On a Class of Almost Unbiased Ratio Estimators

A class of almost unbiased ratio estimators for population mean σ is derived by weighting sample σ = (1/n) σ y_i, ratio estimators σ and an estimator, σ (y_i/x_i). It is shown that NIETO DE PASCUAL (1961) estimator is a particular member of the class and an optimum estimator in the class (in the minimum variance sense) is identified. The results are illustrated through two numerical examples.     

On the Use of Jack‐Knife Techniques in Systematic Sampling

We have proposed two general classes of ratio and product type estimators to estimate an unknown population parameter of a response variable y under systematic sampling strategy. Jack‐Knife technique is employed to make the classes almost/exactly unbiased and sampling variance of the proposed estimators are derived to the first order of approximation. The merits of the proposed estimators over other estimators are discussed in this paper.     

Estimation of Linear Regression Model with Random Coefficients Ensuring Almost Non-Negativity of Variance Estimators

For a linear regression model with random coefficients, this paper considers the estimation of the mean of coefficient vector which, in turn, involves the estimation of variances of random coefficients. The conventional estimation methods for it sometimes provides negative estimates. In order to circumvent this kind of difficulty, a proposal is forwarded and is examined in the light of existing ones.     

Efficient Estimators for the verianoe of a Finite Population

For the estimation of finite population variance of a character, DAS and TRIPATHI (1978) proposed some efficient estimators when population mean of variance of some other character (associated with main character) is known. We propose here some estimators for population variance using same information and compare with those given by DAS and TRIPATHI (1978). Some examples are given for illustration.     

A ratio code for vibrotactile pitch

Subjective impressions of pitch for 80 different sinusoidal vibrotactile stimuli delivered to the index finger were measured by free magnitude estimation in four subjects. In three of the subjects, pitch at a given frequency decreased as stimulus amplitude increased. The data of these subjects were well described by a model of pitch based on the relative levels of activation of the three major tactile channels. The main element in this model was a ratio of P channel activity to the sum of the activity levels of the P, NPI, and NPIII channels. Activity levels of the channels were estimated on the basis of the psychophysical literature, including a study of vibrotactile loudness using the same subjects and stimuli as those employed here. A fourth subject, whose pattern of loudness judgments had previously been shown to differ from those of the other subjects, did not conform to this pitch model: her data revealed significant increases in pitch with increases in amplitude, and appear to reflect an inability to combine signals across vibrotactile channels. Pitch changes resulting from vibrotactile adaptation were directionally consistent with our ratio model: pitch was slightly increased by adaptation to a 25 Hz stimulus, and slightly decreased by 200 Hz adaptation.     

A Study of Second Order Approximation of Some Ratio Type Strategies

For estimating the mean of a finite population using information on an auxiliary variable, the conventional ratio strategies and strategies due to Srivastava (1967), Reddy (1973), Gupta (1978), Sahai (1979) and Adhvaryu-Gupta (1983) have been studied. Asymptotic expressions for the second order approximations of biases and mean square errors of these strategies have been obtained. The suitability of these strategies have been discussed with the help of live data.     

Estimation and Tests of Mendelian Inheritance in Small Samples of Human Families

Estimation of parameters in human genetics is usually performed by Maximum Likelihood methods for large samples relying on asymptotic results. With the aim of evaluating the importance of the bias resulting from sample size, two sets of human family data have been analysed. The bias is not very important, but programs have been elaborated, giving better estimations. The tests of hypotheses from these estimations have also been considered.     

Tables and Procedures for the Determination of Power and Sample Sizes in Univariate and Multivariate Analyses of Variance and Regression

The available power tables for use in experimental design only serve for limited practical purposes, since they are restricted to very few levels of significance such as .01, .05, and .10. With these values, however, usually no correction for cumulating error probabilities, for example, by the Dunn-Bonferroni method, can be achieved, because (very) low values of a and sometimes even of α are necessary. Therefore, power tables are presented that encompass a wide range of different values for a (.0005 to .40), for power (.50 to .9995), and for 45 different values of the degrees of freedom for the numerator of the F ratio (u = 1 to 150). Four of the 16 tables are printed. Their use is demonstrated for some paradigmatic problems in univariate and multivariate analyses of variance and regression.     

作物品种间杂种优势遗传分析的新方法

本文提出了分析双列杂交试验资料的两个遗传模型。第一个模型包括加性、显性和母体效应;第二个模型只包括简单的加性和显性效应。还介绍了分析杂种优势、估算遗传方差分量以及预测遗传效应值的相应统计分析方法。用所介绍的遗传模型和分析方法以及常用的Griffing配合力分析方法,分析了棉花6个品种双列杂交的产量性状,并进一步比较了不同方法的分析结果。采用本文所介绍的遗传模型和分析方法,可以克服用Griffing的配合力模型及其方法分析杂种优势和配合力遗传表现所存在的局限性。     

NMπ 2.0: Software update to minimize the risk of false positives among determinants of reproductive success

In plant populations, parentage analysis helps understand factors shaping individual reproductive success. However, estimating reproductive success determinants based on parentage counts requires decoupling the effects of individual fecundity and propagule dispersal. The neighbourhood model implemented in the NMπ software provides a standard solution for this problem based on the fixed-effects regression-like approach. Nonetheless, it has been recently shown that the method is prone to false discoveries when important fecundity determinants are omitted. To account for the unexplained variance in fecundity, the Bayesian approach was developed based on the new model (the hierarchical neighbourhood model; HNM). Here, I present the NMπ software update that allows the HNM approach to be used in the framework of a friendly interface. More importantly, the HNM approach is now made available for both dispersed (seedlings) and nondispersed (seeds with known mothers) progeny data. The Bayesian approach, among others, selects significant fecundity determinants, estimates the proportion of variance in reproductive potential explained by selected determinants (R²), and provides individual female and male fecundity values. Although the software was designed to handle microsatellite marker data, a solution is proposed for large sets of single nucleotide polymorphisms. The program can be run on Windows (using either a terminal or a graphical interface) as well as (using a terminal) on Linux, or macOS platforms. In any case, NMπ can utilize multicore processors to speed up the analysis. The updated package containing the code, the executable file, the user manual, and example data is available at https://www.ukw.edu.pl/pracownicy/plik/igor_chybicki/3694/ .