Statistical Modelling in Market Research

    Several market reserach projects where development of statistical models was a substantial part have taken place.
    The activity can be roughly divided into the following four areas:
 
 
Analysis of sales dynamics
Advertisement testing
Probabilistic description of consumer purchase  behaviour
Multivariate statistical analysis of questionaires
 
Analysis of sales dynamics
The objective is to analyze and forecast time series related to sale quantities of certain products. The main difficulties of the problem are due to nonstationarity and small number of observations. The working methodology is in application of the Singular Spectrum Analysis of Time Series and suitable dynamical models to multivariate trends to model interactions between different products.

Advertisement testing
    Assume there is a list of M products from which some number N of respondents select the most preferable one before and after the advertisement of one of these products. The problem is to test the hypothesis that the advertisement is good enough to increase sales of the product up to a certain level. This seemingly easy problem can be approached via quite sophisticated statistical models describing the mechanism of consumer behaviour. Study of these models requires nonstandard statistical thinking.

Probabilistic description of consumer purchase  behaviour
    It is well-known that the Gamma-Poisson and Polya urn schemes are very well suited to  describe  consumer purchase  behaviour in the market.
    Research in the present direction includes numerical and theoretical study of the dynamical models leading to these schemes, study of probability distributions arising under different conditioning arguments, asymptotic properties of various statistical procedures concerning the parameters of the negative binomial and Dirichlet distributions.

Multivariate statistical analysis of questionaires
    The objective is development of a methodology of exploratory analysis of typical questionary data, construction of suitable parametric models and making statistical inference in them. The parametric statistical problems arising include inference in a mixed regression model.
See also: Multivariate Statistical Analysis

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Workshop: Statistical Modelling in Market Research

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