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16
Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative
, 1995
"... . The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly ex ..."
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Cited by 92 (13 self)
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. The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bears closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banachvalued random elements and applying the Banach Central Limit Theorem and Law of Iterated Logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted. 1. Introduction In testing whether or not a parametric statistical model is correctly specified, there are a number of apparently distinct approaches one might take. T...
Penalized Regression with ModelBased Penalties
, 2000
"... Nonparametric regression techniques such as spline smoothing and local fitting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function based on observations t i ,Y i is the minimizer of # {Y i  (t i )} 2 + # # ( ## ) 2 .Since ..."
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Cited by 31 (2 self)
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Nonparametric regression techniques such as spline smoothing and local fitting depend implicitly on a parametric model. For instance, the cubic smoothing spline estimate of a regression function based on observations t i ,Y i is the minimizer of # {Y i  (t i )} 2 + # # ( ## ) 2 .Since # ( ## ) 2 is zero when is a line, the cubic smoothing spline estimate favors the parametric model (t)=# 0+# 1 t. Here the authors consider replacing # ( ## ) 2 with the more general expression # (L) 2 where L is a linear di#erential operator with possibly nonconstant coe#cients. The resulting estimate of performs well, particularly if L is small. They present present a O(n) algorithm for the computation of . This algorithm is applicable to a wide class of L's. They also suggest a method for the estimation of L. They study our estimates via simulation and apply them to several data sets. R ESUM E Les techniques de regression non parametrique telles que l'ajustement local ou ...
Nonparametric Checks For SingleIndex Models
 Ann. Statist
, 2005
"... In this paper we study goodnessoffit testing of singleindex models. The large sample behavior of certain scoretype test statistics is investigated. As a byproduct, we obtain asymptotically distributionfree maximin tests for a large class of local alternatives. Furthermore, characteristic functi ..."
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Cited by 25 (6 self)
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In this paper we study goodnessoffit testing of singleindex models. The large sample behavior of certain scoretype test statistics is investigated. As a byproduct, we obtain asymptotically distributionfree maximin tests for a large class of local alternatives. Furthermore, characteristic function based goodnessoffit tests are proposed which are omnibus and able to detect peak alternatives. Simulation results indicate that the approximation through the limit distribution is acceptable already for moderate sample sizes. Applications to two real data sets are illustrated. 1. Introduction. Suppose
Model selection using wavelet decomposition and applications
 BIOMETRIKA
, 1997
"... In this paper we discuss how to use wavelet decompositions to select a regression model. The methodology relies on a minimum description length criterion which is used to determine the number of nonzero coefficients in the vector of wavelet coefficients. Consistency properties of the selection rule ..."
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Cited by 12 (2 self)
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In this paper we discuss how to use wavelet decompositions to select a regression model. The methodology relies on a minimum description length criterion which is used to determine the number of nonzero coefficients in the vector of wavelet coefficients. Consistency properties of the selection rule are established and simulation studies reveal information on the distribution of the minimum description length selector. We then apply the selection rule to specific problems, including testing for pure white noise. The power of this test is investigated via simulation studies and the selection criterion is also applied to testing for no effect in nonparametric regression.
Scale Economies in Electricity Distribution: A Semiparametric Analysis
 Journal of Applied Econometrics
"... Ontario, Canada for the period 1993–5. The data reveal substantial evidence of increasing returns to scale with minimum ecient scale being achieved by firms with about 20,000 customers. Larger firms exhibit constant or decreasing returns. Utilities which deliver additional services (such as water/se ..."
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Cited by 10 (0 self)
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Ontario, Canada for the period 1993–5. The data reveal substantial evidence of increasing returns to scale with minimum ecient scale being achieved by firms with about 20,000 customers. Larger firms exhibit constant or decreasing returns. Utilities which deliver additional services (such as water/sewage), have significantly lower costs, indicating the presence of economies of scope. Our basic specifications comprise semiparametric variants of the translog cost function where output enters nonparametrically and remaining variables (including their interactions with output) are parametric. We rely upon nonparametric dierencing techniques and extend a previous dierencing test of equality of nonparametric regression functions to a panel data setting. Copyright # 2000 John Wiley & Sons, Ltd. 1.
Model Fitting and Testing for NonGaussian Data with Large Data Sets
, 1996
"... We consider the application of the smoothing spline to the generalized linear model in large data set situations. First we derive a Generalized Approximate Cross Validation function (GACV ), which is an approximate leaveoutone cross validation function used to choose smoothing parameters. In order ..."
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Cited by 5 (2 self)
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We consider the application of the smoothing spline to the generalized linear model in large data set situations. First we derive a Generalized Approximate Cross Validation function (GACV ), which is an approximate leaveoutone cross validation function used to choose smoothing parameters. In order to apply the GACV function to a large data set situation, we propose a corresponding randomized version of it. To reduce the computational intensity of calculating the smoothing spline estimate, we suggest an approximate solution and a clustering method to choose a subset of the basis functions. Combining randomized GACV with this approximate solution, we apply it to binary response data from the Wisconsin Epidemiological Study of Diabetic Retinopathy in order to establish the accuracy of the model when applied to a large data set.
Testing the Generalized Linear Model Null Hypothesis versus `Smooth' Alternatives
, 1995
"... We consider y i ; i = 1; :::n independent observations from an exponential family with canonical parameter j(x i ), where the predictor variable x is in some index set and j is a `smooth' function of x. The usual GLIM models suppose that j has a parametric form j(x) = P p =1 fi OE (x) where ..."
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Cited by 3 (1 self)
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We consider y i ; i = 1; :::n independent observations from an exponential family with canonical parameter j(x i ), where the predictor variable x is in some index set and j is a `smooth' function of x. The usual GLIM models suppose that j has a parametric form j(x) = P p =1 fi OE (x) where the OE are given. This paper is concerned with testing the hypothesis that j is in the span of a given (low dimensional) set of OE versus general `smooth' alternatives. In the Gaussian case, studied by Cox, Koh, Wahba and Yandell(1988), test statistics are available whose distributions are independent of the nuisance fi , whereas in general this is not the case. We propose a symmetrized KullbackLeibler (SKL) distance test statistic, based on comparing a smoothing spline (penalized likelihood) fit and a GLIM fit, for testing the hypothesis j `parametric' vs j `smooth', in the nonGaussian situation. The spline fit uses a smoothing parameter obtained from the data via either the unbiased risk ...
doi:http://dx.doi.org/10.5705/ss.2012.230 A NOTE ON A NONPARAMETRIC REGRESSION TEST THROUGH PENALIZED SPLINES
"... Abstract: We examine a test of a nonparametric regression function based on penalized spline smoothing. We show that, similarly to a penalized spline estimator, the asymptotic power of the penalized spline test falls into a smallK or a largeK scenarios characterized by the number of knots K and t ..."
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Abstract: We examine a test of a nonparametric regression function based on penalized spline smoothing. We show that, similarly to a penalized spline estimator, the asymptotic power of the penalized spline test falls into a smallK or a largeK scenarios characterized by the number of knots K and the smoothing parameter. However, the optimal rate of K and the smoothing parameter maximizing power for testing is different from the optimal rate minimizing the mean squared error for estimation. Our investigation reveals that compared to estimation, some undersmoothing may be desirable for the testing problems. Furthermore, we compare the proposed test with the likelihood ratio test (LRT). We show that when the true function is more complicated, containing multiple modes, the test proposed here may have greater power than LRT. Finally, we investigate the properties of the test through simulations and apply it to two data examples. Key words and phrases: Goodness of fit, likelihood ratio test, nonparametric regression, partial linear model, spectral decomposition. 1.