Asymptotic Standard Deviation Research Articles

On the robust regression for a censored response data in the single functional index model

Let be an independent and identically distributed (iid) sequence of interest random variables (rv) distributed as T when the latter is subject to an independent censored rv C. In this work, we built and study a family of robust non parametric estimators for a regression function based on a kernel method. The covariates data are random functional type iid linked to single-index model. Under general conditions, we establish the pointwise almost sure convergence with rate an asymptotic normality of the estimator. The asymptotic standard deviation is explicitly given. By product, confidence bands are given and the special case is studied. Finally, simulations are drawn to illustrate both quality of fit and robustness.

A novel moment method using the log skew normal distribution for particle coagulation

A novel moment method is proposed to predict the detailed size distribution for particle coagulation. The method uses the log skew normal distribution (LSND) to approximate the actual size distribution. The LSND is a four-parameter distribution that generalizes the conventional log-normal distribution to allow for asymmetrical characteristics. The moment closure is achieved by applying the Gauss-Hermite quadrature for the integral terms in the moment equations. With this approach, no further treatments are needed for specific coagulation kernels. Then the method is validated by comparing it with other recognized numerical methods for Brownian coagulation in the continuum regime and the free-molecular regime. The results show that the present method well predicts the detailed size distribution over the entire coagulation time for both regimes. Moreover, the tails of the self-preserving size distribution are well reproduced by the present method. The asymptotic characteristics of Brownian coagulation are also analyzed based on the LSND. The results validate the LSND in analytically representing the self-preserving size distribution and predicting the asymptotic geometric standard deviation.

A new approximation approach for analytically solving the population balance equation due to thermophoretic coagulation

The analytical solution of the population balance equation (PBE) for coagulation by differential settling velocities remains a challenging issue due to the absolute value in the collision kernel. A geometric mean approximation approach is first proposed in this study to handle the integration of the absolute value and convert the moment equation into an integrable form. Using this approach along with the log-normal method of moments, the PBE is first analytically solved for thermophoretic coagulation in the low Knudsen number limit. The present analytical solution is validated by comparing the size distribution parameters with the sectional method. The maximum relative errors in this study are quite acceptable as compared with previous analytical solutions for Brownian coagulation. Moreover, the self-preserving size distribution predicted by the present analytical solution compares well with the sectional method and previous numerical studies on thermophoretic coagulation. Based on the analytical solution, the characteristics of the size distribution evolution during thermophoretic coagulation are investigated theoretically. The results show that the coagulation process is faster with a larger initial geometric standard deviation and the time required to reach the self-preserving distribution increases with the difference between the initial and asymptotic geometric standard deviations.

Morphology and mobility diameter of carbonaceous aerosols during agglomeration and surface growth

Agglomeration and surface growth of fractal-like carbonaceous aerosols in the absence of oxidation and condensation of volatiles are investigated by Discrete Element Modeling (DEM) from the free molecular to transition regime, accounting for primary particle polydispersity and chemical bonding (aggregation). That way, carbon black or soot formation is elucidated in plasma reactors, quenched flames and combustion engines running at high exhaust gas recirculation where oxidation of carbon is limited or non-existent. During nascent soot formation polydisperse spheres and aggregates are formed, attaining an asymptotic geometric standard deviation of 1.2 ± 0.01, in agreement with experiments in premixed, diffusion flames and wood combustion. When surface growth stops, mature soot grows by agglomeration of these polydisperse spheres and aggregates before oxidation and condensation take over. The evolution from nascent to mature soot morphology quantified by its fractal dimension, Df, and mass-mobility exponent, Dfm, is in good agreement with measurements in premixed, diffusion flames and the Cast soot generator. The mobility diameter, dm, can be related to the average number of primary particles per agglomerate by nva = (dm/dva)0.45 and the relative effective density of soot by ρeff/ρs = (dm/dva)−0.78, where dva is the primary particle diameter and ρs the soot bulk density.

Inferring population size: extending the multiplier method to incorporate multiple traits with a likelihood‐based approach

Estimating population size is an important task for resource planning and policy making. One method is the “multiplier method” that uses information about a binary trait to infer the size of a population. This paper presents a likelihood‐based estimator that generalizes the multiplier method to accommodate multiple traits as well as any number of categories in a trait. To provide guidelines for study design, we quantify the advantage of using multiple traits (multiple multipliers) by studying the estimator's asymptotic standard deviation (ASD). Inclusion of multiple traits reduces the ASD most effectively when the traits are uncorrelated and of low prevalence (roughly less than 10%), but the amount of reduction in ASD diminishes when the number of traits becomes large. A Bayesian implementation of our method is applied to both simulated data and real data pertaining to an injection‐drug user population. Copyright © 2016 John Wiley & Sons, Ltd.

Formula omitted] regularized multiplicative iterative path algorithm for non-negative generalized linear models

In regression modeling, often a restriction that regression coefficients are non-negative is faced. The problem of model selection in non-negative generalized linear models (NNGLM) is considered using lasso, where regression coefficients in the linear predictor are subject to non-negative constraints. Thus, non-negatively constrained regression coefficient estimation is sought by maximizing the penalized likelihood (such as the l1-norm penalty). An efficient regularization path algorithm is proposed for generalized linear models with non-negative regression coefficients. The algorithm uses multiplicative updates which are fast and simultaneous. Asymptotic results are also developed for the constrained penalized likelihood estimates. Performance of the proposed algorithm is shown in terms of computational time, accuracy of solutions and accuracy of asymptotic standard deviations.

Crescimento de genótipos de frangos tipo caipira

RESUMOObjetivou-se com este trabalho comparar o padrão de crescimento, mediante ajustes das respectivas curvas de crescimento por modelos não lineares, bem como estudar o desenvolvimento de cortes de carcaça em relação ao peso da carcaça em diferentes genótipos de frangos tipo caipira. Foram utilizados 840 pintos de um dia, machos, distribuídos em delineamento inteiramente ao acaso, dos seguintes genótipos da linhagem Redbro: Caboclo, Carijó, Colorpak, Gigante Negro, Pesadão Vermelho, Pescoço Pelado e Tricolor. As aves foram alojadas em 28 boxes, sendo 30 aves/boxe, em galpão de alvenaria com acesso a um piquete de 45m², com quatro repetições. O peso corporal individual dos frangos foi medido ao nascer, aos 14, 28, 42, 56, 70 e 84 dias de idade. Para a determinação das curvas de crescimento do peso corporal das aves, os dados coletados foram avaliados por meio dos modelos não lineares: Brody, Gompertz, Logístico, Richards e von Bertalanffy. Foi empregado o PROC NLIN do SAS, utilizando-se o método interativo de Gauss-Newton. Os critérios usados para escolha do modelo de melhor ajuste da curva de crescimento foram o coeficiente de determinação, o desvio padrão assintótico, o desvio médio absoluto dos resíduos e o índice assintótico. As análises para obtenção dos coeficientes alométricos foram realizadas por meio do PROC GLM do SAS para os genótipos Carijó, Colorpak, Pesadão Vermelho, Pescoço Pelado e Tricolor. Foram avaliados os pesos da carcaça, do peito, das coxas, das sobrecoxas, das pernas e das asas das aves abatidas aos 85 dias de idade. Apenas as equações propostas por Gompertz, von Bertalanffy e Logístico atingiram a convergência, e o modelo proposto por von Bertalanffy foi o mais adequado para descrever o crescimento dos genótipos de frangos caipiras. Todos os cortes avaliados apresentaram crescimento tardio em relação ao peso da carcaça em genótipos de frangos tipo caipira.

Crescimento de codornas de diferentes grupos genéticos por meio de modelos não lineares

RESUMOObjetivou-se com o presente trabalho ajustar modelos não lineares para descrever o padrão de crescimento de genótipos de codornas de corte e de postura do nascimento aos 35 dias de idade. Foram utilizados dados de 1280 codornas machos e fêmeas, provenientes de sete genótipos de codornas de corte (EV1, EV2, UFV1, UFV2, UFV3, LF1, LF2) e um de postura. Todas as codornas foram pesadas a cada sete dias, do nascimento aos 35 dias de idade. Foram ajustados os modelos Brody, Gompertz, Logístico, Richards e von Bertalanffy aos dados de peso corporal de todos os genótipos. As análises estatísticas foram realizadas utilizando-se o PROC NLIN do SAS (Statistical Analysis System, versão 9.0). Os critérios empregados para a escolha do melhor modelo para descrever a curva de crescimento foram o coeficiente de determinação ajustado (R2), o desvio padrão assintótico (DPA), o desvio médio absoluto dos resíduos (DMA), o índice assintótico (IA), o critério de informação bayesiano (BIC), o critério de Akaike (AIC) e o quadrado médio do erro (QME). Todos os modelos não lineares testados convergiram, com exceção do modelo Brody, que não convergiu para nenhum genótipo avaliado. O modelo Richards não convergiu para o genótipo postura. Os parâmetros da curva de crescimento estimados pelos modelos indicaram maior precocidade, em geral, do genótipo postura comparado aos demais genótipos. O modelo Richards apresentou superestimação do ponto de inflexão para todos os genótipos, exceto para o genótipo postura. Os modelos Gompertz, Logístico e von Bertalanffy são recomendados para descrever o crescimento de codornas de corte dos grupos genéticos em estudo. O modelo Brody não convergiu, por isso não é recomendado para descrever o crescimento dos grupos genéticos de codornas em estudo.

Panel data models with nonadditive unobserved heterogeneity: Estimation and inference

This paper considers fixed effects estimation and inference in linear and nonlinear panel data models with random coefficients and endogenous regressors. The quantities of interest—means, variances, and other moments of the random coefficients—are estimated by cross sectional sample moments of generalized method of moments (GMM) estimators applied separately to the time series of each individual. To deal with the incidental parameter problem introduced by the noise of the within-individual estimators in short panels, we develop bias corrections. These corrections are based on higher-order asymptotic expansions of the GMM estimators and produce improved point and interval estimates in moderately long panels. Under asymptotic sequences where the cross sectional and time series dimensions of the panel pass to infinity at the same rate, the uncorrected estimators have asymptotic biases of the same order as their asymptotic standard deviations. The bias corrections remove the bias without increasing variance. An empirical example on cigarette demand based on Becker, Grossman, and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.

Growth curve of female collared peccaries (Pecari tajacu) raised in captivity in the Brazilian Amazon Region

This work aims to determine the most suitable nonlinear model to describe the growth of female collared peccaries (Pecari tajacu). The monthly records of the weight of 10 captive female collared peccaries over a period of two years in the Brazilian Amazon Region were used. The growth models used were the Von Bertalanffy, Brody, Gompertz and Logistic. The parameters were estimated by using the NLIN procedure from the SAS application. The criteria used to verify the adjustment of the models were: asymptotic standard deviation (ASD); coefficient of determination (R²); average absolute residual deviation (ARD) and the asymptotic rate (AR). The Brody model and the Logistic model estimated the highest (19.44kg) and the lowest (19.18kg) asymptotic weight (A), indicating the lowest (0.0070kg/day) and the highest (0.0121kg/day) maturation rate (K). These results and the coefficients of phenotypic correlation that varied from -0.75 and -0.47 confirmed the antagonistic nature between these parameters. The Brody model estimated the lower value for ARD, a limiting factor for describing the lowest value for AR through this model. The Brody model showed the best adjustment for AR, although the other models also showed a suitable adjustment to the weight data of said species/gender. Based on the AR obtained in this work, the Brody model is recommended for adjusting the growth curve of the female collared peccaries. Depending on the estimated values, especially for K, this trait can be included in a selection index.

Assessing a Binary Measurement System With Varying Misclassification Rates When a Gold Standard Is Available

In manufacturing, we often use a binary measurement system (BMS) for 100% inspection to protect customers from receiving nonconforming product. We can assess the performance of a BMS by estimating the consumer's and producer's risks, the two misclassification rates. Here, we consider assessment plans and their analysis when a gold standard system (GSS) is available for the assessment study but is too expensive for everyday use. We propose a random-effects model to allow for variation in the misclassification rates within the populations of conforming and nonconforming parts. One possibility, here denoted the standard plan, is to randomly sample n parts and measure them once with the GSS and r times with the inspection system. We provide a simple analysis and planning advice for standard plans. In practice, the misclassification rates are often low and the underlying process has high capability. This combination of conditions makes the assessment of the BMS challenging. We show that we need a very large number of measurements with the standard plan in order to get precise estimators of the average misclassification rates and the true process performance. We consider an alternate design, here denoted the conditional assessment plan, where we select random samples from the sets of previously passed and failed parts. The sampled parts are measured once with the GSS and r times with the inspection system. When we augment the data from the conditional plans with available baseline information on the overall pass rate, we show that we can precisely estimate the parameters of interest with many fewer measurements. In the online supplementary materials, we provide R code to find maximum likelihood estimates and corresponding approximate standard errors, and to find the asymptotic standard deviation of the estimators with a selected plan size and assumed parameter values for both the standard and the conditional sampling plans.

Assessing a Binary Measurement System with Varying Misclassification Rates Using a Latent Class Random Effects Model

When no gold standard measurement system is available, we can assess a binary measurement system by making repeated measurements on a random sample of parts and then using a latent class model for the analysis. However, there is widespread criticism of the model assumptions that, given the true state of the part, the repeated measurements are independent and have the same misclassification probability. We propose a latent class random effects model that relaxes these assumptions by modeling the distribution of the two misclassification rates with Beta distributions. We start by finding the likelihood, the maximum likelihood estimates (MLEs) and their approximate standard deviations with the standard assessment plan that selects parts at random from the process. However, to estimate the model parameters with reasonable precision, the standard plan requires extremely large sample sizes in the common industrial situation where the proportion of conforming parts is high and the misclassification probabilities are small. More realistic sample sizes are possible when we instead sample randomly from the population of previously failed parts and supplement the likelihood with baseline information on the overall pass rate. We show using simulation that, for feasible designs, the asymptotic standard deviation based on the expected information provides a reasonably close approximation to the simulated standard deviation. We then use these approximations to investigate how the properties of the MLEs for the unknown parameters depend on the baseline size, the number of parts in the sample, and the number of repeated measurements per part.

Classical nonlinear models to describe the growth curve for Murrah buffalo breed

With the objective of to adjust nonlinear models for the growth curves for a buffaloes herd raised in floodable lands in Rio Grande do Sul state, monthly records measured from birth to two years-old of 64 males and 63 females born between 1982 and 1989 were used. The models used were: Von Bertalanffy, Brody, Gompertz and Logistic. The parameters were estimated by NLIN procedure and the criteria used to evaluate the adjustment given by the models were: asymptotic standard deviation; coefficient of determination; average absolute deviation of residues and asymptotic index. Von Bertalanffy and Brody models overestimated the male asymptotic weight (A) in 15.9 and 171.3kg, respectively, and the Gompertz and Logistic models underestimated it in 4.5 and 13.4kg, respectively. For females, the Logistic model underestimated the asymptotic weight (-2.09kg), and Gompertz, Von Bertalanffy and Brody overestimated this parameter in 8.04, 17.7, and 280.33kg, respectively. The biggest average deviation was estimated by Brody model for both sexes, characterizing the biggest index. Considering the criteria, it is recommended the Gompertz and Logistic models for adjust females and males Murrah buffaloes breed growth curves.

The Numerical Computation of Rational Structures and Asymptotic Standard Deviations in Causal Time Series Data

Problem statement: The specific properties of data series are of primary importance in several sciences. In the field of time series analysis, several researchers have considered the rational approximation theory, particularly the Pade Approximation and Orthogonal Polynomials. Approach: In this study, an approach for the statistical significance of two numerical methods, the r-s and q-d algorithm, was proposed which made possible to identify and compute certain rational structures associated with chronological data. Consideration was given to both univariate and multivariate cases. Results: Both algorithms were illustrated empirically through the use of simulated ARMA and TF models and economic data, some of which were taken from previous studies to compare results. Conclusion: This study highlighted the usefulness of several numerical methods (which were all closely related to the PA and OP) in identifying the rational structures associated with data series.

Effects of outliers on the identification and estimation of GARCH models

Abstract. This paper analyses how outliers affect the identification of conditional heteroscedasticity and the estimation of generalized autoregressive conditionally heteroscedastic (GARCH) models. First, we derive the asymptotic biases of the sample autocorrelations of squared observations generated by stationary processes and show that the properties of some conditional homoscedasticity tests can be distorted. Second, we obtain the asymptotic and finite sample biases of the ordinary least squares (OLS) estimator of ARCH(p) models. The finite sample results are extended to generalized least squares (GLS), maximum likelihood (ML) and quasi‐maximum likelihood (QML) estimators of ARCH(p) and GARCH(1,1) models. Finally, we show that the estimated asymptotic standard deviations are biased estimates of the sample standard deviations.

On the Control of an Interacting Particle Estimation of Schrödinger Ground States

We consider a general Schrodinger operator $L+V$ on a domain $E\subset {\mathbb R}^{d}$ and its associated positive ground state h solution to the maximal eigenvalue problem $L(h) +Vh=\lambda h$. In this work, an interacting particle model approximating the pair $(h,\lambda)$ is studied. When $V \leq 0$, a basic version of this particle system consists of N walkers evolving independently according to the Markov generator L, each walker dying at a rate given by the value of the potential $|V|$ at the walker’s current location; when a walker dies, any other one splits in two. The long time distribution of the particle system is then an estimator of h. Under some reasonable assumptions (with examples for $E={\mathbb R}^{d}$), we get a nonasymptotic control of the $\mathbb{L}^{p}$ deviations (resp., the bias) of this estimator with the genuine rate of convergence in $1/\sqrt{N}$ (resp., $1/\sqrt{N}$). We also compute explicitly the asymptotic standard deviation of the estimation of λ, which remains bounded in...

A note on the estimator of the alpha coefficient for standardized variables under normality

The asymptotic standard deviation (SD) of the alpha coefficient with standardized variables is derived under normality. The research shows that the SD of the standardized alpha coefficient becomes smaller as the number of examinees and/or items increase. Furthermore, this research shows that the degree of the dependence of the SD on the number of items is a function of the average correlation coefficients. When the average correlation approaches 1, the SD of the alpha coefficient decreases rapidly as the number of items increase, with the order of p. On the other hand, when the items are only weakly correlated, increasing the number of items decreases the SD of the alpha coefficient at a much slower rate.

A simulation study on the accuracy of position and effect estimates of linked QTL and their asymptotic standard deviations using multiple interval mapping in an F2 scheme

Approaches like multiple interval mapping using a multiple-QTL model for simultaneously mapping QTL can aid the identification of multiple QTL, improve the precision of estimating QTL positions and effects, and are able to identify patterns and individual elements of QTL epistasis. Because of the statistical problems in analytically deriving the standard errors and the distributional form of the estimates and because the use of resampling techniques is not feasible for several linked QTL, there is the need to perform large-scale simulation studies in order to evaluate the accuracy of multiple interval mapping for linked QTL and to assess confidence intervals based on the standard statistical theory. From our simulation study it can be concluded that in comparison with a monogenetic background a reliable and accurate estimation of QTL positions and QTL effects of multiple QTL in a linkage group requires much more information from the data. The reduction of the marker interval size from 10 cM to 5 cM led to a higher power in QTL detection and to a remarkable improvement of the QTL position as well as the QTL effect estimates. This is different from the findings for (single) interval mapping. The empirical standard deviations of the genetic effect estimates were generally large and they were the largest for the epistatic effects. These of the dominance effects were larger than those of the additive effects. The asymptotic standard deviation of the position estimates was not a good criterion for the accuracy of the position estimates and confidence intervals based on the standard statistical theory had a clearly smaller empirical coverage probability as compared to the nominal probability. Furthermore the asymptotic standard deviation of the additive, dominance and epistatic effects did not reflect the empirical standard deviations of the estimates very well, when the relative QTL variance was smaller/equal to 0.5. The implications of the above findings are discussed.

Estimation of Q-factors and resonant frequencies

We estimate the quality factor Q and resonant frequency f/sub 0/ of a microwave cavity based on observations of a resonance curve on an equally spaced frequency grid. The observed resonance curve is the squared magnitude of an observed complex scattering parameter. We characterize the variance of the additive noise in the observed resonance curve parametrically. Based on this noise characterization, we estimate Q and f/sub 0/ and other associated model parameters using the method of weighted least squares (WLS). Based on asymptotic statistical theory, we also estimate the one-sigma uncertainty of Q and f/sub 0/. In a simulation study, the WLS method outperforms the 3-dB method and the Estin method. For the case of measured resonances, we show that the WLS method yields the most precise estimates for the resonant frequency and quality factor, especially for resonances that are undercoupled. Given that the resonance curve is sampled at a fixed number of equally spaced frequencies in the neighborhood of the resonant frequency, we determine the optimal frequency spacing in order to minimize the asymptotic standard deviation of the estimate of either Q or f/sub 0/.

Estimation of the neutron lifetime: Comparison of methods which account for background

In the first stage of each run of a neutron lifetime experiment, a magnetic trap is filled with neutrons. In the second stage of each run, neutron decay events plus background events are observed. In a separate experiment of multiple runs, only background signals are measured after refilling the trap. In one approach, the mean lifetime of the neutron is estimated by fitting a two-parameter exponential model to the background-corrected data. In a second approach, the neutron lifetime is estimated by fitting a more complicated model to the ``neutron decay plus background'' data and the ``background-only'' data coming from both experiments. In the second approach, we assume knowledge of a statistical model for the background. For each approach, we compute the asymptotic standard deviation of the lifetime estimate in terms of the time spent filling the trap, ${T}_{f},$ the time spent observing decay events, ${T}_{d},$ and the ratio, R, of the number of runs of ``background only'' experiments to primary ``neutron decay plus background'' experiments. For each approach, we minimize the asymptotic standard deviation of the lifetime estimate in terms of ${T}_{f},$ ${T}_{d},$ and R, for various cases. In one case, the background rate is assumed to be stationary. In another case, the background rate is nonstationary. The comparison of the two approaches is made on the basis of the minimized asymptotic standard deviations. For both cases, the second ``joint'' estimation strategy is superior to the ``background-correction'' estimation strategy for all cases studied.