Asymptotic properties of integrated square error and cross-validation for kernel estimation of a regression function

1984 ◽  
Vol 67 (2) ◽  
pp. 175-196 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Cross Validation ◽  
Asymptotic Properties ◽  
Kernel Estimation ◽  
Regression Function

scholarly journals User-Adaptive A Posteriori Restoration for Incorrectly Segmented Utterances in Spoken Dialogue Systems

2017 ◽  
Vol 8 (2) ◽  
pp. 206-224
Author(s):  
Kazunori Komatani ◽  
Naoki Hotta ◽  
Satoshi Sato ◽  
Mikio Nakano
Keyword(s):  
Cross Validation ◽  
Regression Function ◽  
Dialogue Systems ◽  
Classification Methods ◽  
A Posteriori ◽  
Spoken Dialogue Systems ◽  
Spoken Dialogue ◽  
User Adaptation ◽  
Linear Regression Function ◽  
Crucial Part

Ideally, the users of spoken dialogue systems should be able to speak at their own tempo. Thus, the systems needs to interpret utterances from various users correctly, even when the utterances contain pauses. In response to this issue, we propose an approach based on a posteriori restoration for incorrectly segmented utterances. A crucial part of this approach is to determine whether restoration is required. We use a classification-based approach, adapted to each user. We focus on each user’s dialogue tempo, which can be obtained during the dialogue, and determine the correlation between each user’s tempo and the appropriate thresholds for classification. A linear regression function used to convert the tempos into thresholds is also derived. Experimental results show that the proposed user adaptation approach applied to two restoration classification methods, thresholding and decision trees, improves classification accuracies by 3.0% and 7.4%, respectively, in cross validation.

scholarly journals The One Standard Error Rule for Model Selection: Does It Work?

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 868-892
Author(s):  
Yuchen Chen ◽  
Yuhong Yang
Keyword(s):  
Variable Selection ◽  
Standard Error ◽  
Cross Validation ◽  
Housing Prices ◽  
Regression Function ◽  
Real Data ◽  
Estimation Accuracy ◽  
Regression Estimation ◽  
Large Sample Size ◽  
Estimation Formula

Previous research provided a lot of discussion on the selection of regularization parameters when it comes to the application of regularization methods for high-dimensional regression. The popular “One Standard Error Rule” (1se rule) used with cross validation (CV) is to select the most parsimonious model whose prediction error is not much worse than the minimum CV error. This paper examines the validity of the 1se rule from a theoretical angle and also studies its estimation accuracy and performances in applications of regression estimation and variable selection, particularly for Lasso in a regression framework. Our theoretical result shows that when a regression procedure produces the regression estimator converging relatively fast to the true regression function, the standard error estimation formula in the 1se rule is justified asymptotically. The numerical results show the following: 1. the 1se rule in general does not necessarily provide a good estimation for the intended standard deviation of the cross validation error. The estimation bias can be 50–100% upwards or downwards in various situations; 2. the results tend to support that 1se rule usually outperforms the regular CV in sparse variable selection and alleviates the over-selection tendency of Lasso; 3. in regression estimation or prediction, the 1se rule often performs worse. In addition, comparisons are made over two real data sets: Boston Housing Prices (large sample size n, small/moderate number of variables p) and Bardet–Biedl data (large p, small n). Data guided simulations are done to provide insight on the relative performances of the 1se rule and the regular CV.

scholarly journals Double Kernel Estimation of Sensitivities

2009 ◽  
Vol 46 (03) ◽  
pp. 791-811
Author(s):  
Romuald Elie
Keyword(s):  
Asymptotic Properties ◽  
Kernel Estimation ◽  
Score Function ◽  
Random Variable ◽  
Kernel Functions ◽  
Contingent Claim ◽  
Main Interest ◽  
Stringent Condition ◽  
Technical Interest ◽  
The One

In this paper we address the general issue of estimating the sensitivity of the expectation of a random variable with respect to a parameter characterizing its evolution. In finance, for example, the sensitivities of the price of a contingent claim are called the Greeks. A new way of estimating the Greeks has recently been introduced in Elie, Fermanian and Touzi (2007) through a randomization of the parameter of interest combined with nonparametric estimation techniques. In this paper we study another type of estimator that turns out to be closely related to the score function, which is well known to be the optimal Greek weight. This estimator relies on the use of two distinct kernel functions and the main interest of this paper is to provide its asymptotic properties. Under a slightly more stringent condition, its rate of convergence is the same as the one of the estimator introduced in Elie, Fermanian and Touzi (2007) and outperforms the finite differences estimator. In addition to the technical interest of the proofs, this result is very encouraging in the dynamic of creating new types of estimator for the sensitivities.

scholarly journals Non-parametric estimation of residual moments and covariance

2008 ◽  
Vol 464 (2099) ◽  
pp. 2831-2846 ◽  
Author(s):  
Dafydd Evans ◽  
Antonia J Jones
Keyword(s):  
Data Analysis ◽  
Asymptotic Properties ◽  
Regression Function ◽  
Parametric Estimation ◽  
Residual Distribution ◽  
Parametric Regression ◽  
Finite Set ◽  
Non Parametric Estimation ◽  
Response Vector ◽  
Non Parametric

The aim of non-parametric regression is to model the behaviour of a response vector Y in terms of an explanatory vector X , based only on a finite set of empirical observations. This is usually performed under the additive hypothesis Y = f ( X )+ R , where f ( X )= ( Y | X ) is the true regression function and R is the true residual variable. Subject to a Lipschitz condition on f , we propose new estimators for the moments (scalar response) and covariance (vector response) of the residual distribution, derive their asymptotic properties and discuss their application in practical data analysis.

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