Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

A Practitioner's Guide to Robust Covariance Matrix Estimation

Abstract: Publisher Summary This chapter discusses the concept of robust covariance matrix estimation. In many structural economic or time-series models, the errors may have heteroscedasticity and temporal dependence of unknown form. Thus, to draw accurate inferences from estimated parameters, it has become increasingly common to construct test statistics using a heteroskedasticity and autocorrelation consistent (HAC) or robust covariance matrix. The key step in constructing a HAC covariance matrix is to estimate the spectral density matrix at frequency zero of a vector of residual terms. In some empirical problems, the regression residuals are assumed to be generated by a specific parametric model. In a rational expectations model, for example, the Euler equation residuals typically follow a specific moving-average (MA) process of known finite order. HAC covariance matrix estimation procedures can be classified into two broad categories: nonparametric kernel-based procedures and parametric procedures. Each kernel-based procedure uses a weighted sum of the auto-covariances to estimate the spectral density at frequency zero, where the weights are determined by the kernel and the bandwidth parameter. Each parametric procedure estimates a time-series model and then constructs the spectral density at frequency zero that is implied by this model.

Use and Misuse of the Likert Item Responses and Other Ordinal Measures.

Abstract: Likert, Likert-type, and ordinal-scale responses are very popular psychometric item scoring schemes for attempting to quantify people's opinions, interests, or perceived efficacy of an intervention and are used extensively in Physical Education and Exercise Science research. However, these numbered measures are generally considered ordinal and violate some statistical assumptions needed to evaluate them as normally distributed, parametric data. This is an issue because parametric statistics are generally perceived as being more statistically powerful than non-parametric statistics. To avoid possible misinterpretation, care must be taken in analyzing these types of data. The use of visual analog scales may be equally efficacious and provide somewhat better data for analysis with parametric statistics.

Testing for dependence in the input to a linear time series model

Abstract: This paper presents a simple test for dependence in the residuals of a linear parametric time series model fitted to non gaussian data. The test statistic is a third order extension of the standard correlation test for whiteness. but the number of lags used in this test is a function of the sample size. The power of this test goes to one as the sample size goes to infinity for any alternative which has non zero bicovariances c e3(r,s)= E[e(t)e(t + r)e(t + s)] for a zero mean stationary random time series. The asymptotic properties of the test statistic are rigorously determined. This test is important for the validation of the sampling properties of the parameter estimates for standard finite parameter linear models when the unobserved input (innovations) process is white but not gaussian. The sizes and power derived from the asymptotic results are checked using artificial data for a number of sample sizes. Theoretical and simulation results presented in this paper support the proposition that the test wi...

Applied nonparametric instrumental variables estimation

Abstract: Instrumental variables are widely used in applied econometrics to achieve identification and carry out estimation and inference in models that contain endogenous explanatory variables. In most applications, the function of interest (e.g., an Engel curve or demand function) is assumed to be known up to finitely many parameters (e.g., a linear model), and instrumental variables are used identify and estimate these parameters. However, linear and other finite-dimensional parametric models make strong assumptions about the population being modeled that are rarely if ever justified by economic theory or other a priori reasoning and can lead to seriously erroneous conclusions if they are incorrect. This paper explores what can be learned when the function of interest is identified through an instrumental variable but is not assumed to be known up to finitely many parameters. The paper explains the differences between parametric and nonparametric estimators that are important for applied research, describes an easily implemented nonparametric instrumental variables estimator, and presents empirical examples in which nonparametric methods lead to substantive conclusions that are quite different from those obtained using standard, parametric estimators.

Curve-fitting with piecewise parametric cubics

Abstract: Parametric piecewise-cubic functions are used throughout the computer graphics industry to represent curved shapes. For many applications, it would be useful to be able to reliably derive this representation from a closely spaced set of points that approximate the desired curve, such as the input from a digitizing tablet or a scanner. This paper presents a solution to the problem of automatically generating efficient piecewise parametric cubic polynomial approximations to shapes from sampled data. We have developed an algorithm that takes a set of sample points, plus optional endpoint and tangent vector specifications, and iteratively derives a single parametric cubic polynomial that lies close to the data points as defined by an error metric based on least-squares. Combining this algorithm with dynamic programming techniques to determine the knot placement gives good results over a range of shapes and applications.