scholarly journals Estimating with kernel smoothers the mean of functional data in a finite population setting. A note on variance estimation in presence of partially observed trajectories

2015 ◽  
Vol 99 ◽  
pp. 156-166 ◽  
Author(s):  
Hervé Cardot ◽  
Anne De Moliner ◽  
Camelia Goga
Keyword(s):  
Functional Data ◽  
Finite Population ◽  
Variance Estimation ◽  
Partially Observed ◽  
The Mean ◽  
Kernel Smoothers

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

scholarly journals A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike
Keyword(s):  
Iterative Procedure ◽  
Gene Frequency ◽  
Finite Population ◽  
Transition Matrices ◽  
Single Cycle ◽  
Gene Frequencies ◽  
Mean And Variance ◽  
The Mean ◽  
The One ◽  
Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

scholarly journals On sojourn times at particular gene frequencies

1975 ◽  
Vol 25 (2) ◽  
pp. 89-94 ◽  
Author(s):  
Edward Pollak ◽  
Barry C. Arnold
Keyword(s):  
Markov Chains ◽  
Gene Frequency ◽  
Overlapping Generations ◽  
Finite Population ◽  
Diffusion Method ◽  
Gene Frequencies ◽  
Sojourn Times ◽  
The Mean ◽  
Number Of Visits ◽  
Finite Markov Chains

SUMMARYThe distribution of visits to a particular gene frequency in a finite population of size N with non-overlapping generations is derived. It is shown, by using well-known results from the theory of finite Markov chains, that all such distributions are geometric, with parameters dependent only on the set of bij's, where bij is the mean number of visits to frequency j/2N, given initial frequency i/2N. The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.

scholarly journals A Study on the Chain Ratio-Type Estimator of Finite Population Variance

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yunusa Olufadi ◽  
Cem Kadilar
Keyword(s):  
Finite Population ◽  
Numerical Comparison ◽  
Mean Square ◽  
Auxiliary Variables ◽  
Population Variance ◽  
Two Phase ◽  
First Order ◽  
Phase Sampling ◽  
The Mean ◽  
Two Phase Sampling

We suggest an estimator using two auxiliary variables for the estimation of the unknown population variance. The bias and the mean square error of the proposed estimator are obtained to the first order of approximations. In addition, the problem is extended to two-phase sampling scheme. After theoretical comparisons, as an illustration, a numerical comparison is carried out to examine the performance of the suggested estimator with several estimators.

scholarly journals Estimation of Population Mean in Chain Ratio-Type Estimator under Systematic Sampling

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Mursala Khan ◽  
Rajesh Singh
Keyword(s):  
Finite Population ◽  
Real Data ◽  
Survey Sampling ◽  
Systematic Sampling ◽  
Auxiliary Variables ◽  
Data Set ◽  
Population Mean ◽  
First Order ◽  
The Mean ◽  
A Chain

A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

scholarly journals The effect of random selection coefficients on populations of finite size – some particular models

1977 ◽  
Vol 29 (2) ◽  
pp. 97-112 ◽  
Author(s):  
P. J. Avery
Keyword(s):  
Finite Population ◽  
Finite Size ◽  
Random Selection ◽  
Heterozygote Advantage ◽  
Expected Heterozygosity ◽  
Reasonable Degree ◽  
Equal Variance ◽  
The Mean ◽  
Mutant Genes ◽  
Steady State Solutions

SUMMARYThe model of random selection coefficients is considered in the context of a finite population of diploids. The selection coefficients of the homozygotes are allowed to vary with equal variance while the fitness of the heterozygote is kept fixed. Steady-state solutions are found in the case of equal two-way mutation rates with particular reference to the expected heterozygosity. Increasing the variance of the selection coefficients of the homozygotes is found to uniformly increase the heterozygosity for all values of the average selection coefficients and its effect is largest when the selection coefficients of the homozygotes are fully correlated. The fate of mutant genes is also considered in the case of random selection coefficients by looking at the probability of ultimate fixation and the mean times to fixation and extinction. The errors in previous calculations (e.g. Kimura, 1954; Ohta, 1972) are pointed out. It is found that a small average heterozygote advantage together with a reasonable degree of variance in the coefficients can cause an unexpectedly large amount of heterozygosity to be maintained. It is also seen that probabilities of fixation and mean times to boundaries are usually increased by increasing the variance showing that it in fact helps to keep the population heterozygous for much longer than the non-random case. This is in contradiction to some conclusions of Karlin & Levikson (1974) because their haploid results are not easily extendable to the consideration of this sort of diploid model.

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