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In this article, a method is proposed to get the limiting distributions and asymptotic properties of estimators based on the minimum and/or maximum of a given srs of a truncated distribution. Following a common outline, a review is carried out by considering different kinds of truncated distributions, some new results are also developed. [ABSTRACT FROM AUTHOR]

We propose a diagnostic to assess the influence of a unit ui in the sample s, selected from a finite population U={u1,....,uN} using a sampling design D, on θ^(s) as an estimator of a population parameter θ=θ(Y1,...,YN). We adjust the definition of conditional bias (Muñoz-Picardo et al., 1995), in order to obtain an influence diagnostic in survey sampling. Conditional bias as an influence measure of unit ui (ui∈s) on θ^(s), depends on Yi and on the sampling design, D. This is a distinctive feature of sample surveys. Only in particular cases is the proposed influence measure a case-deletion diagnostic. [ABSTRACT FROM PUBLISHER]

We propose a method for detecting outlier components in two-way contingency tables, using the hypothesis of homogeneity, based on the adjusted residuals. [ABSTRACT FROM PUBLISHER]

In sample surveys that collect information on skewed variables, it is often desirable to assess the influence of sample units on the sampling error of survey-weighted estimators of finite population parameters. The conditional bias is an attractive measure of influence that accounts for the sampling design and the estimation method. It is defined as the design expectation of the sampling error conditional on a given unit being selected in the sample. The estimation of the conditional bias is relatively straightforward for simple sampling designs and estimators. However, for complex designs or complex estimators, it may be tedious to derive an explicit expression for the conditional bias. In those complex surveys, variance estimation is often achieved through replication methods such as the bootstrap. Bootstrap methods of variance estimation are typically implemented by producing a set of bootstrap weights that is provided to users along with the survey data. In this article, we show how to use these bootstrap weights to obtain an estimator of the conditional bias. Our bootstrap estimator is evaluated in a simulation study and illustrated using data from the Canadian Survey of Household Spending. [ABSTRACT FROM AUTHOR]

Performance feature extraction is the primary problem in equipment performance degradation assessment. To handle the problem of high-dimensional performance characterization and complexity of calculating the performance indicators in flexible material roll-to-roll processing, this paper proposes a PCA method for extracting the degradation characteristic of roll shaft. Based on the analysis of the performance influencing factors of flexible material roll-to-roll processing roller, a principal component analysis extraction model was constructed. The original feature parameter matrix composed of 10-dimensional feature parameters such as time domain, frequency domain, and time-frequency domain vibration signal of the roll shaft was established; then, we obtained a new feature parameter matrix Z org ∗ by normalizing the original feature parameter matrix. The correlation measure between every two parameters in the matrix Z org ∗ was used as the eigenvalue to establish the covariance matrix of the performance degradation feature parameters. The Jacobi iteration method was introduced to derive the algorithm for solving eigenvalue and eigenvector of the covariance matrix. Finally, using the eigenvalue cumulative contribution rate as the screening rule, we linearly weighted and fused the eigenvectors and derived the feature principal component matrix F of the processing roller vibration signal. Experiments showed that the initially obtained, 10-dimensional features of the processing rollers' vibration signals, such as average, root mean square, kurtosis index, centroid frequency, root mean square of frequency, standard deviation of frequency, and energy of the intrinsic mode function component, can be expressed by 3-dimensional principal components F 1 , F 2 , and F 3 . The vibration signal features reduction dimension was realized, and F 1 , F 2 , and F 3 contain 98.9% of the original vibration signal data, further illustrating that the method has high precision in feature parameters' extraction and the advantage of eliminating the correlation between feature parameters and reducing the workload selecting feature parameters. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of local divergences between two probability distributions and illustrate its usefulness in model selection. Explicit expressions of the proposed local divergences are derived when the underlying distributions are members of the exponential family of distributions or they are described by multivariate normal models. In addition, a local model selection criterion, termed the local divergence information criterion (LDiv.IC), is proposed. Simulations and applications are presented in order to study and exemplify the performance of the proposed criterion. [ABSTRACT FROM AUTHOR]

Summary: This article derives a new family of estimators, namely the minimum density power divergence estimators, as a robust generalization of the maximum likelihood estimator for the polytomous logistic regression model. Based on these estimators, a family of Wald‐type test statistics for linear hypotheses is introduced. Robustness properties of both the proposed estimators and the test statistics are theoretically studied through the classical influence function analysis. Appropriate real life examples are presented to justify the requirement of suitable robust statistical procedures in place of the likelihood based inference for the polytomous logistic regression model. The validity of the theoretical results established in the article are further confirmed empirically through suitable simulation studies. Finally, an approach for the data‐driven selection of the robustness tuning parameter is proposed with empirical justifications. [ABSTRACT FROM AUTHOR]

This paper focuses on the consequences of assuming a wrong model for multinomial data when using minimum penalized φ-divergence, also known as minimum penalized disparity estimators, to estimate the model parameters. These estimators are shown to converge to a well-defined limit. An application of the results obtained shows that a parametric bootstrap consistently estimates the null distribution of a certain class of test statistics for model misspecification detection. An illustrative application to the accuracy assessment of the thematic quality in a global land cover map is included. [ABSTRACT FROM AUTHOR]

Influential units occur frequently in surveys, especially in business surveys that collect economic variables whose distributions are highly skewed. A unit is said to be influential when its inclusion or exclusion from the sample has an important impact on the sampling error of estimates. We extend the concept of conditional bias attached to a unit and propose a robust version of the double expansion estimator, which depends on a tuning constant. We determine the tuning constant that minimizes the maximum estimated conditional bias. Our results can be naturally extended to the case of unit nonresponse, the set of respondents often being viewed as a second-phase sample. A robust version of calibration estimators, based on auxiliary information available at both phases, is also constructed. [ABSTRACT FROM AUTHOR]

A test approach to the model selection problem based on characteristic functions (CFs) is proposed. The scheme is close to that proposed by Vuong (Econometrica 57:257-306, ), which is based on comparing estimates of the Kullback-Leibler distance between each candidate model and the true population. Other discrepancy measures could be used. This is specially appealing in cases where the likelihood of a model cannot be calculated or even, if it has a closed expression, it is either not easily tractable or not regular enough. In this work, the closeness is measured by means of a distance based on the CFs. As a prerequisite, some asymptotic properties of the minimum integrated squared error estimators are studied. From these properties, consistent tests for model selection based on CFs are given for separate, overlapping and nested models. Several examples illustrate the application of the proposed methods. [ABSTRACT FROM AUTHOR]

Copyright of Lithuanian Journal of Statistics / Lietuvos Statistikos Darbai is the property of Lithuanian Statistical Association and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The hiring problem is a simple model for on-line decision-making, inspired by the well-known and time-honored secretary problem (see, for instance, the surveys of Freeman Int Stat 51:189-206, or Samuels Handbook of sequential analysis, ). In the combinatorial model of the hiring problem (Archibald and Martínez Proc. of the 21st Int. Col. on Formal Power Series and Algebraic Combinatorics (FPSAC), ), there is a sequence of candidates of unknown length, and we can rank all candidates from best to worst without ties; all orders are equally likely. Thus any finite prefix of the sequence of candidates can be modeled as a random permutation. Candidates come one after another, and a decision must be taken immediately either to hire or to discard the current candidate, based on her relative rank among all candidates seen so far. In this paper we analyze in depth the strategy hiring above the $$m$$ -th best candidate (or hiring above the $$m$$ -th best, for short), formally introduced by Archibald and Martínez (Proc. of the 21st Int. Col. on Formal Power Series and Algebraic Combinatorics (FPSAC), ). This hiring strategy hires the first $$m$$ candidates in the sequence whatever their relative ranks, then any further candidate is hired if her relative rank is better than the $$m$$ -th best candidate seen so far. The close connection of this hiring strategy to the notion of records in sequences and permutations is quite evident; records and their generalizations (namely, $$m$$ -records) have been throughly studied in the literature (see, for instance, the book of Arnold et al. Records, Wiley Series in Probability and Mathematical Statistics, ), and we explore here that relationship. We also discuss the relationship between this hiring strategy and the seating plan $$(0,m)$$ for the well-known Chinese restaurant process (Pitman Combinatorial stochastic processes, ). We analyze in this paper several random variables (we also call them hiring parameters) that give us an accurate description of the main probabilistic features of 'hiring above the $$m$$ -th best', from the point of view of the hiring rate (number of hired candidates, waiting time to hire a certain number of candidates, time between consecutive hirings,...) and also of the quality of the hired staff (rank of the last hired candidate, best discarded candidate,...). We are able to obtain the exact and asymptotic probability distributions for the most fundamental parameter, namely, the number of hired candidates, and also for most of the other parameters. Another novel quantity that we analyze here is the number of replacements, a quantity naturally arising when we consider 'hiring above the $$m$$ -th best' endowed with a replacement mechanism: that is, an incoming candidate can be: (1) hired anew, because the candidate is among the $$m$$ best seen so far, (2) hired to replace some previously hired worse candidate, or (3) discarded. [ABSTRACT FROM AUTHOR]

Sinha & Rao (2009) proposed estimation procedures designed for small-area means, based on robustified maximum likelihood estimators and robust empirical best linear unbiased predictors. Their methods are of the plug-in type and may be biased. Bias-corrected estimators have been proposed by Chambers et al. (2013). Here, we investigate two new approaches: one relying on the work of Chambers (1986), and the second using the concept of conditional bias to measure the influence of units in the population. These two classes of estimators also include correction terms for the bias but are both fully bias-corrected, in the sense that the corrections account for the potential impact of the other domains on the small area of interest. Monte Carlo simulations suggest that the Sinha–Rao method and the bias-adjusted estimator of Chambers et al. (2013) may exhibit a large bias, while the new procedures often offer lower bias and mean squared error. A parametric bootstrap procedure is considered for constructing confidence intervals. [ABSTRACT FROM AUTHOR]

We argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling. We use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units. Under the model-based approach to inference, our proposed robust estimator is closely related to the well-known estimator of Chambers (1986). Under the design-based approach, it possesses the desirable feature of being applicable with most sampling designs used in practice. For stratified simple random sampling, it is essentially equivalent to the estimator of Kokic & Bell (1994). The proposed robust estimator depends on a tuning constant. In this paper, we propose a method for determining the tuning constant and show that the resulting estimator is consistent. Results from a simulation study suggest that our approach improves the efficiency of standard nonrobust estimators when the population contains units that may be influential if selected in the sample. [ABSTRACT FROM AUTHOR]

In most cases, we use a symmetric loss such as the quadratic loss in a usual estimation problem. But, in the non-regular case when the regularity conditions do not necessarily hold, it seems to be more reasonable to choose an asymmetric loss than the symmetric one. In this paper, we consider the Bayes estimation under the linear exponential (LINEX) loss which is regarded as a typical example of asymmetric loss. We also compare the Bayes risks of estimators under the LINEX loss for a family of truncated distributions and a location parameter family of truncated distributions. [ABSTRACT FROM AUTHOR]

The research team measured the enterprise web accessibility levels of the Forbes 250 largest enterprises using the fully automatic accessibility evaluation tool Sortsite, and presented the compliance of the evaluated websites to WCAG 1.0, WCAG 2.0 and Section 508 accessibility levels. Given the recent attention to organizational leaders having ethical duties towards their dedicated employees, we propose that 'societal citizenship behaviour' concerns ethical duties of organizational leaders towards society in general and in particular to those who have less means to assert their needs. In effect, we found enterprise website accessibility levels to be in need of significant improvement. An interpretation of a positive path forward to better enterprise website accessibility levels is put forth based on a focus-group interaction and using BNML-a novel Business Narrative Modelling Language. [ABSTRACT FROM AUTHOR]

In non-regular cases when the regularity conditions does not hold, the Chapman-Robbins (1951) inequality for the variance of unbiased estimators is well known, but the lower bound by the inequality is not attainable. In this article, we extend the Kiefer-type information inequality applicable to the non-regular case to the asymptotic situation, and we apply it to the case of a family of truncated distributions, in which the lower bound by the Kiefer-type inequality derived from an appropriate prior distribution is attained by the asymptotically unbiased estimator. It also follows from the completeness of the sufficient statistic that the lower bound is asymptotically best. Some examples are also given. [ABSTRACT FROM AUTHOR]

Several methods have been suggested to detect influential observations in the linear regression model and a number of them have been extended for the multivariate regression model. In this article we consider the multivariate general linear model, Y = XB + ε, which contains the linear regression model and the multivariate regression model as particular cases. Assuming that the random disturbances are normally distributed, the BLUE of ΛB is also normally distributed. Since the distribution of the BLUE of ΛB and the distribution of the BLUE of ΛB in the model with the omission of a set of observations differ, to study the influence that a set of observations has on the BLUE of ΛB , we propose to measure the distance between both distributions. To do this we use Rao distance. [ABSTRACT FROM AUTHOR]

Presents a study that determined the bounds for the maximum likelihood estimator of a sample size in Stirling numbers. Background on Stirling numbers and their application in statistics; Analysis of the ordering of the estimators; Derivation of the bounds for the moments of the maximum likelihood estimator.

SUMMARY We define a variation of Efron's method II based on the outlier bootstrap sample concept. A criterion for the identification of such samples is given, with which a variation in the bootstrap sample generation algorithm is introduced. The results of several simulations are analyzed in which, in comparison with Efron's method II, a higher degree of closeness to the estimated quantities can be observed. [ABSTRACT FROM AUTHOR]