Inference for monotone single-index conditional means: A Lorenz regression approach

2022 ◽  
Vol 167 ◽  
pp. 107347
Cédric Heuchenne ◽  
Alexandre Jacquemain
2017 ◽  
Vol 28 (3) ◽  
pp. 749-760 ◽  
Chathura Siriwardhana ◽  
Meng Zhao ◽  
Somnath Datta ◽  
KB Kulasekera

In this work we propose a method for optimal treatment assignment based on individual covariate information for a patient. For the K treatment ([Formula: see text]) scenario, we compare quantities that are suitable surrogates to true conditional probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient specific scores constructed from patient-specific covariates. As opposed to methods based on conditional means, our method can be applied for a broad set of models and error structures. Furthermore, the proposed method has very desirable large sample properties. We suggest Single Index Models as appropriate models connecting outcome variables to covariates and our empirical investigations show that correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a Single Index Model structure. Furthermore, selection of a treatment using the proposed metric appears to incur no losses in terms of the average reward for cases when two treatments are close in terms of this metric. We also conduct a real data analysis to show the applicability of the proposed procedure. This analysis highlights possible gains both in terms of average response and survival time if one were to use the proposed method.

1997 ◽  
Vol 13 (1) ◽  
pp. 3-31 ◽  
Hyungtaik Ahn

This paper develops a theory of estimating parameters of a generated regressor model in which some explanatory variables in the equation of interest are the unknown conditional means of certain observable variables given other observable regressors. The paper imposes a weak nonparametric restriction on the form of the conditional means and maintains a single-index assumption on the distribution of the dependent variable in the equation of interest. The estimation method follows a two-step approach: The first step estimates the conditional means in the index nonparametrically, and the second step estimates the parameters by an analytically convenient weighted average derivative method. It is established that the two-step estimator is root-n-consistent and asymptotically normal. The asymptotic variance exceeds that of the one-step hypothetical estimator, which would be obtainable if the first-step regression were known.

1996 ◽  
Vol 8 (3) ◽  
pp. 133-144 ◽  
María del Mar del Pozo Andrés ◽  
Jacques F A Braster

In this article we propose two research techniques that can bridge the gap between quantitative and qualitative historical research. These are: (1) a multiple regression approach that gives information about general patterns between numerical variables and the selection of outliers for qualitative analysis; (2) a homogeneity analysis with alternating least squares that results in a two-dimensional picture in which the relationships between categorical variables are graphically presented.

1986 ◽  
Vol 14 (3) ◽  
pp. 139-159 ◽  
A. G. Veith

Abstract A system, called the “Driving Severity Monitor” (DSM), has been developed for characterizing tire force distribution as related to treadwear in either normal tire use or in tire fleet testing in a convoy. The system consists of an accelerometer for monitoring lateral accelerations, a wheel revolution counter, and a module for signal processing and read-out. The output of the DSM is reduced to a single index, the Driving Severity Number (DSN), which characterizes a vehicle journey. The DSN is equal to the sum of squares of lateral acceleration measured once per tire revolution during a trip, divided by the number of wheel revolutions. The DSN had a high degree of correlation (R ≧ 0.95) with treadwear in two wear programs when pavement abrasiveness was held constant. This supports the concept that the three basic treadwear components: tire force distribution, pavement abrasiveness, and ambient temperature, can be separated for better understanding of tire treadwear.

Sign in / Sign up

Export Citation Format

Share Document