…

基于投影的偏差稳健回归估计AI 解读

A new class of bias-robust estimates of multiple regression is introduced. If $y$ and $x$ are two real random variables, let $T(y, x)$ be a univariate robust estimate of regression of $y$ on $x$ through the origin. The regression estimate $\mathbf{T}(y, \mathbf{x})$ of a random variable $y$ on a random vector $\mathbf{x} = (x_1,\cdots, x_p)'$ is defined as the vector $\mathbf{t} \in \mathfrak{R}^p$ which minimizes $\sup_{\|\mathbf{\lambda}\| = 1} \mid T(y - \mathbf{t'x, \lambda' x}) \mid s(\mathbf{\lambda'x})$…

摘要暂缺

通过最小化高效尺度构造高崩溃点回归估计AI 解读

A new class of robust estimates, τ estimates, is introduced. The estimates have simultaneously the following properties: (a) they are qualitatively robust, (b) their breakdown point is .5, and (c) they are highly efficient for regression models with normal errors. They are defined by minimizing a new scale estimate, τ, applied to the residuals. Asymptotically, a τ estimate is equivalent to an M estimate with a ψ function given by a weighted average of two ψ functions, one…

随机过程的定性稳健性AI 解读

In this paper we generalize Hampel's concept of qualitative robustness of a sequence of estimators to the case of stochastic processes with non-i.i.d. observations, defining appropriate metrics between samples. We also present a different approach to qualitative robustness which formalizes the notion of resistance. We give two definitions based on this approach: strong and weak resistance. We show that for estimating a finite dimensional real parameter, $\pi$-robustness is…

兼具高崩溃点与高效率的稳健回归估计AI 解读

A class of robust estimates for the linear model is introduced. These estimates, called MM-estimates, have simultaneously the following properties: (i) they are highly efficient when the errors have a normal distribution and (ii) their breakdown-point is 0.5. The MM-estimates are defined by a three-stage procedure. In the first stage an initial regression estimate is computed which is consistent robust and with high breakdown-point but not necessarily efficient. In the…

时间序列的影响泛函AI 解读

A definition is given for influence functionals of parameter estimates in time-series models. The definition involves the use of a contaminated observations process of the form $y^\gamma_t=(1-z^\gamma_t){x_t+z^\gamma_tw_t}$, $p=1,2,...,0\leq\gamma\leq1$ where $x_t$ is a core process (usually Gaussian), $w_t$ is a contaminating process, and $z^\gamma_t"$ is a zero-one process with $P(z^\gamma_t=1)={\gamma+0(\gamma)}$. This form is sufficiently general to model such diverse…

ARMA 模型的稳健估计AI 解读

Two new classes of robust estimates for ARMA models are introduced: estimates based on residual autocovariances (RA estimates), and estimates based on truncated residual autocovariances (TRA estimates). A heuristic derivation of the asymptotic normal distribution is given. We also perform a Monte Carlo study to compare the robustness properties of these estimates with the least squares, M, and GM estimates. In this study we consider observations that correspond to a Gaussian…

线性模型中 M 估计量的渐近行为AI 解读

This paper deals with $M$-estimators for the linear model $y_i = \mathbf{x}'_i\mathbf{\theta} + u_i1 \leqslant i \leqslant n$, where the $\mathbf{x}_i$ are fixed $p$-dimensional vectors, and the $u_i$ are i.i.d. random variables with distribution $F$. The estimators considered are solutions $\hat\mathbf{\theta}$ of the equation $\sum^n_{j = 1}\psi(y_j - \mathbf{x}'_i\hat{\mathbf{\theta}})\mathbf{x_j = 0}$ for some function $\psi$. Let $\mathbf{X}$ be the matrix whose $i$th…

检测均值系统性变化的二变量检验AI 解读

Let (xi, yi ), i = 1, …, n, be a sequence of observations such that yi = bi + cxi + ui , where bi and c are unknown parameters, and {ui } and {xi } are independent sequences of independent, identically distributed random variables. The likelihood ratio test is derived for the hypothesis that bi = b (i = 1, …, n), against the alternative that bi = b (i ≤ i 0) and bi = b + d (i > i 0) for some b, i 0, and d ≠ 0, assuming the ui 's are normal. Quantiles of the test statistic…

无限方差自回归过程最小二乘估计的渐近行为AI 解读

Let $y_t$ be an order $p$ autoregressive process of the form $y_t + \sum^p_{s=1} \beta_s y_{t-s} = u_t$, where the $u_t$'s are i.i.d. variables with a symmetric distribution $F$ such that $E \log^+ |u_t| < \infty$. For the Yule-Walker version $\beta_T^\ast$ of the least-squares estimate of $\beta = (\beta_1,\cdots, \beta_p)$, it is shown that $T^\frac{1}{2}(\beta_T^\ast - \beta)$ is bounded in probability.

线性模型中的稳健估计AI 解读

The purpose of this paper is to present robust estimates for the regression parameters in the general linear model. We start with a family of $M$-estimators, and using the observations, we estimate the asymptotic efficiency of each member in the family. Then we choose the estimate in the family with greatest estimated asymptotical efficiency. We prove that this procedure has the same asymptotical efficiency as the member of the family with the greatest asymptotical…

用于估计的渐近最优贝叶斯序贯实验设计AI 解读

The purpose of this paper is to find asymptotically optimal Bayes sequential procedures for estimating a function $g(\theta_1, \theta_2,\cdots, \theta_k)$ when there are $k$ experiments $E_1, E_2,\cdots, E_k$ and the performance of the experiment $E_i$ conducts to the observation of a random variable whose distribution depends on the vector parameter $\theta_i$. The term asymptotical refers here to the cost of experimentation tending to zero. The methods used are a…