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外文摘要
引文資料
題名:
A Two Model Approach for Regression Diagnostics Applied to Furniture Design
書刊名:
品質學報
作者:
曾世賢
/
徐堯
作者(外文):
Tseng, Shih-hsien
/
Hsu, yao
出版日期:
2016
卷期:
23:1
頁次:
頁1-24
主題關鍵詞:
線性模式
;
一般最小平方法
;
模型選擇
;
調整判定係數
;
期望平均方誤根
;
Linear models
;
Ordinary least squares
;
Model selection
;
Adjusted R²
;
Root expected mean squared error
原始連結:
連回原系統網址
相關次數:
被引用次數:期刊(
1
) 博士論文(0) 專書(0) 專書論文(0)
排除自我引用:0
共同引用:0
點閱:4
為能提供迴歸分析中有關偏差(bias)等診斷資訊,本文提出一雙模形分析方法(twomodel approach)來加以處理,並以家具設計為例來展示此方法的有效性。本研究所提出之方法具備迴歸分析中常使用之調整的判定係數(adjusted R^2)之優點並同時提供模型預測偏誤誤差之資訊。此外,本方法修正一般在使用C_p時因自由度問題而無法使用一般最小平方法估計模型偏誤之缺點。本研究所提出之模型診斷方式具有簡單表達模型預測誤差值的特性,其主要表達方式為模型預測值增或減一期望預測誤差值,並透過所設計之測試平臺可同時針對偏誤、多重共線性與實驗設計中資料點分布不對稱性進行探討與測試,最後並透過一家具設計案例說明此方法之應用。
以文找文
This paper proposes a two model approach for regression in order to provide diagnostic information about the bias and other summative information related to furniture design. In the context of regression, the resulting quantity, like the commonly used adjusted R^2 statistic, provides a measure of explanatory power, but which also explicitly accounts for bias errors. Unlike the familiar C_p statistic, the proposed diagnostic can be estimated even if the bias sources are inestimable using ordinary least squares. Interpreted in simple terms, the proposed diagnostic is the expected plus or minus prediction errors in the units of the response. The proposed diagnostic is studied using a test-bed, also proposed here, which accounts for bias, multicollinearity, and mismatches between region of interest moments and the input pattern or experimental design moments. An application to furniture design is used to illustrate the methods.
以文找文
期刊論文
1.
Box, G. E. P.、Draper, N. R.(1963)。The choice of a second order rotatable design。Biometrika,50(3/4),335-352。
2.
Karson, M. J.、Manson, A. R.、Hader, R. J.(1969)。Minimum bias estimation and experimental design for response surfaces。Technometrics,11(3),461-475。
3.
Kupper, L. L.、Meydrech, E. F.(1973)。A new approach to mean squared error estimation of response surfaces。Biometrika,60(3),573-579。
4.
Allen, T. T.、Tseng, S. H.(2011)。Variance plus bias optimal response surface designs with qualitative factors applied to STEM choice modeling。Quality and Reliability Engineering International,27(8),1199-1210。
5.
Allen, T. T.、Yu, L.、Schmitz, J.(2003)。An experimental design criterion for minimizing meta-model prediction errors applied to die casting process design。Journal of the Royal Statistical Society Series C: Applied Statistics,52(1),103-117。
6.
Beattie, S. D.、Fong, D. K. H.、Lin, D. K. J.(2002)。A two-stage bayesian model selection strategy for supersaturated designs。Technometrics,44(1),55-63。
7.
Cabrera-Rios, M.、Salazar-Aguilar, M. A.、Villarreal-Marroquin, M. G.、Moreno-Rodríguez, G. J.、Rodriguez-Sarasty, J. A.(2011)。Generating multiple time series forecasts with artificial neural networks in a telecommunications。International Journal of Industrial Engineering: Theory, Applications and Practice,18(11),591-598。
8.
Chantarat, N.、Allen, T. T.、Ferhatosmanoglu, N.、Bernshteyn, M.(2006)。A combined array approach to minimize expected prediction errors in experimentation involving mixture and process variables。The International Journal of Industrial and Systems Engineering,1(1/2),129-147。
9.
Chipman, H.(1996)。Bayesian variable selection with related predictors。The Canadian Journal of Statistics,24(1),17-36。
10.
Dalton, L. A.、Dougherty, E. R.(2012)。Optimal mean-square-error calibration of classifier error estimators under Bayesian models。Pattern Recognition,45(6),2308-2320。
11.
Kokoszka, P.、Maslova, I.、Sojka, J.、Zhu, L.(2008)。Testing for lack of dependence in the functional linear model。Canadian Journal of Statistics,36(2),207-222。
12.
Mallows, C. L.(1997)。Cp and prediction with many regressors: comments on Mallows。Technometrics,39(1),115-116。
13.
Sinha, S. K.(2008)。Robust methods for generalize linear models with non-ignorable missing covariates。The Canadian Journal of Statistics,36(2),277-299。
14.
Smadi, H.、Kamrani, A.(2011)。Product quality-based methodology for machine failure analysis and prediction。International Journal of Industrial Engineering: Theory, Applications and Practice,18(11),568-581。
15.
Box, G. E. P.、Draper, N. R.(1959)。A basis for the selection of a response surface design。Journal of the American Statistical Association,54,622-654。
16.
George, E. I.、McCulloch, R. E.(1993)。Variable selection via Gibbs sampling。Journal of the American Statistical Association,88(423),881-889。
17.
Mallows, C. L.(1973)。Some comments on Cp。Technometrics,15(4),661-675。
學位論文
1.
Delouille, V. A.(1998)。Bayesian variable selection with related predictors using the Gibbs sampler(碩士論文)。University of Kent,Canterbury。
圖書
1.
Rossi, P. E.、Allenby, G. M.、McCulloch, R. E.(2005)。Bayesian Statistics and Marketing。Hoboken, NJ。
2.
Allen, T. T.(2006)。Introduction to Engineering Statistics and Six Sigma。London:Springer。
3.
Box, G. E. P.、Draper, N. R.(1987)。Empirical Model Building and Response Surfaces。New York:John Wiley & Sons。
4.
Gilks, W. R.、Richardson, S.、Spiegelhalter, D. J.(1996)。Markov Chain Monte Carlo in Practice。Chapman & Hall。
5.
DeGroot, Morris H.(1970)。Optimal Statistical Decisions。McGraw-Hill Book Company。
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