Multisensor Fusion under Unknown Distributions Finite-Sample Performance Guarantees

2002 ◽  
pp. 295-329 ◽  
Author(s):  
N. S. V. Rao
Keyword(s):  
Multisensor Fusion ◽  
Finite Sample ◽  
Performance Guarantees

scholarly journals A Statistical Learning Approach to Personalization in Revenue Management

2021 ◽  
Author(s):  
Xi Chen ◽  
Zachary Owen ◽  
Clark Pixton ◽  
David Simchi-Levi
Keyword(s):  
Statistical Learning ◽  
Choice Model ◽  
Model Fitting ◽  
Learning Task ◽  
Model Parameters ◽  
Finite Sample ◽  
Customer Data ◽  
Performance Guarantees ◽  
Out Of Sample ◽  
Joint Pricing

We consider a logit model-based framework for modeling joint pricing and assortment decisions that take into account customer features. This model provides a significant advantage when one has insufficient data for any one customer and wishes to generalize learning about one customer’s preferences to the population. Under this model, we study the statistical learning task of model fitting from a static store of precollected customer data. This setting, in contrast to the popular learning and earning paradigm, represents the situation many business teams encounter in which their data collection abilities have outstripped their data analysis capabilities. In this learning setting, we establish finite-sample convergence guarantees on the model parameters. The parameter convergence guarantees are then extended to out-of-sample performance guarantees in terms of revenue, in the form of a high-probability bound on the gap between the expected revenue of the best action taken under the estimated parameters and the revenue generated by a decision maker with full knowledge of the choice model. We further discuss practical implications of these bounds. We demonstrate the personalization approach using ticket purchase data from an airline carrier. This paper was accepted by J. George Shanthikumar, special issue on data-driven prescriptive analytics

From Finite Sample to Asymptotic Methods in Statistics

2009 ◽  
Author(s):  
Pranab K. Sen ◽  
Julio M. Singer ◽  
Antonio C. Pedroso de Lima
Keyword(s):  
Asymptotic Methods ◽  
Finite Sample

One Size Fits All?

Methodology ◽  
2012 ◽  
Vol 8 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Manuel C. Voelkle ◽  
Patrick E. McKnight
Keyword(s):  
Repeated Measures ◽  
Structural Equation ◽  
Type I Error ◽  
Equation Modeling ◽  
Type I ◽  
Finite Sample ◽  
Traditional Methods ◽  
Repeated Measures Anova ◽  
Special Cases ◽  
Latent Curve

The use of latent curve models (LCMs) has increased almost exponentially during the last decade. Oftentimes, researchers regard LCM as a “new” method to analyze change with little attention paid to the fact that the technique was originally introduced as an “alternative to standard repeated measures ANOVA and first-order auto-regressive methods” (Meredith & Tisak, 1990, p. 107). In the first part of the paper, this close relationship is reviewed, and it is demonstrated how “traditional” methods, such as the repeated measures ANOVA, and MANOVA, can be formulated as LCMs. Given that latent curve modeling is essentially a large-sample technique, compared to “traditional” finite-sample approaches, the second part of the paper addresses the question to what degree the more flexible LCMs can actually replace some of the older tests by means of a Monte-Carlo simulation. In addition, a structural equation modeling alternative to Mauchly’s (1940) test of sphericity is explored. Although “traditional” methods may be expressed as special cases of more general LCMs, we found the equivalence holds only asymptotically. For practical purposes, however, no approach always outperformed the other alternatives in terms of power and type I error, so the best method to be used depends on the situation. We provide detailed recommendations of when to use which method.

Hybrid maize breeding with doubled haploids: Comparison between selection criteria

2006 ◽  
Vol 54 (3) ◽  
pp. 343-350 ◽  
Author(s):  
C. F. H. Longin ◽  
H. F. Utz ◽  
A. E. Melchinger ◽  
J.C. Reif
Keyword(s):  
Selection Criteria ◽  
Doubled Haploids ◽  
Optimum Allocation ◽  
Finite Sample ◽  
Sample Sizes ◽  
Maize Breeding ◽  
Selection Gain ◽  
Breeding Programmes ◽  
Hybrid Maize ◽  
Breeding Resources

The optimum allocation of breeding resources is crucial for the efficiency of breeding programmes. The objectives were to (i) compare selection gain ΔGk for finite and infinite sample sizes, (ii) compare ΔGk and the probability of identifying superior hybrids (Pk), and (iii) determine the optimum allocation of the number of hybrids and test locations in hybrid maize breeding using doubled haploids. Infinite compared to finite sample sizes led to almost identical optimum allocation of test resources, but to an inflation of ΔGk. This inflation decreased as the budget and the number of finally selected hybrids increased. A reasonable Pk was reached for hybrids belonging to the q = 1% best of the population. The optimum allocations for Pk(q) and ΔGkwere similar, indicating that Pk(q) is promising for optimizing breeding programmes.

Double-smoothing in Kernel Hazard Rate Estimation

2008 ◽  
Vol 47 (02) ◽  
pp. 167-173 ◽  
Author(s):  
A. Pfahlberg ◽  
O. Gefeller ◽  
R. Weißbach
Keyword(s):  
Hazard Rate ◽  
Nearest Neighbor ◽  
Bandwidth Selection ◽  
Study Data ◽  
Computational Effort ◽  
Finite Sample ◽  
Adaptive Smoothing ◽  
Rate Estimation ◽  
Data Adaptive ◽  
Double Smoothing

Summary Objectives: In oncological studies, the hazard rate can be used to differentiate subgroups of the study population according to their patterns of survival risk over time. Nonparametric curve estimation has been suggested as an exploratory means of revealing such patterns. The decision about the type of smoothing parameter is critical for performance in practice. In this paper, we study data-adaptive smoothing. Methods: A decade ago, the nearest-neighbor bandwidth was introduced for censored data in survival analysis. It is specified by one parameter, namely the number of nearest neighbors. Bandwidth selection in this setting has rarely been investigated, although the heuristical advantages over the frequently-studied fixed bandwidth are quite obvious. The asymptotical relationship between the fixed and the nearest-neighbor bandwidth can be used to generate novel approaches. Results: We develop a new selection algorithm termed double-smoothing for the nearest-neighbor bandwidth in hazard rate estimation. Our approach uses a finite sample approximation of the asymptotical relationship between the fixed and nearest-neighbor bandwidth. By so doing, we identify the nearest-neighbor bandwidth as an additional smoothing step and achieve further data-adaption after fixed bandwidth smoothing. We illustrate the application of the new algorithm in a clinical study and compare the outcome to the traditional fixed bandwidth result, thus demonstrating the practical performance of the technique. Conclusion: The double-smoothing approach enlarges the methodological repertoire for selecting smoothing parameters in nonparametric hazard rate estimation. The slight increase in computational effort is rewarded with a substantial amount of estimation stability, thus demonstrating the benefit of the technique for biostatistical applications.

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