Pointwise universal consistency of nonparametric linear estimators

This paper presents sufficient conditions for pointwise universal consistency of nonparametric delta estimators. We show the applicability of these conditions for some classes of nonparametric estimators

Automatic spectral density estimation for Random fields on a lattice via bootstrap

This paper considers the nonparametric estimation of spectral densities for second order stationary random fields on a d-dimensional lattice. I discuss some drawbacks of standard methods, and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number. I prove uniform consistency and study the uniform asymptotic distribution, when the optimal smoothing number is estimated from the sampled data.

POINTWISE UNIVERSAL CONSISTENCY OF NONPARAMETRIC LINEAR ESTIMATORS

This paper presents sufficient conditions for pointwise universal consistency of nonparametric delta estimators. We show the applicability of these conditions for some classes of nonparametric estimators.

Automatic spectral density estimation for random fields on a lattice via bootstrap.

We consider the nonparametric estimation of spectral densities for secondorder stationary random fields on a d-dimensional lattice. We discuss some drawbacks of standard methods and propose modified estimator classes with improved bias convergence rate, emphasizing the use of kernel methods and the choice of an optimal smoothing number.We prove the uniform consistency and study the uniform asymptotic distribution when the optimal smoothing number is estimated from the sampled data.Spatial data; Spectral density; Smoothing number; Uniform asymptotic distribution; Bootstrap;

A valid theory on probabilistic causation

In this paper several definitions of probabilistic causation are considered, and their main drawbacks discussed. Current notions of probabilistic causality have symmetry limitations (e.g. correlation and statistical dependence are symmetric notions). To avoid the symmetry problem, non-reciprocal causality is often defined in terms of dynamic asymmetry. But these notions are likely to consider spurious regularities. In this paper we present a definition of causality that does non have symmetry inconsistences. It is a natural extension of propositional causality in formal logics, and it can be easily analyzed with statistical inference. The modeling problems are also discussed using empirical processes.Causality, Empirical Processes and Classification Theory, 62M30, 62M15, 62G20

Pointwise universal consistency of nonparametric density estimators.

This paper presents sufficient conditions for pointwise universal consistency of nonparametric delta estimators and shows the application of these conditions for some classes of nonparametric estimators.Delta estimators; Pointwise approximation; Pointwise universal consistency;

Do business density and variety determine retail performance?

Outlet location plays a crucial role in retail strategy. In this paper we study the relationship between spatial density (concentration) of retailers in the trade area and their economic performance. This analysis will help managers figure out the economic potential of starting a retail business in a given area, reducing business start-up risks. We find that retail businesses located in high and low retail density zones enjoy higher performance levels, consistent with competitive advantage arising from agglomeration economies and local market power respectively. We also find that retail businesses located in intermediate density areas use a differentiation strategy based on business variety (diversification across stores). Outlets located in areas with the highest variety enjoy performance levels similar to those achieved in the agglomeration and low density areas. The results suggest that retail companies should jointly consider variety and density to determine location

Optimal duration of magazine promotions

The planning of promotions and other marketing events frequently requires manufacturers to make decisions about the optimal duration of these activities. Yet manufacturers often lack the support tools for decision making. We assume that customer decisions at the aggregated level follow a state-dependent Markov process. On the basis of the expected economic return associated with dynamic response to stimuli, we determine the ideal length of marketing events using dynamic programming optimization and apply the model to a complex promotion event. Results suggest that this methodology could help managers in the publishing industry to plan the optimal duration of promotion event

Modified Whittle estimation of multilateral models on a lattice.

In the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d≥2, the achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the “edge effect”, which worsens with increasing d. The other is the possible difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, due mainly to the Jacobian term. This is especially a problem in “multilateral” models, which are naturally expressed in terms of lagged values in both directions for one or more of the d dimensions. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the computational problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally convenient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. The asymptotic regime allows increase in both directions of all d dimensions, with the central limit theorem established after re-ordering as a triangular array. However our work offers something new for “unilateral” models also. When the data are non-Gaussian, asymptotic variances of all parameter estimates may be affected, and we propose consistent, non-negative definite estimates of the asymptotic variance matrix.Spatial data; Multilateral modelling; Whittle estimation; Edge effect; Consistent variance estimation;

Magazine sales promotion : a dynamic response analysis

This paper studies the impact and effectiveness of a type of non-price promotion often used in the European periodical magazines industry to stimulate sales, in which a value pack is sold containing the magazine issue plus another product. Magazines are sold simultaneously with and without promotion at different prices, and promotions are serialized by fractioning the additional product across different issues of the magazine. We find that promoted magazines contemporarily cannibalize non-promoted sales; but this loss is compensated by a medium term increase of non-promoted sales. These results show that this sales promotion strategy is an effective way to diminish the decline rate of periodical sales