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Parametric statistics
About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.
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TL;DR: In this paper, an analysis of covariance model where the covariate effect is assumed only to be smooth is considered, and tests of equality and of parallelism across groups are constructed.
Abstract: An analysis of covariance model where the covariate effect is assumed only to be smooth is considered. The possibility of different shapes of covariate effect in different groups is also allowed and tests of equality and of parallelism across groups are constructed. These are implemented using Gasser-Maller smoothing, whose properties enable problems of bias to be avoided. Accurate moment-based approximations are available for the distribution of each test statistic. Some data on Spanish Onions are used to contrast the non-parametric approach with that of a nonlinear, but parametric, model. A simulation study is also used to explore the properties of the non-parametric tests.
133 citations
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TL;DR: Lower bounds on the asymptotic variance for regular distribution-free estimators of the parameters of the binary choice model and the censored regression (Tobit) model were derived in this paper.
Abstract: We derive lower bounds on the asymptotic variances for regular distribution-free estimators of the parameters of the binary choice model and the censored regression (Tobit) model. A distribution-free (or semiparametric) estimator is one that does not require any assumption about the distribution of the stochastic error term in the model, apart from regularity conditions. For the binary choice model, we obtain an explicit lower bound for the asymptotic variance for the slope parameters, or more generally the parameters of a nonlinear regression function in the underlying latent variable model, but we find that there is no regular semiparametric estimator of the constant term (identified by requiring the error distribution to have zero median). Lower bounds are also obtained under the further assumption that the error distribution is symmetric, and in this case there is a finite lower bound for the constant term too. Comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution. We give the conditions for equality of the parametric and semiparametric lower bounds (in which case adaptive estimation may be possible), both with and without the assumption of a symmetric error distribution. In general, adaptive estimation is not possible, but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution. The Tobit model considered here is the censored nonlinear regression model, with a fixed censoring point. We again give an explicit lower bound for the asymptotic variance for the regression parameters, this time including a constant term (if the error term has zero median). Comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model.
133 citations
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TL;DR: This short chapter introduces the SPSS software, including an overview of its capabilities, and Topics such as data preparation, data import, options of parametric and nonparametric statistical tests, export and editing of statistical results, and creation of charts and tables are covered.
Abstract: IBM SPSS Statistics (“Statistical Package for the Social Sciences”) is a software used for the statistical analysis, data management, and data documentation. This short chapter introduces the SPSS software, including an overview of its capabilities. Topics such as data preparation, data import, options of parametric and nonparametric statistical tests, export and editing of statistical results, and creation of charts and tables are covered.
133 citations
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TL;DR: This paper presents a practical discrete-time fractional order terminal sliding mode (DFOTSM) control strategy for high-precision tracking tasks based on a linear motor and synthesizes a novel DFOTSM control law to drive the sliding mode dynamics into the stable region in finite steps theoretically.
Abstract: This paper presents a practical discrete-time fractional order terminal sliding mode (DFOTSM) control strategy for high-precision tracking tasks based on a linear motor. In particular, the practical parametric uncertainties involving sliding friction, uncertain payload, and disturbance in tracking tasks are considered in this paper. Combining Grunwald–Letnikov fractional order definition and terminal sliding mode technique, the proposed method synthesizes a novel DFOTSM control law to drive the sliding mode dynamics into the stable region in finite steps theoretically, even though the system is suffering from uncertainties and disturbances, and the motion on the surface can guarantee higher tracking precision than the conventional discrete-time terminal sliding surface by selecting suitable controller parameters. The theoretical analyses give out the guideline of parameter selection, and experiments are carried out on the linear-motor-based test platform to demonstrate that the proposed controller is easily implemented and can achieve high-precision tracking, fast response, and considerable robustness to uncertainties.
133 citations
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TL;DR: In this paper, the authors investigate a class of semiparametric ARCH(∞) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the news impact function.
Abstract: We investigate a class of semiparametric ARCH(∞) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the “news impact” function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric part and the nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 index returns. We find evidence of asymmetric news impact functions, consistent with the parametric analysis.
133 citations