scholarly journals Quantifying the closeness to a set of random curves via the mean marginal likelihood

2020 ◽  
Author(s):  
Cédric Rommel ◽  
Joseph Frédéric Bonnans ◽  
Baptiste Gregorutti ◽  
Pierre Martinon
Keyword(s):  
Marginal Likelihood ◽  
Marginal Density ◽  
Random Curves ◽  
Practical Applications ◽  
Random Functions ◽  
Practical Usefulness ◽  
Class Of Estimators ◽  
The Mean ◽  
Multivariate Density ◽  
Aircraft Trajectories

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

Optimal stationary strategies in leavable Markov decision processes

1990 ◽  
Vol 27 (01) ◽  
pp. 134-145
Author(s):  
Matthias Fassbender
Keyword(s):  
Transition Probabilities ◽  
Practical Applications ◽  
Stationary Strategies ◽  
Countable State ◽  
Markov Decision ◽  
Bias Optimality ◽  
The Mean ◽  
Optimal Stationary Strategies ◽  
The Cost ◽  
Reward Criterion

This paper establishes the existence of an optimal stationary strategy in a leavable Markov decision process with countable state space and undiscounted total reward criterion. Besides assumptions of boundedness and continuity, an assumption is imposed on the model which demands the continuity of the mean recurrence times on a subset of the stationary strategies, the so-called ‘good strategies'. For practical applications it is important that this assumption is implied by an assumption about the cost structure and the transition probabilities. In the last part we point out that our results in general cannot be deduced from related works on bias-optimality by Dekker and Hordijk, Wijngaard or Mann.

scholarly journals AVERAGING OF AN INCREASING NUMBER OF MOMENT CONDITION ESTIMATORS

2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton
Keyword(s):  
Moment Condition ◽  
Moment Conditions ◽  
Parameter Heterogeneity ◽  
Class Of Estimators ◽  
Optimal Weighting ◽  
The Mean ◽  
The Moment ◽  
Image Position ◽  
Nonlinear Estimators ◽  
Available Information

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.

scholarly journals Program Quality and Developmental Outcomes Related to Youth Volleyball in Ethiopia: Assessing Relationships and Variations

2021 ◽  
Vol 11 (4) ◽  
pp. 1388-1405
Author(s):  
Abdulaziz Mussema ◽  
Tefera Tadesse ◽  
Zelalem Melkamu
Keyword(s):  
Developmental Outcomes ◽  
Central Zone ◽  
Youth Sport ◽  
Program Quality ◽  
Cross Sectional Survey ◽  
Cross Sectional ◽  
Practical Applications ◽  
The Mean ◽  
Project Site

This study aims to assess program quality and developmental outcomes of a youth volleyball project in one of the regional states in Ethiopia, and further examine variations between groups across gender and project site zones. We applied a cross-sectional survey design, collecting quantitative data from youth volleyball players (n = 215) with a mean age of 16.18 years (SD = 0.69) through a self-reported questionnaire. The results indicated that young players’ perceptions did not vary significantly across gender, except for the mean score of the perceived experience variable for girls (M = 2.68, SD = 0.318) was significantly higher than the mean score of boys (M = 2.58, SD = 0.258). One-way (project site zone) analyses of variance (ANOVAs) identified that youth volleyball projects in the central zone were consistently rated higher than those in the western zone, except for the current practice rating. Moreover, correlation analysis results indicated the presence of a significant relationship, both within and between program quality and developmental outcome variables. Furthermore, the results of regression analysis indicated that the program quality variables together predicted each of the developmental outcomes, accounting for 18.9% to 31.7% of the variances. It is concluded that the quality of the youth volleyball program in Ethiopia varies considerably across the project site zones and the program quality variables significantly relate to the developmental outcomes measured with differential effects. The data from this study reveals several practical applications for Ethiopia and beyond in terms of guiding youth volleyball projects. Moreover, the findings of the study showed that youth sport and the manner in which it is structured and delivered to youth players influences the attainment of positive developmental outcomes. These results suggest that contextual differences really do have an effect on the quality of youth sport program processes and developmental outcomes.

scholarly journals Evaluation of the relationship between spatial abilities and anatomy learning

2020 ◽  
Vol 14 (2) ◽  
pp. 139-144
Author(s):  
Mustafa Aydın ◽  
Mehmet Tuğrul Yılmaz ◽  
Muzaffer Şeker
Keyword(s):  
Mental Rotation ◽  
Spatial Ability ◽  
Significant Contribution ◽  
Spatial Abilities ◽  
School Students ◽  
Mental Rotation Test ◽  
Practical Applications ◽  
Significant Difference ◽  
The Mean ◽  
The Relationship

Objectives: The aim of this study was to examine the relationship between the spatial abilities of medical school students and their learning in anatomy. Methods: The spatial abilities of the 120 students (74 females, 46 males) were examined using Mental Rotation Test (MRT). The relationship between the mental rotation scores and the mean scores of their practical and theoretical anatomy examinations was determined in terms of gender. Results: The study revealed that mental rotation skills of female participants were lower than males; however, there was no significant difference in their exam (theoretical and practical anatomy examinations) scores in terms of gender. The spatial ability of the students had a low level significant effect on their anatomy scores, regarding practical applications. Conclusion: The results of the study revealed a significant relationship between students’ spatial ability and their success in practical anatomy examinations. This suggests that improving spatial ability skills may have a significant contribution to practical anatomy learning and may be considered as a part of anatomy education.

Optimal stationary strategies in leavable Markov decision processes

1990 ◽  
Vol 27 (1) ◽  
pp. 134-145
Author(s):  
Matthias Fassbender
Keyword(s):  
Transition Probabilities ◽  
Practical Applications ◽  
Stationary Strategies ◽  
Countable State ◽  
Markov Decision ◽  
Bias Optimality ◽  
The Mean ◽  
Optimal Stationary Strategies ◽  
The Cost ◽  
Reward Criterion

This paper establishes the existence of an optimal stationary strategy in a leavable Markov decision process with countable state space and undiscounted total reward criterion.Besides assumptions of boundedness and continuity, an assumption is imposed on the model which demands the continuity of the mean recurrence times on a subset of the stationary strategies, the so-called ‘good strategies'. For practical applications it is important that this assumption is implied by an assumption about the cost structure and the transition probabilities. In the last part we point out that our results in general cannot be deduced from related works on bias-optimality by Dekker and Hordijk, Wijngaard or Mann.

Distribution of the branching-process population among generations

1971 ◽  
Vol 8 (4) ◽  
pp. 655-667 ◽  
Author(s):  
M. L. Samuels
Keyword(s):  
Normal Form ◽  
Density Function ◽  
Branching Process ◽  
Random Variables ◽  
Normal Density ◽  
Asymptotically Linear ◽  
Random Functions ◽  
Normal Density Function ◽  
Age Dependent ◽  
The Mean

SummaryIn a standard age-dependent branching process, let Rn(t) denote the proportion of the population belonging to the nth generation at time t. It is shown that in the supercritical case the distribution {Rn(t); n = 0, 1, …} has asymptotically, for large t, a (non-random) normal form, and that the mean ΣnRn(t) is asymptotically linear in t. Further, it is found that, for large n, Rn(t) has the shape of a normal density function (of t).Two other random functions are also considered: (a) the proportion of the nth generation which is alive at time t, and (b) the proportion of the nth generation which has been born by time t. These functions are also found to have asymptotically a normal form, but with parameters different from those relevant for {Rn(t)}.For the critical and subcritical processes, analogous results hold with the random variables replaced by their expectations.

Applications of the Ogilvie-Tuck Formulae to Ship Hydrodynamics

2010 ◽  
Author(s):  
Piotr J. Bandyk ◽  
Robert F. Beck ◽  
Xinshu Zhang
Keyword(s):  
Steady Flow ◽  
Degrees Of Freedom ◽  
Hydrodynamic Coefficients ◽  
Practical Applications ◽  
Classical Work ◽  
Strip Theory ◽  
The Mean ◽  
And Mathematics ◽  
Original Derivation ◽  
Ship Speed

The work of Ogilvie and Tuck [1] was critical in extending strip theory to problems with forward speed. Salvesen et al. [2] used some of those findings in their classical work to determine the hydrodynamic coefficients in five degrees-of-freedom. Other methods have also utilized the formulae with success. The original derivation makes several assumptions about the hull shape and the steady flow around it. In practice, these assumptions do not hold exactly. Other simplifications are usually made, i.e. the mean ship speed is used instead of the actual steady flow around the hull. These may violate the original assumptions, but the results are generally satisfactory. The truly elegant aspect of the Ogilvie-Tuck hydrodynamic coefficients is that they can be calculated from zero-speed results. This is a product of the approach, assumptions, and mathematics done in Appendix A of the original work [1] to derive the Ogilvie-Tuck theorem, also called Tuck’s theorem by many authors. The Ogilvie-Tuck formulae include the hydrodynamic coefficients, expressions of the mj terms, and the Ogilvie-Tuck theorem. This paper discusses the original derivation and several practical applications, including those where the assumptions may be violated. Several qualitative or quantitative statements can be made about the errors introduced by simplifications. Some computational results are presented to emphasize the significance in practical use.

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

scholarly journals Workload assessment for mental arithmetic tasks using the task-evoked pupillary response

2015 ◽  
Author(s):  
Gerhard Marquart ◽  
Joost de Winter
Keyword(s):  
Mental Arithmetic ◽  
Pupil Diameter ◽  
Mental Workload ◽  
Self Report ◽  
Blink Rate ◽  
Eye Tracker ◽  
Practical Applications ◽  
The Mean ◽  
Nasa Tlx ◽  
Diameter Change

Pupillometry is a promising method for assessing mental workload and could be helpful in the optimization of systems that involve human-computer interaction. The present study focuses on replicating the studies by Ahern (1978) and Klingner (2010), which found that for three levels of difficulty of mental multiplications, the more difficult multiplications yielded larger dilations of the pupil. Using a remote eye tracker, our research expands upon these two previous studies by statistically testing for each 1.5 s interval of the calculation period (1) the mean absolute pupil diameter (MPD), (2) the mean pupil diameter change (MPDC) with respect to the pupil diameter during the pre-stimulus accommodation period, and (3) the mean pupil diameter change rate (MPDCR). An additional novelty of our research is that we compared the pupil diameter measure with a self-report measure of workload, the NASA Task Load Index (NASA-TLX), and with the mean blink rate (MBR). The results showed that the findings of Ahern and Klingner were replicated, and that the MPD and MPDC discriminated just as well between the lowest and highest difficulty levels as did the NASA-TLX. The MBR, on the other hand, did not interpretably differentiate between the difficulty levels. Moderate to strong correlations were found between the MPDC and the proportion of incorrect responses, indicating that the MPDC was higher for participants with a poorer performance. For practical applications, validity could be improved by combining pupillometry with other physiological techniques.

scholarly journals Minimum Covariance Determinant-Based Quantile Robust Regression-Type Estimators for Mean Parameter

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Usman Shahzad ◽  
Nadia H. Al-Noor ◽  
Noureen Afshan ◽  
David Anekeya Alilah ◽  
Muhammad Hanif ◽  
...  
Keyword(s):  
Quantile Regression ◽  
Robust Regression ◽  
Real Life ◽  
Minimum Covariance Determinant ◽  
Mean Squared Errors ◽  
Regression Estimators ◽  
Chi Squared ◽  
Class Of Estimators ◽  
The Mean ◽  
Ratio Estimators

Robust regression tools are commonly used to develop regression-type ratio estimators with traditional measures of location whenever data are contaminated with outliers. Recently, the researchers extended this idea and developed regression-type ratio estimators through robust minimum covariance determinant (MCD) estimation. In this study, the quantile regression with MCD-based measures of location is utilized and a class of quantile regression-type mean estimators is proposed. The mean squared errors (MSEs) of the proposed estimators are also obtained. The proposed estimators are compared with the reviewed class of estimators through a simulation study. We also incorporated two real-life applications. To assess the presence of outliers in these real-life applications, the Dixon chi-squared test is used. It is found that the quantile regression estimators are performing better as compared to some existing estimators.

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